{ "cells": [ { "cell_type": "markdown", "metadata": { "id": "CnNlDCMUH6gy" }, "source": [ "# Basic principles of pricing and hedging" ] }, { "cell_type": "markdown", "metadata": { "id": "m2La_36jH6g4" }, "source": [ "We shall first go through basic principles of modeling in mathematical Finance before we introduce concepts of interest rate theory." ] }, { "cell_type": "markdown", "metadata": { "id": "gPQlpWmRH6g5" }, "source": [ "We shall denote by $ S^i $ the price of asset $i$ and by $ H^i $ the holdings in asset $i$ (can be any real number here, no market frictions assumed). $ H^i_t $ is determined at time $ t- 1 $ with all the information available there.\n", "\n", "First we learn to write portfolio values, i.e. $ V_t = \\sum_{i=0}^d H^i_tS^i_t $ as P & L processes in case the portfolio is self-financing. Self-financing means that\n", "$$\n", "\\sum_{i=0}^d H^i_{t+1}S^i_t = \\sum_{i=0}^d H^i_tS^i_t \\, ,\n", "$$\n", "which in turn leads to\n", "$$\n", "V_{t+1} - V_t = \\sum_{i=0}^d H^i_{t+1} (S^i_{t+1} - S^i_{t}) \\, .\n", "$$\n", "This means that the change in value of the portfolio comes from the change in value of the prices and nothing else.\n", "\n", "This formula allows for a simplification. If we divide everything by the value of $S^0$, the price of the $0$-th asset, then in the above sum one term vanishes. We denote $ X^i_t = S^i_t/S^0_t $\n", "When discounted, e.g. by $S^0$, this means\n", "$$\n", "\\frac{V_t}{S^0_t} - \\frac{V_0}{S^0_0} = (H \\bullet X)_t = \\sum_{s \\leq t} \\sum_{i=1}^d H^i_{t+1} (X^i_{s+1} - X^i_{s})\\, .\n", "$$\n", "Notice that the inner sum only starts at $1$ because $ X^0_t = 1 $.\n", "\n", "The right hand side is a P & L process. The argument can be turned around: given a portfolio value which is given by a constant plus a P & L process, then we can of course construct a self-financing portfolio." ] }, { "cell_type": "markdown", "metadata": { "id": "cSDQ3mWJH6g7" }, "source": [ "Notice that this argument holds for any numeraire $S^0$: it only has to be default-free, i.e. never attaining the price $0$. We can calculate self-financing portfolios with respect to convenient numeraires and then switch back to the original undiscounted terms." ] }, { "cell_type": "markdown", "metadata": { "id": "3GkrRDhqH6g8" }, "source": [ "### A model is free of arbitrage if there is no self-financing portfolio which starts at zero and has a positive outcome" ] }, { "cell_type": "markdown", "metadata": { "id": "lI7EDqeSH6g8" }, "source": [ "### We assume from now on that any positive outcome of a self-financing portfolio cannot come for free, i.e. the initial capital $x$ has to be positive, too." ] }, { "cell_type": "markdown", "metadata": { "id": "7wkdiCiMH6g9" }, "source": [ "This leads us the valuation problem: what is the value of a payoff $f$ at time $T$? We can answer that by constructing appropriate (super-)hedging portfolios. Superhedging just means hear \"dominating\".\n", "\n", "Let us consider this question in a one period case, i.e. $T=1$. The states of the world are denoted by $\\omega$, hence we are interested in the question to find the smallest $ x $ such that for all $ \\omega $\n", "$$\n", "f(\\omega) \\leq x + \\sum_{i=1}^d H_0^i (X^i_1(\\omega)-X^i_0(\\omega)) \\, .\n", "$$\n", "This is equivalent to characterize the cone $ C:= \\{ (H \\bullet X)_1 - g \\text{ for all possible strategies } H \\text{ and } g \\geq 0\\} $." ] }, { "cell_type": "markdown", "metadata": { "id": "ozuvgWYZH6g9" }, "source": [ "This is a geometric question: the solution is $ C = \\{ e \\text{ such that } E_Q[e] \\leq 0 \\text{ for all equivalent martingale measures } $Q$\\} $. This yields the beautiful formula\n", "$$\n", "\\sup_{Q \\in \\mathcal{M}} E_Q[f] = \\inf \\{x \\text{ such that there is a strategy } H \\text{ with } f \\leq x + (H \\bullet X)_1 \\} \\, .\n", "$$\n", "The set $\\mathcal{M} $ is the set of equivalent martingale measures. A super-hedging portfolio is a self-financing portfolio (i.e. the value process is the initial value of the portfolio plus the P&L process -- all in discounted terms) dominating a certain payoff." ] }, { "cell_type": "markdown", "metadata": { "id": "D4qev8QqH6g_" }, "source": [ "This generalizes of course to the multi-period case." ] }, { "cell_type": "markdown", "metadata": { "id": "nya98xqLH6hA" }, "source": [ "### This yields the following pricing formula: if a payoff's contract is liquidly traded at price $ \\pi_t(f) $ at intermediate times $ t $, then there exists an equivalent martingale measure for the given market constituted by $X^1,\\dots,X^d$ such that\n", "$$\n", "E_Q\\big[ \\frac{f}{S^0_T} | \\mathcal{F}_t \\big] = \\frac{\\pi_t(f)}{S^0_t} .\n", "$$\n", "Let us consider these principles in the following modeling situations. Furthermore models are free of arbitrage if and only if there exists an equivalent pricing measure, which associates in particular to P & L processes the value $0$. Whence prices of payoffs can be calculated by taking expectations (i.e. a Monte Carlo evaluation is possible) with respect to this equivalent pricing measure.\n", "\n", "\n", "First we draw the tree in undiscounted terms in the format time / numeraire / stock price. For simplicity we take the numeraire equal to $1$ but one can easily adapt that. Next the draw the tree in discounted terms in the format time / price. " ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 390 }, "id": "AXOe0p6cH6hA", "outputId": "204294f8-9f6a-4c31-a276-cff378b9fa3f" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "Reading package lists... Done\n", "Building dependency tree \n", "Reading state information... Done\n", "libgraphviz-dev is already the newest version (2.40.1-2).\n", "0 upgraded, 0 newly installed, 0 to remove and 37 not upgraded.\n", "Requirement already satisfied: graphviz in /usr/local/lib/python3.7/dist-packages (0.10.1)\n", "Requirement already satisfied: pygraphviz in /usr/local/lib/python3.7/dist-packages (1.7)\n" ] }, { "output_type": "execute_result", "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "execution_count": 1 } ], "source": [ "!apt install libgraphviz-dev\n", "%pip install graphviz\n", "%pip install pygraphviz\n", "import numpy as np\n", "from itertools import product\n", "\n", "\n", "# EUROPEAN\n", "S0 = 100.\n", "u = 1.2\n", "d = 0.9\n", "payoffE = lambda S: np.maximum(S-S0,0.)\n", "\n", "timesteps = 2\n", "bin = set((0,1))\n", "trajectories = set(product(bin, repeat = timesteps))\n", "\n", "\n", "import pygraphviz as PG\n", "from IPython.display import Image\n", "binomialtreeforward = PG.AGraph(directed=True, strict=True)\n", "binomialtreeforward.edge_attr.update(len='2.0',color='blue')\n", "binomialtreeforward.node_attr.update(color='red')\n", "binomialtreeforwarddiscounted = PG.AGraph(directed=True, strict=True)\n", "binomialtreeforwarddiscounted.edge_attr.update(len='2.0',color='blue')\n", "binomialtreeforwarddiscounted.node_attr.update(color='red')\n", "binomialtreebackward = PG.AGraph(directed=True, strict=True)\n", "binomialtreebackward.edge_attr.update(len='2.0',color='blue')\n", "binomialtreebackward.node_attr.update(color='red')\n", "process = {(omega,0):S0 for omega in trajectories}\n", "numeraire = {(omega,0):1. for omega in trajectories}\n", "discountedprocess = {(omega,0):S0 for omega in trajectories}\n", "\n", "#construct process by forward steps\n", "for time in range(1,timesteps+1):\n", " for omega in trajectories:\n", " shelper = process[(omega,time-1)]*u**(omega[time-1])*d**(1.-omega[time-1])\n", " process.update({(omega,time):shelper})\n", " \n", "for time in range(1,timesteps+1):\n", " for omega in trajectories:\n", " #shelper = process[(omega,time-1)]*u**(omega[time-1])*d**(1.-omega[time-1])\n", " numeraire.update({(omega,time):1.0})\n", " \n", "for time in range(1,timesteps+1):\n", " for omega in trajectories:\n", " binomialtreeforward.add_edge('%d / %d / %d'% (time-1,numeraire[(omega,time-1)],process[(omega,time-1)]),\n", " '%d / %d / %d'% (time,numeraire[(omega,time)],process[(omega,time)]))\n", "\n", "#for time in range(1,timesteps+1):\n", "# for omega in trajectories:\n", "# binomialtreeforward.add_edge('%d, %d'% (time-1,numeraire[(omega,time-1)]),'%d, %d'% (time,numeraire[(omega,time)]))\n", "\n", "Image(binomialtreeforward.draw(format='png',prog='dot')) " ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "id": "zcehYnf4H6hE", "outputId": "d6b4d9af-e190-4f5b-e4c1-0fdfd4d8f704", "colab": { "base_uri": "https://localhost:8080/", "height": 268 } }, "outputs": [ { "output_type": "execute_result", "data": { "image/png": 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4oFIlvaWxLeZuDOHhwNKlekujcBKU60BRmA0bgBUrOH12NSMLFHRjWLZMdWNQWA81olVcwxG7JmiF6sagsCJqRKsowBG7JmiFuRvDtGl6S6JwBpShVQAo6JowaZJjdU3Qitq1gfHjgfffV90YFBVHuQ4UABy7a4JWqG4MCiuhXAeuRFoai8PciKN3TdCKkroxnDoFDB3KCmAKRWkoQ+tC7NgBREYCzz4LXLjAfRkZwGuvseNAly56SmefdOoEPPEE8MorQGYmR7kzZzLm9ssvGQKnUJSGSjR0IXbtYs3VRYsYwjVzJoteZ2fTP6somhkzgMaNeYP680/6bPPzWWxn1y5GaSgUJaEMrQuxfTsNRH4+R7RDhwJVq7JMoDN0TdAKNzf6apcupXHNz+d+g4GGdtgwfeVT2D/KdeAimEzAvn2F94nQdfDuu8DLL/O5ogAR4OuvgQYNgN9+499GY8HrRiM7MygUpaEMrYsQHw9kZd2832ikEf7sM06Pv/vO9rLZIwcOAB07ctR/8SLb+BTFkSP03SoUJaEMrYuwaxenvcVhNDJAf+hQ4OBB28llr3h4ACkpdBuUFABZ1ExBobgRZWhdhNKaKnp6AnXqsPB18+a2k8teadaMdWnvvLPkG5SXV9EhcwrF9ShD6yL8/nvx0193d+Cuu4D9+4GmTW0rlz0TGMii56NGFd8h12hUXRkUpaMMrQuQmQkcPVr8608/zcynqlVtJ5Oj4O4OTJkCfPMNR/03jm5NJkZzKBQloQytC7B3780ZTO7uNByLFgGff65at5TG4MHA1q1AtWo3Z8+lpQH//quPXArHQBlaF+B//ytsHDw9OS3+/XdmhCksIyKC7pUWLQp/n+Z4WoWiOJShdQFiYgqC7D082J5m716gQwd95XJEatYEdu4EBg4s8Nt6eipDqygZNWG0N/LygNRUzkczMpgfCxQUJ/DyAvz8+DwgAPD3Z1pXUFCxh4yJoevAYAAefRRYsEAVs64IPj5MZGjWDBg3DsjNLcFPKwKcPw+cO0d9ZmQUZD1culTg06lSpcABXLUqWz0EBlKvXl6afyaFtqgyiXpw9iznoEePFmzHjjGQ1WxQy4qHBw1ujRqseNKwIdCwIf4Nao3afdrAzQ2YOhV4/XXrfhRX5+elGRj4dCVIPpD+nw/gcfIY603++y9vlufPV/wklSvT6NasyWLBderwsV49Tk/CwooPi1DYA3OVodUao5Hz9C1bgD17+PzECb4WFHTNIKJhQyAkBLj1VhrM6tU5yjEPPatW5cV05UpBild6OreUFBrv1FS2SEhIoPFOTMSqnN4YhoVY3mAs7uuay3Sne+7hRaooG8eO0W/w55/scRMbCyQnIx7N8IDhR6yoOwptbsuiEaxdu2CmYd78/TkLMQc0Xz+KTU8v8O+kpwOXL3MUfP48t7Q01mY8fpy/n6SkAiPu78/g55YtgVat6Exu3VqtcNoPytBqwunTzGXdsIFL1ZcucaTZoQPQrh23tm1LnO5bBZMJ/52ahk7ee3Dbqd9o5PfsoaFu2JAGt3dv4N57AW9vbWVxRA4dYtzbjh00sMnJnMa3bMkVsRYtaNiaN8d535o4dYov2YxLlyij2egfPMibwIULdC+FhwNRUcDdd7Peoyo2rBfK0FqNtDRW0I6O5nK+nx9/4N260aDZSybAlSt02m7axGj8PXs4InrgAfYZ79Gj5FQoZ+bKFX4va9awEvqxY7wZdurEQr6RkbxJ2rODW4TGd+dO3iB27ODspkoVoHt3oGdPoE8f4JZb9JbUlVCGtsLs28dA1MWL+SO/5x6gf3/g4YcLFq3smVOn2PJ2xQpenCEhwJNPAiNHcvrr7JhM/NwrVrAOYmoqV7n69OFNsksXx5+CHzvGm+rGjbyBZGfThfTkk8Bjj/FGq9CSuRBF2TGZRH78UaRdOxFA5PbbRT7/XCQzU2/JKkZCgsjo0SLBwSKeniJPPSVy9KjeUmlDaqrI+++L1K5doMPp00VOntRbMm25fFlkyRKR+++njitVEnn6aZH9+/WWzJn5TBnasrJunUj79iIGg8hDD4nExOgtkfXJzhb58kuRxo1FPDxEhgwROXZMb6msQ1ycyLBhIj4+IoGBvLEcPKi3VPqQliYye7ZIs2a82XTpIvLddxxIKKyJMrQWk5go0qcPf5B9+oj88YfeEmmP0Sjy9dcijRqJ+PqKvPuuSE6O3lKVj6NHRQYPFnFzo2GZN4+jOwUN64YNHOW6uYnccYfImjV6S+VMKENbKvn5IlOm0NA0bSqyebPeEtme3FyRDz8U8fMTue02kd9/11siy0lLExkxgiPzJk1EoqPViK0kDhwQ6duXA4pOnUT27dNbImfgM5WCWxIpKcB99wFvvQVMmMAkg65d9ZbK9nh6AmPGsE1Do0b8Dj74wP57bS9ZwoWtn39mOlxcHBcqVXB/8bRsCfzwAwtkGAwMSRw1quj2HArL0dvU2y0xMSIhISL164vs2aO3NPaDySQyc6aIl5dIjx4i6el6S3QzaWkivXtzGvzccyIXL+otkWNiMnGRt2pVkbAw51yPsA1qRFsk69YxtKdtW5bZb9dOb4nsB4MBeOUVJvebR/hnz+otVQH79lFvcXFMFpk7l9lYirJjMADPPMOZTNOmQOfO/D4VZUYZ2htZvZrB+/37A99/ry7S4mjfnsHwFy8yoP/MGb0lYrJIp07sMrl3L58rKk5oKPDTT8DYscALLwAjRhSkCyssQhna64mJAR5/nHfx//7X8QPVtaZ+fRpbAOjbl/n5erFkCTBoEPDcc8DatUBwsH6yOCNubsDbb3Pw8c03LGSsjK3FqMwwMydO0EXQsSPrFLhqGmp5SEhgIZNOnTgjsPViU3Q0jexrr7FEmUJbfv0VePBBoF8/1otUi4ulMVeNaAGmzg4fzmpLS5cqI1tWGjakgf3pJ/bGsSWxseyRPnKkMrK2ont3jmyXLQNmztRbGodAGVoA+OILYPNmugusXJ/AZDJh5syZiIyMLNf/h4eH4+TJk0W+lpeXh7feegv169eHl5cXatasiVGjRiHbXCz8OrZv346oqChUqlQJoaGheOONN3DlypVyyVQkd97JRbLXX2f9BFuQkQE88ghnIh99pMkptNSfped455130KxZM1SpUgXe3t5o2LAhxowZg8zMzJveq7mezXTvzhC/N98scB8pikfvuAfdyckRCQ0VeeUVqx/6yJEjEhUVJQCkdevWZf7/xMREiYiIKPb1559/Xnx8fGTp0qWSnp4uv/32m1SpUkUGDRpU6H1xcXHi6+srEyZMkMzMTNm5c6cEBwfL0KFDyyxTiWRlidSrJzJypHWPWxxjxzKN9vRpTQ6vtf4sPUfnzp1lzpw5cu7cOUlPT5fly5eLp6en9OjRo9D7bKZnMyYTw+hatmQWoaI4VGaYzJ8v4u1t9Yt1//790q9fP1m8eLG0adOmXBfq5MmTZcaMGUW+9s8//4ibm5uMGDGi0P7x48cLAImPj7+2b+DAgRIWFiam6zKipk2bJgaDQQ4dOlRmuUpk9mzWEUhOtu5xb+T0aRZE+egjTQ6vtf7Kco7evXuL8QZDNmDAAAEgJ06cuLbPpno28/ffLE6zaJE2x3cOlKGVO+5g9SIN6dChQ7ku1LZt28rJYqpJLVu2TADIwoULC+3fvn27AJCZM2eKiEheXp5UrlxZhgwZUuh9cXFxAkCmTJlSZrlK5PJlkaAgkalTrXvcG3njDVbeys7W9jyijf4qeo7nn39eAMjhw4dFRAc9X8+IEUzNVhSHiycspKSwIv0jj+gtyU0kJCTAx8cHtWrVKvJ1t6vtUHx9fQvtb9SoEQDg0KFDAIDExERkZmaiTp06hd7XoEEDAMCBAwesKjcqVWJx6fXrrXvcG1m5Ehg82G6LcJemv4py6tQp+Pr6IiwsDIAOer6ep58GjhzhwqSiSFzb0G7cyNYkd92ltyQ3ER0djf79+xf7epMmTQAUGFQzQVfb46SmpgIAzlxNJPC/obizj48PfH19kZKSYjWZr3Hffcwc0yo/PjYW+Ocf4KGHtDm+FShNfxUhKysLmzdvxjPPPAOvqx1yddGzmfBwoFYthkUqisS1De2RIwxNssNOCCtXrsQjJYy0W7ZsiR49emDOnDnYvHkzcnJycObMGaxevRoGgwF5eXkAcG3F2b2IkDVPT88iIxQqTKtWbAtjbkJpbeLjmUzStq02x7cCpemvInzwwQcIDQ3Fe++9d22fLno2YzDQ2N5w01cU4NqG9uxZdp21M44cOQI/Pz/UrFmzxPctW7YM/fv3x5NPPonAwEBERUXhu+++g4hcG9n6XJ1aG43Gm/4/Nzf3JteDVQgJ4aNWo6hTp3gOO413tlR/5WH16tWIjo7G+vXrC41eddHz9dSqxRbriiJx7RzTzEy7HM0uX77comlnQEAA5s2bV2hfcnIyli5diho1agAAQq4avfT09ELvy8rKQk5ODkJDQ60k9XWYDUBGhvWPDbAdd5Uq2hzbCliqv7KybNkyzJgxA1u2bLmmXzO66Pl6AgLYlVdRJK5taIOD6euzM1atWoW1a9eW63/37NkDAOh6tW5uWFgY/P39kZSUVOh9CQkJAIBWrVpVQNJiMFfz0qrTakiIfRSxKYaK6K84Zs2ahfXr12Pz5s2oXLnyTa/roufrSU5m8RlFkbi2oQ0J4Q/Ejjh8+DACAgJuGrFYyoIFCxAWFobOnTsDADw8PNCrVy9s27YNJpPpWrTCunXrYDAY0LdvX6vJfo3Tp/molVumZk3gwgXOSIowOnpSUf3diIjgzTffxIULF/D999/Do5hCR7ro+XqSkug+UBSJa/to77gDOH4cKCVF0paUZdoZHh6OpKQkGI1GHD9+HKNGjcLGjRuxcOHCa6vRADBhwgSkpKTg7bffxuXLlxETE4Np06ZhyJAhaNy4sfU/xPbtnC1o1a48IoL+Wa1DyMqBtd0G8fHxmDp1KhYsWABPT08YDIZC2/Tp06+91+Z6NpOVxTRcVZayePSO5NWV7GxmF90Q9G8NYmJiJCoqSkJDQwWAAJCQkBCJjIyUrVu3Fvt/LVu2lNMWZql1795dqlatKh4eHlKtWjXp3bu37CmmG8TWrVslPDxcvL29JTQ0VEaPHi05WjVa7NaNjRC1pHNnTc9hC/1Zco7Y2NhrrxW1TZs2rdAxbapnMytWiLi7s4W7oig+U2US+/WjT3H7dr0lcQ6OHQNuu431YTWKIwXAQkAvvAAcPgzUq6fdeRQlIwJERgKBgcCaNXpLY6+oMol47TVOe1QFIuswfTpdBlonEwwZwsLjEyZoex5FyaxeDezeDbz7rt6S2DVqRAuwxB/AHlNu6t5Tbv7+G2jThiULn39e+/OtXAkMHMiRVI8e2p9PUZhz57jOceedwOLFektjz8xVhhYADhxgD6zp04EXX9RbGsfEZGLzvsuXgV272KLcFgwZwoLj+/YpF4ItMZmA++8HDh7kd69aB5WEch0AYMrof/7Dbf9+vaVxTN57j1PIr76ynZEFgDlzgBo16Gs/f95253VlROhy27wZWLFCGVkLUIbWzLhxDBu6/36VSlhWvvkGmDgR+PRToGVL257bzw/48UfG1d5zD5CWZtvzuxoiwEsvAZ99xn5h4eF6S+QQKENrxtOTPr9q1ejvs7NEBrvl++/Zb23MGODZZ/WRISwM2LKFqbldurBZpML6ZGcDTz0FfP45+4UNGKC3RA6DMrTXExAArFtH/1NUFHD0qN4S2TcLF7KW79NPA5Mn6ytL3bpczKxUiT3EfvxRX3mcjWPHeE2sWcPvtl8/vSVyKJShvZFatYDff2eeflQUWysrCmM00p/9zDN0ucydax8tp2vVArZtY/zugw9yiqtVYRtXQQT48kuWpBQB9uxhvWFFmVCGtiiCgoBNm4Bu3ehGGDuWxkXBGrNdutAfu3AhMGmS3hIVxscHWLCA/sMlS4DmzRmVoCg7CQnsdjt8OPDEE8DOnYxdVh9tSyoAACAASURBVJQZZWiLw8+PF+r8+cDHHwMdOnBV3VXJz+cKf+vWXHjavRsYOlRvqYrn8cfp+unZE3jgARqMvXv1lsoxOHeObcRbtSrImvzkE0DrmrZOjDK0pTF8OPDHH/TfRkQAzz0HXG0T4zL8739Ax47Aq69ywWvPHo4U7Z1q1Xij3LyZlb7Cw4GHHwb++ktvyeyTtDTgrbcYj/z118C0aYyR7dhRb8kcHz0rLTgcixeLhIaKVK7MLqzOXkRj926R3r1FAJEuXUQOHtRboorx448irVvz83TtKrJ6tcgNbbxdkv37RYYNE/H1FQkMFJkyhd2MFdbCxbvglpXBg+m3mjgRWLSIYUUvv8zCJs6CyUSfZo8eHAGeOwf88gvw229As2Z6S1cx+vRh1+MNG+gaeuQR9ox76y3n0qElnD/PMK277mLadEwMMGMGffBvvMHoDYXVUCm45eXyZWDePAZuHzsG3H033Qx9+thle5xSOX6cPukFC1jEuXt3ugqcuYZAQgJdC0uXsg9Z27bAoEHU4dW27U7FuXOs4RsdzTBGd3egb1/+bu+5xz4iR5wTVeugwphMHPHNncsfr7c3s8v692cYzA3tn+2KxEQmHERHc3GrWjUGpD/3HEsdugomExMevv2WLbMvXOBIt2dPoFcvhvnZsx6Lw2hkSvn69cDataxBYTBwUDB4MCusOeLncjyUobUqqaksGxcdzeB5g4HRCt26cbvjDn2nZGfOsBzkr78CGzeyX1q1aow57d+fMtqyToE9kp/PafTatbxx/vUXK7q1bMkOAhERdKnUr29/ld7OnuXCbUwMIwV27+YiYGgobxo9e3KmEhCgt6SuhjK0mpGWxljcjRtp2JKSAA8PZDRpD++2LeDVrhXQuDFHTnXqWLd1dlYWp8UJCcDBg0iLOYrgA5s5PXZ3Z+ZU9+40rJGRyriWhPnmtGMH40j/+APIy+MNs1kzGuBmzajHunW5BQZqJ09ODt08SUl8jI8H4uKA2NiCaJhGjajXqCg+Nmum3AL6ogytzTh+HNizB8Pfq4fEk57YbLinoNqUlxcX1kJC2NDwlluA6tXp6zVP7fz9AQ8P5pvn5HDklZ7OzKfkZBr21FQuZpw6xf9xc8PxWp3Q4vQGfPfU9+j+WDCNrBrRlJ/s7ALDFhcHxMVh459B+CctAM9iPt/j70+DGxTELTCQFa6qVmVChTke1c+PuhcBLl7kPqOROr18mb+P8+fpW01LY9PL67r/SpUAzKw6Ce1a5eKuezxp9Fu14m9HYU8oQ2tLdu/mzHPJEtarxrlzHHUePcrH1FReSKmpvLCys4FLl/jP6ek0rr6+vFg9PHhB+/vTOFevzq1mTY6uGjXio7c3HnqowDb4+Oj6FTgdV64wh6NF03ysnJLAkWZSEht+njtXYCjPnaMxzc2lEQU4rc/L4/Nq1fjo6cnOvn5+NNDmLSiI5SDr1SsYOVerhocfZiDFX38pd6sdowytrTAaWVs8ONj25RNOnuTsccwY1fnF2kycyLj++HjaPluTmgq0aMF1rXnzbH9+hUWowt+24tNPeTHOmmX7c9euDYwfD7z/PnDkiO3P76wkJAAffgi8844+RhbgJGb+fIbErlunjwyK0lEjWhuQnAw0bcpiUu+8o48MRiPDRENDGY2mqDi9e9NL8Oef+q8nPvYYC5fFxmq7FqcoF2pEawtefpnrIG++qZ8MHh6sCbNhA7BqlX5yOAvmmP/Zs/U3sgDDuN3cgFde0VsSRVGoEa3GbNjAvIWffmIeg9489RRrrBw6xDUXRdnJyOAM5d57gf/+V29pCtiwgYl80dHMLlbYDWoxTEuurUi3YJcce+DcOYbvDh3KRRxF2XntNfagPHzY/iKphg8HfviBUSa33qq3NIqrKNeBlkyezBX/6dP1lqSAoCA2rP34Y1UtsDzExtJdMGWK/RlZgHoNCNCvfZuiaNSIViMSEhg//u67wKhRektTGHNLNA8PLqCopCHLEGEWbl4eS/TaWwaumc2bmfj31Vesf67QHTWi1YqXXwYaNOCjveHmxoWxmBi2g1JYxsKFrMsyf779GlmANWNeeIHbyZN6S6MA1IhWE1asYObX5s1sr2WvvPgiKwQePsxECkXxnD8PNGnColczZ+otTelkZQG3384yGhs2qFmLzqgRrbXJyGAZ1yFD7NvIAkxg8PZmI1tFyYwZw3o8EyfqLYllVKpE18FvvzGZQaEvytBambffZomCDz/UW5LSqVKFkQdffEE3gqJodu9mQw3zQpOj0LEjMHo08PrrXDNQ6IdyHViRuDiWnJ09GxgxQm9pLKdbt4JSph4eektjX+hZo8Ia5OZSfn9/lki2ZjVOhcUo14G1EGFITZs2jGV0JObOZQ2EOXP0lsT+0LNGhTXw8mJD2z17+FkU+qAMrZVwlBXpomjUiNPLCRMKStkqWKPinXeYOt2kid7SlJ/WrVlU6D//AQ4e1Fsa10S5DqyAeUV60CD68RyR7GxmsIWHMxJBAQwYQP9sfLzjN4U1Ghk7bTQyBtge6jO4EMp1YA3MK9KTJuktSfnx9aXrYNkyVW4PYEjUihX8ThzdyAL0vX/1FWtcOMJCrbOhRrQV5KauCQ6O6sZgnzUqrMWMGcAbbzDKpF07vaVxGVRRmYrg6CvSRaG6MRR0TTh4kJ1jnAmTiZljqanAvn2uezO1Mcp1UBEcfUW6KFy9G4O5a8KkSc5nZAEu1C5axBuqXkXoXRE1oi0n5q4JL7/s2L7ZonDlbgz21DVBS+bPB55/nrG1nTrpLY3To1wH5cWZVqSL4vffgc6d6aPs109vaWyDo9SosAYivKkcOQLs36+KwGuMMrTlwdw14eef+WN1VlypG4O9dk3QktOnWcrz8ceBTz7RWxqnRvloy8qVK2yy+PDDzm1kAeCjjxhf62yukaJwpBoV1qJGDcZ9z5rFwYNCO5ShLSP22DVBK4KDWbjc2bsxxMWxPsXkyfbZNUFLnniCg4Zhw4CLF/WWxnlRroMyYM9dE7TC2bsxOErXBC1JS2PMcJ8+wIIFekvjlCjXQVmw564JWnF9N4avvtJbGuvjyDUqrEVwMD//woXAmjV6S+OcqBGthURHA48+6hor0kXhjN0YnKFGhTV54glg0yZmBQYF6S2NU6GiDizBFVekbyQ9nd/B/fdz9OMMDB/OEdzhw45V0FsrLl2ia6xTJ6aUK6yGch1YgiuuSN9IlSrA1KnO043BUbsmaElAAN0Hy5ZxBqewHmpEWwrmrglz5gDPPKO3NPrjDN0YnLFGhTV57jlg1Sq6EEJC9JbGKVCug5JQK9I3c/Qop5dTpzKe2BGZMYNFsP/6y7ELemvF5cvsFNK0KfDjj3pL4xQo10FJqBXpmzF3Yxg/3jG7MZi7JrzxhjKyxeHnB3z5JbB2LR8VFUeZDzD98MYuoefPA2PHAi+8ANx+uz5y2SvjxzOwv6hY4u++Y2SG3mzaxFF3Xl7h/S+/DFStyvY0iuKJiuKM5ZVXgBMnbn79zBkuniksRBQSEiLi6Sny9tsi2dncN2wY91+8qKtodsu6dSKAyNq1/Puff0R69OC+UaP0lU1EZMIEynLbbSJbt3Lfhg3c99NP+srmKOTkiDRvLnLPPSImU8H+ZctEqlUTWbFCP9kcjM9c3tCeOsWLDxBxdxepU0fkk09E3Nz4g1IUzwMPiDRsyBuUlxdvVoBIx456SybStauIwUCdAiKDBlHWhx/WWzLHYt8+6nX2bJG0NJH+/fl9GgwiI0boLZ3D8JnLL4atXg088ghNLUBfrMkE3HYbV6Tr1NFXPnsmOhoYORK4cAHIzy/Y7+UFZGbqV89VhOFomZkF+zw8qNuxY+n6cHfXRzZHZMIEFhiqXJn1EMzumNq1i3YrKG5CLYbt2lXYIJhMfDx2jMZ24kQgN1cX0eyWM2dYWu/RR3nhXW9kAX5fcXH6yAYwAeF6IwswpCs3lwthd9zBOFpF6aSns5xidjZw7lxhn/fJk0Bion6yORIub2h37izakOblsSTiu+8y1GXnTtvLZm/k57OkXsOGHM2K0IDdiIcHb2B6sXt38VEiJhOLtUdEcLEnPd22sjkS27ez2MzXX/Nv8yDEjLs7sHGj7eVyRFza0Obns0FdaRw5Ytn7nJ2sLGD9esZZ3riafyN6jhh37SrZNWA00mikpjp3u5rykpvLaJu77uJotqibqRlVx9YyXNrQHjzIKVFxeHgwpvCXX1hUxdXx9wd++gl46y2WSyyuZKLRyJKKerFtW/E3Ajc3yv3228zn9/W1rWyOgJcXZ3FeXiWXxczP5zrGjSNdxc24tKEtaeTj4UFn/+7dTDtVEIOBHReWLuWFWFwabmKiPoWks7Ppoy0KDw+21/7uO/rena22rjUZPpy9xBo1KjnVOj2djSwVJePyhrYoX567O3D33fwBqeyhohk4kGnJt9xCg3sjIsDevbaXa+/emxfnALoIatTgjfOBB2wvlyPSpAlrWjz3HP8u6sbk6an8tJbg0ob299+LnmKOGgWsW6eqOpVGmzasF9C+/c0zAy8vfRbEbowiASjbnXdyhNa8ue1lcmR8fLgAumoV3Wg3frdGo+u1pC8PLmtoMzIKp926u/NH9PXXwJQpqraBpQQHM931yScL7zca9YnUiIm52Wf49NM0BtWq2V4eZ6FfP4bstWpV2JUgQj2XtNahcGFDu3dvwQXp6cmK8jt2sMq8omx4e7Mg+vz5vGGZkz70qFu7YwddB+7uNAgLFwKff66iC6xB3brU6dixdCOYByO5ufzeFcXjOBVF09K4ZWQUVLO4fLkgCNY8XPH15fJ49eocbhVzhe3eXfBjuf12loO79VYbfA4nZsQIICyMmXaZmcwYO34cqFeviDdnZjIC/vx5Doeysrg/OxvIyeFzH5+CsIBKlfg8KAgIDGSa0g0kJwMpKdRrtWrUaUSEFp/UdfH05GJo27YclOTkcPby66+lLBproG9Hwn4MbXY2cOAAcOgQ5/Tm7dQpGtiSgvlKolo1Vi+uX59LqFe3mC2dIeKFJ58E5s0rekFHUXa6dwf27byC3r2AIye8sWvCz6hXdT0tblISg1fPn694up2XFy/A6tVpyevVw+6MuwE8iNaNsvHTOnfUqq+UqhV9+9KVMGAAF0XXrs7Gh+1+po6Tkmyib9Spw2F2w4ZAs2acWtkp+tU6OHaMzr1duziPj4ujMfXx4Rdn3mrV4pd7661c4g4I4IgVoHfey4uOInMsUU4OR7xpaVTymTPcrjfe58+jLpLweuAivNQ1lqs5XboA7dqpJPiycukS55N79rAkf2wskJCAdGMlDDYsQSO/05jR5mteEHXrUo+BgQUjlaAg6tHHh8fz9S14npNT4PzLyeEMxjwqMj+mpFy7sMceeBRJmUH4QobB1yOPN9WWLbm1b8/hbZUq+nxPzsIN+jYeiMfbRx/HVNMoJLvXQnCoJ42gDfSNpCRmVJhM9BPZr75t2GEhJ4crEmvX0sAmJvILb9eOX0q7dtzq19c8wPFS4jnsXXEM9xjX08jv2sV5Z9WqQNeu7ML40EPKl1AUaWlMB9q6lasg8fH8odevD7RuzZzNli2BFi1gqt8QP67zxIMP2ka0bduAuyLy2AYiLo5GPy6OM6XERPqJmjdnsdW77qKeVbvXkrFQ3xszOsCzbg10vsfGk+Q8h9C3xobWHPuxfDkdZpmZQHg4nTnduvGOYy9z9vh43gA2bmTl6uxsKmfAAG6BgXpLqB/79wM//8yb5O7dHPWHhwORkdwiIjjbsGdSUjgS27GDBmPPHhqMDh2AXr3Y3rd1a72ltA+Uvq3NXG3q0SYni0yZwuKugEizZvz71ClNTmd1srNFfvxR5IknRPz9Rby9WYjz11/1lsx2JCWJfPyxyO23U4e33MLvIzraOaqhZ2ZSxyNGiNSqxc/YtCmL6x49qrd0tkfpW0usXPj7779FHn+clYKrVxd54w2RxESrnsLmZGSIzJsn0ro1ldOhg8jPP+stlTbk5YksXy7SqRMrO996q8hLL4nExBQuse9smEwiO3aIjBzJ363BIHLXXWwhkJent3TaofRtK31bydAmJoo89ZSIh4dIkyYiX3/NPhjOxvbtIn37UjHh4SK//KK3RNbhwgXOOGrXZkuChx5irxqjUW/JbE9ensiaNWwf4ebGWdmHHzrHqM6M0ncBttF3BQ1tdrbIpEkivr5szvTNN66hrL17Re6/nyPcBx4QOX5cb4nKR2amyAcfiAQGilStKvL66yLHjuktlf3wzz8ir74qEhAgEhTEC/DyZb2lKj9K3yWjnb4rYGi3bGETpsqVRaZNE8nNtYZAjsXGjSKNG4tUqiQyfbrjTLfy80XmzuVU0d9f5K23nGvEZm0uXBAZN46/9dBQkQULHEfXIkrfZcX6+i6Hoc3P5yjW3Z3T6JMnKyKA43Plisi779Iv3aOHyNmzektUMgcPikRFUd5XXxVJTdVbIschJYU+TA8P+vQOH9ZbotJR+i4/1tN3GQ3txYsi3bpxFf7TT8t7Uudk1y6RsDCRGjVE9uzRW5qbMZnol/PyEmnfXmT/fr0lclz27RO54w5eB/Y6k1H6th4V13cZDO3p01x5r1GDPkrFzVy4wFGtv799hYJdvCjy4IMc1Uyb5hp+dK3JyxOZPJmjnUceEUlP11uiApS+rU/F9G1hu/FTpxi87+nJBIQiq4QoADBTZehQYMUKYOVKoE8ffeVJSmJGTGYmE0c6ddJXHmdjyxa2Aw4MZEO12rX1lUfpW1vKp28LMsMyM2lkc3KYhle9ujXEdW5EWMpqyRIqpn17feQ4dowpxYGBzPIJCdFHDmfn1CmgZ0/m5m/ezBx/PVD6tg1l13cphlaEfT9272Y6W1iYVeV1aoxGljj64w/WU6hVy7bn//df5ngHB7OGnSunENuCtDSmlV+6xLTPGjVse36lb9tSNn2XYmg//xwYOZIj2chIq8vq9GRkcDRbvz5HGLYiNxfo3Jmd87ZvV60FbMW5c5yqBwdzpGOrauNK3/pgub5LqHWQlCRSpQrTaK3EpEmTpGnTpuLv7y9eXl7SoEEDGT16tGRkZJTpOO3bt5cTJ04U+/q3334r7dq1k8qVK0udOnVkyJAhkpycXOR78/PzZcaMGRIREVEmGSxmxw5mnCxapM3xi+LFF7kgd+iQVQ9rK/2JWKaX33//XSIjI8XX11dCQkJkzJgxklNERmJZfg8VJi5OxM9P5LXXtDl+UbiIvq8nOztbGjduLOPGjbPK+8qNZfouIepgxAiRBg2Y/WUlOnfuLHPmzJFz585Jenq6LF++XDw9PaVHjx4WHyMxMbFEZSxbtkwAyIcffigXL16UP//8U+rXry9t2rSRvBvymI8cOSJRUVECQFq3bl3uz1UqI0eykMWVK9qdw8y+fUwRXrzY6oe2hf5ELNNLXFyc+Pr6yoQJEyQzM1N27twpwcHBMnTo0ELvK8vvwWosWsSb619/aXP863ERfd/Ia6+9JgBKNaCWvq9ClK7vYgztmTMiPj4i8+dbVZ7evXuL8YZQkwEDBgiAUu94ZiZPniwzZswo9vWuXbtKjRo1xHRdrNvs2bMFgGzfvv3avv3790u/fv1k8eLF0qZNG20N7b//Mp7RFqPabt1Yh0GD2E5b6M9SvQwcOFDCwsIK6XnatGliMBjk0HUjO0t/D1bFZBLp2FGkVy9tjn89LqLv69mxY4fce++9pRpQS99XYUrXdzGG9oMPWCbNiqPZ4nj++ecFgBy2MOuibdu2crKEbLSGDRtK27ZtC+374YcfBIB8++23Rf5Phw4dtDW0IiJPPskLQkv27GH9hS1btD3PdVhbf9dTnF7y8vKkcuXKMmTIkEL74+LiBIBMmTLl2r7y/B6swq+/Uhd//qndOVxE39eTlZUlkZGREh8fX6IBtfR9VqNkfX9WdBfcX34BevcuaDGhIadOnYKvry/CLIhoSEhIgI+PD2qVsIJfv359nD17ttC+M2fOXHtNNx5+mNEHqananWPlSkaGdO6s3TluwNr6s4TExERkZmaiTp06hfY3aNAAAHDgwIFr+3T7PXTrRl2sWqXdOVxE39czbtw4jBw5EtVLCTO19H1WoxR932xoMzMZynXvvVqLhqysLGzevBnPPPMMvCzotBAdHY3+/fuX+J6xY8fizJkzmDVrFjIyMnDw4EF8/PHHuO+++9CxY0driV52unZlpfrNm7U7xw8/0KDbCC30ZwlmQ+lv7h13FR8fH/j6+iIlJeXaPl1/Dw88AHz/vXbHdxF9m9mxYwf++ecfDBo0yCrvszol6fumQW5sLIfA8fHaDrVFZNy4cXLbbbdJuoXpbLfffrv8+++/pb5v/PjxAuDaVqtWrRKnLzZxHYiw0tc772hz7Lw8FvpZuVKb4xeBVvozU5xeNmzYIACK9P1VqVJFIiMjC+0r6+/BaixbxpRNLVJgXUjfInQFtGvX7trxUlNTi3QJWPo+TShe30W4DsyjAY17Aq1evRrR0dFYv379TSOTojhy5Aj8/PxQs2bNEt83btw4fP7559i0aRMyMzORmJiIyMhIRERE4OTJk9YSv3zcemvB92ttkpOB/HyglO/HWmilP0vwuerSMhbRgj43Nxe+vr7X/tb191CzJhNXtNC5C+kb4MxkxIgRpR7P0vdpQgn6vtnQXr7Mx8qVNZNn2bJlmDJlCrZs2YJ6FtZNWL58eanTkOTkZHz44YcYMWIE7r77bvj5+SEsLAwLFizA6dOnMW3aNCtIXwH8/ZnEoAXp6Xy0QXtlrfRnKSFXU0vTzZ/5KllZWcjJyUFoaCgAO/g9BATw8dIl6x/bhfS9fft2xMbGYvjw4VZ5n2aUoO+bDW1wMB/T0jSRZdasWVi8eDE2b96MGmVIU1y1ahUeeeSREt9z9OhR5Ofn33TcKlWqIDAwEAcPHiyXzFbj7FntWpib89qv+i+1Qkv9WUpYWBj8/f2RlJRUaH9CQgIAoFWrVgDs4PeQnMxHLdJxXUjfCxcuxKZNm+Dm5gaDwQCDwXBtkev999+HwWDA3r17LX6fZpSg75sNrdkQnD5tVRlEBG+88QZiY2Px/fffo3IZRsyHDx9GQEBAqYo2r24mmz/wVTIyMnD+/HnU1ruyUnKydi6ZwEBGiZw4ocnhbaE/S/Hw8ECvXr2wbds2mEyma/vXrVsHg8GAvn37ArCD38OJE5wZmkc61sSF9L1o0SKISKEt9Wr0zrhx4yAiaNeuncXv04wS9H2zoa1XDwgKYqEEKxIfH4+pU6diwYIF8PT0vHbHMW/Tp08v9n8tnYaEhYWha9euWLBgAbZt24bs7GycPHkSzz77LABg2LBhVvs8Zeb4cRb+0ErRBgPrUaxfr8nhbaG/sjBhwgSkpKTg7bffxuXLlxETE4Np06ZhyJAhaNy4MQA7+D388ot2ZQpdTN8OQUn6LnL1bOBAFrC2IrGxsYVWfm/cpk2bVuz/tmzZUk6fPm3RedLS0uSVV16Rhg0bire3t1SuXFmioqLku+++K/S+mJgYiYqKktDQ0GsyhISESGRkpGzdurVCn7VI5s9nDyIt03Bnz2Z9Cg0STWylv7LoZevWrRIeHi7e3t4SGhoqo0ePvqnWgaW/B6uTlcUc+HnztDuHi+n7eiyNJrBZ1EHJ+i4mM2zJElZnT0rSVDaXokMHkf79tT1HcjJTp1WbIf356CM27dSyh5zSt/1Qsr6LyQx75BE6dGfMqNhQWkF++w3YtQt49VVtzxMSArz4IvDOOwWr0grbc/Ei8MEH1LeWmUlK3/aBBfouvh7tJ58AY8cCf/0FNGyopZjOTX4+cOedXLjQMivMzIUL1NfDD7OesML2DB0KrFkDHD2qzULY9Sh960/p+i6hHm1enkjbtiKRkWwxrigf06ezcldsrO3O+dNPLJ1nyxq4CrJgAb/777+33TmVvvXDMn2X0gX3jz/oq/3gA6vK5jLs3Uu/zbvv2v7cY8bw3L/9ZvtzuyobN4r4+oqMHWv7cyt92x7L9W1Bu/FZs2ixly2zimwuw7FjIiEhIvfdx9mBrcnLY/RIpUoimzbZ/vyuxi+/8KIbPFif9t5K37albPq2wNCKiLz6Klc316ypsHwuwcmTLCDTunVZ+79bF6ORPwRfX3Wj1JJvvuH1MWSIPkbWjNK3bSi7vi00tPn5IsOG0Y3w1VcVktHpOXRIpE4dkRYtRE6d0lsa/hBeeYWzkldeEcnN1Vsi5+HKFbYpMhhERo+2j7UMpW/tKL++LTS0ImzX8J//8CTjx+t757ZX1q4VCQriAuL583pLU5glSxhQ3bGjbRfmnJW//hJp355NEVes0Fuam1H6ti4V03cZDK2Zzz/n1OSuuzhFVnDUMHo0b0JPPCFy+bLeEhVNXBwTJ7y8eLO0QasipyMrS+TNNzm7i4y0eudZq6L0XXGso+9yGFoRWvcmTUSqVROZO9c+pkx6sXOnSJs2HD04QnhNfj7Tgf396eKYP1+fxTpHIz9fJDpapH59pr1+/LFjzOqUvsuHdfVdTkMrIpKZKTJqFC19eLjIrl3lPpRDkpIi8swzbDPcrZvI33/rLVHZOHlSZPhwVoRv2lRk+XLHMBy2Ji+PC0tNmvC3/uyz9uF7LytK35ahjb4rYGjNxMbSjQCI3H8/Y0edmbNn6Sbw8xOpUUNk6VK9JaoYR46IPPYYbxh164pMnWp//mU9SEsTmTKFo0A3N67mJyToLVXFUfouGm31bQVDa2btWo5sDQaRnj0ZCuZMLoWDB0VeeIEG9tZbRWbMsF9fbHlISGAYX0AAYzGfekpk/XrXGvXk5YmsW0c/u6+vSNWqIq+/LvLPP3pLZn2Uvm2pbysaWjNr1nAqbTCIhIWJTJ7suFXAMjJEvv1WpEsXjtgbNhSZOdO5DOyNpKeLzJnDRRSASRevvCKydatz+vZyc0U2bxZ5gyj0XgAAAtlJREFU6SXeQAGRiAiuPWRk6C2d9ih920LfnxVfVKai/P03MHcu8PXXrG7TsSMwYADw4IMsLm6vXLrEYsrR0cDatUBeHtCrF/D880D37oBb0QXPnJKEBGDJEmDpUuDwYaBqVX4HPXuyj73eHSvKS1ISsHEjsG4d8OuvrHzVtCnw2GPAoEFAgwZ6S6gPSt9aMVc7Q2smN5cfMjqafegvXmS1oW7dqMSoKO36aFlCVhawbx9l3LgR2L2b+7t2Bfr3Bx56qKCPmiuTkMAf6tq1wJYtQE4OL7yoKFb6j4gAmjcHrutAaxdkZQEHDwIxMcDOncD27cCpU5SzSxfeRHv2dF3jWhxK39bEBob2enJz+eE3buSdZd8+lhGsVYstXtq2BZo1Axo1ojG2phLz83lnS0jgaPuPP3j++Hi+FhZWYPzvvpvtfBRFk53NG9L27QU/6AsXAHd3oH59oGVLXoSNGwN163IGU6OGdrOB/Hz2Yzt+nNvff/Nii40FEhMBk4k9tiIjuUVFAe3b25+RsFeUviuKjQ3tjVy6BOzZA+zdS6O3bx+/OLNItWrxLlq9OreQELbsDgigEn18+OUZjQVtvNPT2TI9LY391c+eZafQY8do6AEq4Y47aNjbteNmz+4Me8dk4g0sNhaIi+MWG1v4O/f0pC5DQvj9BwbyZhYYCHh7F9Tx9PQsaHWfmUnXDcDfypUrwPnzwLlzBY8pKcDJkwXv8/Lixd+iRYEBaNWKN26Dwbbfi7Oi9F1WdDa0RZGTQyUmJLCQ7qlTNJqpqfySMzJoTPPz+d7sbN5Zzf3tAwJofM3G+dZb+WgeJTdqRGUrtMdkYjflpCTeQJOSqEfzhWPecnPpUgL4/PJlPvfz44UEANWq8aK88aKtXr1gFFWvHhAa6lp+dHtC6bs47NDQKhQKhXMx1+5vBQqFQuHoKEOrUCgUGqMMrUKhUGiMB4AVeguhUCgUTswf/w/CerLIw2KxwwAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "execution_count": 2 } ], "source": [ "for time in range(0,timesteps+1):\n", " for omega in trajectories:\n", " shelper = process[(omega,time)]/numeraire[(omega,time)]\n", " discountedprocess.update({(omega,time):shelper})\n", " \n", "for time in range(1,timesteps+1):\n", " for omega in trajectories:\n", " binomialtreeforwarddiscounted.add_edge('%d / %d'% (time-1,discountedprocess[(omega,time-1)]),'%d / %d'% (time,discountedprocess[(omega,time)]))\n", "\n", "#for time in range(1,timesteps+1):\n", "# for omega in trajectories:\n", "# binomialtreeforward.add_edge('%d, %d'% (time-1,numeraire[(omega,time-1)]),'%d, %d'% (time,numeraire[(omega,time)]))\n", "\n", "\n", "Image(binomialtreeforwarddiscounted.draw(format='png',prog='dot')) " ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "id": "Ks6RVf_UH6hE" }, "outputs": [], "source": [ "def condprob(omega,time): \n", " omegahelperu = list(omega)\n", " omegahelperd = list(omega)\n", " omegahelperu[time]=1\n", " omegahelperd[time]=0\n", " omegahelperu = tuple(omegahelperu)\n", " omegahelperd = tuple(omegahelperd)\n", " return (discountedprocess[(omega,time)]-discountedprocess[(omegahelperd,time+1)])/(discountedprocess[(omegahelperu,time+1)]-discountedprocess[(omegahelperd,time+1)])" ] }, { "cell_type": "markdown", "metadata": { "id": "Rx67Ga1SH6hE" }, "source": [ "The previous function calculates the conditional probabilities which make the process at each node a martingale. Finally the price of a Eurpean Call payoff is calculated in a backwards manner. The tree is drawn in the format time / stock price / derivative price." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "id": "fzpy-gLpH6hF", "outputId": "a69f38c9-786a-4ce4-bcb8-74c3f853cfee", "colab": { "base_uri": "https://localhost:8080/", "height": 268 } }, "outputs": [ { "output_type": "execute_result", "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "execution_count": 4 } ], "source": [ "processbackward = {(omega,timesteps):(payoffE(process[(omega,timesteps)])/numeraire[(omega,timesteps)]) for omega in trajectories}\n", "#backwardssteps: European\n", "for time in reversed(range(0,timesteps)):\n", " for omega in trajectories:\n", " shelper=0 \n", " omegahelperu = list(omega)\n", " omegahelperd = list(omega)\n", " omegahelperu[time]=1\n", " omegahelperd[time]=0\n", " omegahelperu = tuple(omegahelperu)\n", " omegahelperd = tuple(omegahelperd)\n", " shelper = processbackward[(omegahelperu,time+1)]*condprob(omega,time)+processbackward[(omegahelperd,time+1)]*(1-condprob(omega,time))\n", " processbackward.update({(omega,time):shelper})\n", "\n", "for time in range(1,timesteps+1):\n", " for omega in trajectories:\n", " binomialtreebackward.add_edge('%d / %f / %f'% (time-1,discountedprocess[(omega,time-1)],processbackward[(omega,time-1)]),'%d / %f / %f'% (time,discountedprocess[(omega,time)],processbackward[(omega,time)]))\n", "\n", "Image(binomialtreebackward.draw(format='png',prog='dot')) " ] }, { "cell_type": "markdown", "metadata": { "id": "tFubtCV2H6hF" }, "source": [ "# No arbitrage, hedging and a bit of machine learning" ] }, { "cell_type": "markdown", "metadata": { "id": "QnX212qcH6hG" }, "source": [ "In the sequel we look at the above ideas in a continuous time setting, which can be seen as a limit for many trading times and a particular scenario generation structure. Additionally we shall not 'calculate' the solution withing a given model, but learn it in a model-independent way. The method is called 'deep hedging' and applies machine learning technology.\n", "\n", "Deep Hedging goes back to the following [paper](https://arxiv.org/abs/1802.03042) by Hans Bühler, Lukas Gonon, Josef Teichmann and Ben Wood. \n", "\n", "The main idea is to parametrize the hedging strategies (at each time) via neural networks which can depend on input variables chosen by the user, for instance the current price, the past strategy, etc.\n", "This then allows to solve a potentially high dimensional hedging problem for many assets whose dynamics are described by an arbitrary given arbitrage free model even in the presence of transaction costs.\n", "\n", "Let us exemplify first the idea by the Black Scholes model in one dimension." ] }, { "cell_type": "markdown", "metadata": { "id": "j4ZJqpgbH6hH" }, "source": [ "Let $T$ be a finite time horizon and consider on a filtered probability space $(\\Omega, (\\mathcal{F}_{0\\leq t\\leq T}), \\mathcal{F}_T, P)$ a standard Black Scholes model with interest rate $r=0$ and the price of the risky asset $S$ being described by\n", "\n", "$$\n", "dS_t=S_t\\mu dt + S_t\\sigma dW^{\\mathbb{P}}_t, \\quad S_0=S_0\n", "$$\n", "\n", "under the physical measure $\\mathbb{P}$. Here $\\mu \\geq 0$, $\\sigma \\neq 0$, $S_0 >0$ and $W^{\\mathbb{P}}$ is a Brownian motion (under $\\mathbb{P}$).\n", "\n", "Under the unique risk neutral probability measure, denoted by $\\mathbb{Q}$, the dynamics are then given by\n", "\n", "$$\n", "dS_t= S_t\\sigma dW_t, \\quad S_0=S_0\n", "$$\n", "\n", "where $W$ is a $\\mathbb{Q}$ Brownian motion \n", "\n", "We consider here the problem of hedging a $\\mathcal{F}_T$-measurable claim $f(S_T)$. In the case of the Black Scholes model the hedging strategy can be found by the Delta hedge, i.e. \n", "\n", "$$\n", "\\Delta(t,s)=\\partial_s \\mathbb{E}_{Q}[f(S_T)| S_t=s].\n", "$$\n", "\n", "In more involved models this is no longer possible. In particular in incomplete models not every claim can be hedged and we thus need to optimize a hedging criterion. We here consider a __quadratic hedging criterion__ but other risk measures are of course also possible.\n", "\n", "Let $\\pi$ denote the price of the option, i.e. $\\mathbb{E}_Q[f(S_T)]$. Then the goal is solve the following optimization problem \n", "\n", "$$\n", "\\inf_{H \\text{ predictable }}\\mathbb{E}[( f(S_T)- \\pi- (H\\bullet S)_T)^2],\n", "$$\n", "\n", "where $(H_t)$ ranges over all predictable process and $(H \\bullet S)_T= \\int_0^T H_t dS_t$ denotes the stochastic Ito integral. Optimizing over all predictabel processes is infeasable. \n", "\n", "Therefore we choose to specify $H_t$ in a smaller set: for each $t$ as a neural network whose input can be specified. In complete Markovian models, as it is the case of the Black Scholes model, we know from the delta hedging strategy that it makes sense to parameterize $H_t$ as a function of the current price $S_t$. In the current setting we therefore choose that the input of each neural network in the implementation below depends only on the current price, i.e. \n", "\n", "$$\n", "H_t=g_t(S_t)\n", "$$\n", "\n", "and $g_t$ denotes a neural network.\n", "\n", "We can view the above as supervised learning problem: the input data $x_i$ correspond to trajectories of $(S_t(\\omega_i))_{0 \\leq T}$, the output $y_i$ should be $0$ and the\n", "the loss function is given by \n", "\n", "$$\n", "\\mathcal{L}= \\left(f(S_T(\\omega_i))- \\pi- \\int_0^T g_t(S_t (\\omega_i)) dS_t(\\omega_i)\\right)^2.\n", "$$\n", "\n", "To implement this we need to generate input data which will be our training data set. Consider the log price of $S_t$ under $\\mathbb{Q}$, i.e.\n", "\n", "$$\n", "d\\log(S_t)= -\\frac{\\sigma^2}{2} dt + \\sigma dW_t.\n", "$$\n", "\n", "The practical implementation requires a time discretization.\n", "If we discretize our time interval $[0,T]$ in $N$ time steps of length $T/N$ we can write \n", "\n", "$$\n", "\\log(S_i)= \\log(S_{i-1}) -\\frac{\\sigma^2}{2} \\frac{T}{N} + \\sigma \\sqrt{\\frac{T}{N}} Z_i, i=1, \\ldots, N\n", "$$\n", "\n", "where $Z_i$ are independent $N(0,1)$ distributed random variables. The discretized price $(S_0, S_1, \\ldots S_N)$ is obtained by exponentiation.\n", "\n", "In this disretized form the whole trajetory of the price $(S_0, S_1, \\ldots S_N)$ is therefore determined by $(S_0, Z_1, \\ldots, Z_N)$ or in other words $(S_0, X_1, \\ldots, X_N)$ where $X_i$ are independent $N(-\\frac{\\sigma^2}{2} \\frac{T}{N} ,\\sigma^2 \\frac{T}{N})$ distributed random variables. Considering $K$ many samples thereof constitutes the input training data set. The outputs are simply $K$ zeros.\n", "\n", "In the above loss function we also need to disretize the \n", "stochastic integral\n", "\n", "$$\n", "\\int_0^T g_t(S_t (\\omega)) dS_t(\\omega).\n", "$$\n", "\n", "We do this by choosing $N$ neural networks $g_0, \\ldots, g_{N-1}$ and disretizing the integral as follows:\n", "\n", "$$\n", "\\sum_{i=0}^{N-1} g_i(S_i(\\omega)) (S_{i+1}(\\omega)-S_i(\\omega))\n", "$$\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "id": "AaYuvPjnH6hH", "colab": { "base_uri": "https://localhost:8080/" }, "outputId": "9dfa404f-4720-4dab-d79a-5b9119304be1" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "TensorFlow 1.x selected.\n" ] }, { "output_type": "stream", "name": "stderr", "text": [ "Using TensorFlow backend.\n" ] } ], "source": [ "%tensorflow_version 1.x\n", "import numpy as np\n", "import tensorflow as tf\n", "\n", "from keras.models import Sequential\n", "from keras.layers import Input, Dense, Conv2D, Concatenate, Dropout, Subtract, \\\n", " Flatten, MaxPooling2D, Multiply, Lambda, Add, Dot\n", "from keras.backend import constant\n", "from keras import optimizers\n", "\n", "from keras.engine.topology import Layer\n", "from keras.models import Model\n", "from keras.layers import Input\n", "from keras import initializers\n", "from keras.constraints import max_norm\n", "import keras.backend as K\n", "\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "id": "hqlyn6IvH6hI", "outputId": "b584ae25-986e-4208-e7ce-95371d18953d", "colab": { "base_uri": "https://localhost:8080/", "height": 265 } }, "outputs": [ { "output_type": "display_data", "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" } } ], "source": [ "# Trajectories of the Black scholes model\n", "# Let it run to initialize the following parameters, the trajectories \n", "# are not needed afterwards\n", "\n", "N=20 # time disrectization\n", "S0=1 # initial value of the asset\n", "strike=1 # strike for the call option \n", "T=1.0 # maturity\n", "sigma=0.2 # volatility in Black Scholes\n", "R=10 # number of Trajectories\n", "\n", "logS= np.zeros((N,R))\n", "logS[0,]=np.log(S0)*np.ones((1,R))\n", "\n", "for i in range(R):\n", " for j in range(N-1):\n", " increment = np.random.normal(-(sigma)**2*T/(2*N),sigma*np.sqrt(T)/np.sqrt(N))\n", " logS[j+1,i] =logS[j,i]+increment\n", "\n", "S=np.exp(logS)\n", "\n", "for i in range(R):\n", " plt.plot(S[:,i])\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "id": "G-ka3ebXH6hJ", "outputId": "eb9f2be5-59e0-49e6-fec1-25d18f010fb6", "colab": { "base_uri": "https://localhost:8080/" } }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "Price of a Call option in the Black scholes model with initial price 1 strike 1 maturity 1.0 and volatility 0.2 is equal to 0.07965567455405798\n" ] } ], "source": [ "import scipy.stats as scipy\n", "from scipy.stats import norm\n", "\n", "#Blackscholes price\n", "\n", "def BS(S0, strike, T, sigma):\n", " return S0*scipy.norm.cdf((np.log(S0/strike)+0.5*T*sigma**2)/(np.sqrt(T)*sigma))-strike*scipy.norm.cdf((np.log(S0/strike)-0.5*T*sigma**2)/(np.sqrt(T)*sigma))\n", "\n", "priceBS=BS(S0,strike,T,sigma)\n", "print('Price of a Call option in the Black scholes model with initial price', S0, 'strike', strike, 'maturity', T , 'and volatility' , sigma, 'is equal to', BS(S0,strike,T,sigma))" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "id": "AydbckklH6hJ" }, "outputs": [], "source": [ "#Definition of neural networks for heding strategies\n", "\n", "m = 1 # dimension of price\n", "d = 2 # number of layers in strategy\n", "n = 32 # nodes in the first but last layers\n", "\n", "# architecture is the same for all networks\n", "layers = []\n", "for j in range(N):\n", " for i in range(d):\n", " if i < d-1:\n", " nodes = n\n", " layer = Dense(nodes, activation='relu',trainable=True,\n", " kernel_initializer=initializers.RandomNormal(0,1),#kernel_initializer='random_normal',\n", " bias_initializer='random_normal',\n", " name=str(i)+str(j))\n", " else:\n", " nodes = m\n", " layer = Dense(nodes, activation='linear', trainable=True,\n", " kernel_initializer=initializers.RandomNormal(0,1),#kernel_initializer='random_normal',\n", " bias_initializer='random_normal',\n", " name=str(i)+str(j))\n", " layers = layers + [layer]\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "id": "nNunHVAXH6hJ", "colab": { "base_uri": "https://localhost:8080/" }, "outputId": "129a925b-5d94-4d31-fd87-4b6dfae24913" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "WARNING:tensorflow:From /tensorflow-1.15.2/python3.7/tensorflow_core/python/ops/resource_variable_ops.py:1630: calling BaseResourceVariable.__init__ (from tensorflow.python.ops.resource_variable_ops) with constraint is deprecated and will be removed in a future version.\n", "Instructions for updating:\n", "If using Keras pass *_constraint arguments to layers.\n" ] } ], "source": [ "#Implementing the loss function\n", "# Inputs is the training set below, containing the price S0, \n", "#the initial hedging being 0, and the increments of the log price process \n", "price = Input(shape=(m,))\n", "hedge = Input(shape=(m,))\n", "\n", "inputs = [price]+[hedge]\n", "outputs = []\n", "\n", "for j in range(N):\n", " outputs = outputs + [hedge]\n", " payoff= Lambda(lambda x : 0.5*(K.abs(x-strike)+x-strike) - priceBS )(price) \n", " outputs = outputs + [payoff]\n", " strategy = price\n", " for k in range(d):\n", " strategy= layers[k+(j)*d](strategy) # strategy at j is the hedging strategy at j , i.e. the neural network g_j\n", " incr = Input(shape=(m,))\n", " logprice= Lambda(lambda x : K.log(x))(price)\n", " logprice = Add()([logprice, incr])\n", " pricenew=Lambda(lambda x : K.exp(x))(logprice)# creating the price at time j+1\n", " priceincr=Subtract()([pricenew, price])\n", " hedgenew = Multiply()([strategy, priceincr])\n", " #mult = Lambda(lambda x : K.sum(x,axis=1))(mult) # this is only used for m > 1\n", " hedge = Add()([hedge,hedgenew]) # building up the discretized stochastic integral\n", " inputs = inputs + [incr]\n", " price=pricenew\n", " \n", "outputs = outputs + [hedge]\n", "payoff= Lambda(lambda x : 0.5*(K.abs(x-strike)+x-strike) - priceBS )(price)\n", "outputs = outputs + [payoff]\n", "inputs = inputs\n", "outputs= Concatenate()(outputs)\n", "\n", "model_hedge = Model(inputs=inputs, outputs=outputs)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "id": "K-jnrk08H6hK" }, "outputs": [], "source": [ "Ktrain = 2*10**4\n", "initialprice = S0\n", "\n", "# xtrain consists of the price S0, \n", "#the initial hedging being 0, and the increments of the log price process \n", "xtrain = ([initialprice*np.ones((Ktrain,m))] +\n", " [np.zeros((Ktrain,m))]+\n", " [np.random.normal(-(sigma)**2*T/(2*N),sigma*np.sqrt(T)/np.sqrt(N),(Ktrain,m)) for i in range(N)])\n", "\n", "ytrain=np.zeros((Ktrain,2*N+2))\n", "\n", "Ktest = 1\n", "initialprice = S0\n", "\n", "# xtrain consists of the price S0, \n", "#the initial hedging being 0, and the increments of the log price process \n", "xtest = ([initialprice*np.ones((Ktest,m))] +\n", " [np.zeros((Ktest,m))]+\n", " [np.random.normal(-(sigma)**2*T/(2*N),sigma*np.sqrt(T)/np.sqrt(N),(Ktest,m)) for i in range(N)])\n", "\n", "ytest=np.zeros((Ktest,2*N+2))" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "id": "zfj5ggMjH6hL" }, "outputs": [], "source": [ "from keras import losses\n", "def custom_loss(y_true,y_pred):\n", " z1 = y_pred[:,2*N+1]\n", " z2 = y_pred[:,2*N]\n", " z = z1-z2\n", " z=K.mean(K.square(z))\n", " return z" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "id": "GFGLnEw5H6hM" }, "outputs": [], "source": [ "#sgd=optimizers.SGD(lr=0.0001)\n", "#model_hedge.compile(optimizer=sgd,loss='mean_squared_error')\n", "model_hedge.compile(optimizer='adam',loss=custom_loss)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "id": "zYA71OGUH6hM", "outputId": "4db8cf1f-02de-4e57-b973-2096eb8c935a", "colab": { "base_uri": "https://localhost:8080/", "height": 1000 } }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "WARNING:tensorflow:From /tensorflow-1.15.2/python3.7/keras/backend/tensorflow_backend.py:422: The name tf.global_variables is deprecated. Please use tf.compat.v1.global_variables instead.\n", "\n", "Epoch 1/1\n", "20000/20000 [==============================] - 4s 222us/step - loss: 0.0370\n" ] }, { "output_type": "display_data", "data": { "image/png": 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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sF7T86mu5VDd28PgHOtzSVUprfe9mI4OZnBJNenz4oP30q4uqmTI6mvFJw3tt8qwjb3TKYv/gESdjRWSpiBSKSOHhw4eHtY+JyVE8ds0sljs45G1Oz0zgK9PG8Pi6vVQ16B16XGFPjW9PZtYfEWFeTgoflR6hvbP/i/VqmjooPFA/7NY8wOiYMEZFhugQSz/hiKCvBDL6fJ1uXTbQ8pMYY5YbYwqMMQVJSUnDLmRB3minhLzNXYunYAz8frUOt3SFkpoWvxlx09f83BSOdffyUemRfte/WXQIYxh2/zxY/qBYTshqi94fOCLoVwLXWUffnAk0GmOqgTXAAhGJt56EXWBd5rXS4yNYeu54Vm6tYtOBoV2qrobOdlcpfxhx09fsrASiw4IG7L75z/ZqspOjmDjCawvyUmPYU9PMsW6d5sPX2TO88kVgPTBZRCpE5EYRuVlEbrZusgooA0qBJ4AfABhj6oDfAhutH/dal3m1m8+bQEpMKL/51w56e9073LKyoZ2H3yulqcM3L2UvqWnxq/55m+DAAM6blMS7u2pOeo/VNnewcX/diLptbPJTY+nuNcengVa+K2iwDYwxVw+y3gC3DLBuBbBieKV5psjQIH62aAo/emUrr39eyRWz0l1eQ1dPL3/7eB9/fruE9q4eOrp6+PGCyS6vw5ka27s41NThk7cPtMf83BT+va2aLRUNzBz7xajkNcU11m4bBwT98ROyjcfnqVe+ySNOxnqbS6encVpGHH98cxetx1w73HLzwXq+9teP+H+rdnHWhFGcPWEUz316wOeGfZYen/rA/1r0AOdPSiYwQE7qvlm1rZoJSZEOmfsnIz6C6NAgvULWD2jQD0NAgHDP13KpbT7Go+/vdckxG9u6uPuN7Xz90U9oaOvisWtm8tT1Bfxo/iQa2rp4tbDCJXW4SkmNbTIz/2zRx0YEMzsz4UuzWR5pOcaGfUdZMnUMIiM/bxEQIDplsZ/QoB+mmWPjuXR6Kss/LKO8rs1pxzHG8M8tlVz03+/z4mcH+e45Wbzz4/NYlG/5ZS/ITGDm2Die/KiMHjefM3CkktoWwoIDSI/3rxE3fc3LTWFPTQsHj1reX2uKD9HroG4bm7zUWHZWN/nUe0edTIN+BH62eAoB4rzhlvuOtHLtU5/xw5e2kBYXzspb5/DLr+YSFfrlUytLzx1PeV07bxYdckod7mCb+sDfRtz0Nc82yZm1Vb96+yGyEiOZMtpx/+Xkp8XQ0dVL2WE9IevLNOhHYExsODefN4H/bK9mQ9lRh+33WHcP//POHhb+zzq2ljfw20vyeP0H5wx4wmx+7mgyR0WwfN1en5l4rbS2hUl+MDXxqYwbFUl2chTv7KyhrrWT9WVHWTJ1tEO6bWxs7yntvvFtg466Uaf2/XMn8MrGcr73TCHTMmLJHRNDzpgYclNjmJAURXDg0P6WflJ6hF/8o4iyI6187bRUfvmVHJJjwk75nMAA4ca54/nlP4rYuL+e2VkJI/mW3K6po4vqxg4m+vjNRuwxLzeF5evKeLWwnJ5ew+IhTkk8mPGJkYQGBVBc2cRlMxy6a+VBNOhHKDwkkOXXFfC/nx5gR3UTz64/wDHrDZ5DAgPITomyBL/tD8CYGGIjgk/az5GWY/zuPzt54/NKxo2K4Jnvzua8SfZfJXzFzHT+/PYelq/b6/VBbxtx4+8terDcjOTR9/fyl3dLGDcqgrzUGIfuPygwgJwxekLW12nQO0B+Wiy///o0ALp7etl3pJUd1U3sqG5iZ3Uz7++u5bVNX4yKSYsLP97qzx0TzZGWTu5fs5u2zm5uu3Ait1wwcchTOYSHBHLtmeP4y7sllNa2ePXUvrYRN75+n1h7TM+IIzEqhCMtnSzOd8xomxPlpcawcmsVxhin7F+5nwa9gwUFBpCdEk12SjSXTP9iss7a5g52Vjezo6qJndY/Amt31WAb7HDm+AT+76VTRxTQ1501jsc+2MuTH5Yd/8PjjUpqbCNu7L8Pqq8KDBAunJLMK4UVI5rb5lTy02J5fsNByuvah3TvWeU9NOhdJDk6jOTosC91x7R39rCnppnWzm7OGj9qxK2pUVGhXDErnVcLK/jRgkkkR5+6b99T7altYUJSFIF+POKmr++fN4FxoyKZ6qSrV/P73ENWg9436agbNwoPCeS0jDjOnpDosH+Zvzd3PF29vTy3/oBD9ucOpTXNfnuhVH8mJEVxywUTndatMml0FEEBolMW+zANeh+TlRjJgtwUr50Wobmji6rGDq8+x+BtQoMCyU6J1imLfZgGvQ9aeu54r50W4fiIG23Ru1R+agzFVY0+cx2G+jINeh80a1wCs8bF8+RHZXT39Lq7nCGxTZnrr5OZuUteagxHWjqpbT7m7lKUE2jQ+6ib5lqmRVhTfOp7j3qaPTXNhAYFkJGgJwVd6fgVspXaT++LNOh91PzcFK+cFqFER9y4Rc6YGETQKYt9lAa9jwoMEL43dzxbKxr5bJ/33NirpKbZIXOtq6GJDA0iKzFSW/Q+SoPeh10xK52EyBCe+LDM3aXYxTbixl/vKuVu+amx2qL3URr0PiwsOJDrzhrHOztrKa1tdnc5g/L3u0q5W15qDJUN7dS3drq7FOVgGvQ+7tozxxEaFMCTH+5zdymDKtGhlW5lOyGrrXrfo0Hv42zTIry+uZLa5g53l3NKJTrixq1sM2PqFbK+R4PeD9imRXj2E8+eFkFH3LhXXEQIaXHhFGmL3udo0PuBvtMitB7z3GkRSmpadGpiN8tPi6FYR974HA16P7H03Ak0tnfxamG5u0vpV8uxbiob2rV/3s3yUmPZd7SVFg9uEKih06D3E7PGxTNrXDxPfbzPI6dFsI240cnM3Cs/LQZjYGe1dt/4Eg16P7L0XMu0CG8WH3J3KSex3VVKW/TudXxueu2+8Sl2Bb2ILBKR3SJSKiJ39rN+nIi8KyLbROR9EUnvs65HRLZYP1Y6sng1NPNyUshKjOSJdWUeNy1CSW0LIUEBjNURN26VHBNGYlSoDrH0MYMGvYgEAg8Di4Fc4GoRyT1hsz8BzxpjpgH3Avf1WddujJlu/bjYQXWrYQgMEG6ck8XWikY2DGNaBGMMJTXNPLS2hEse/pjf/WeHw2orqWnWETceIj8tRlv0PsaeFv1soNQYU2aM6QReAi45YZtcYK318Xv9rFce4vi0COvsmxaht9ew+WA9963eyYUPfMD8P6/jT2/toaaxgyc/2seuQ45p+e2padErYj1EfmospbUtdHT1uLsU5SD2BH0a0HeoRoV1WV9bgcutjy8DokVklPXrMBEpFJFPReTS/g4gIkut2xQePnx4COWrobJNi/DuroGnRejs7mXdnsPc/cZ2zrzvXS5/5BOe+nAf6fHh/PbSfD696yLW3H4uUaFB/GnN7hHX1Hp8xI0GvSfIS42hu9ewp8bzp81Q9nHUzcHvAB4Ske8A64BKwNYcGGeMqRSR8cBaEdlujNnb98nGmOXAcoCCggLP6jz2Qdedlcmj7+/liXX7+MMV0wBL2H6w5zBrig+xdlctzR3dhAcHcv7kJBbkpXDh5BRiI4K/tJ+bz5vA/Wt2s+lAHbPGJQy7ni9G3OiJWE/wxdz0TUxLj3NzNcoR7An6SiCjz9fp1mXHGWOqsLboRSQK+LoxpsG6rtL6uUxE3gdmAF8KeuVaCZEhfKMgnVc2VpCXFsMHuw/zYekROrt7iY8IZlHeaBbkjWZudiJhwYED7ueGczL528f7+eObu3lp6ZnDvnn1F3PcaIveE6THhxMTFqRTIfgQe4J+I5AtIllYAv4q4Ft9NxCRRKDOGNML3AWssC6PB9qMMces25wD/NGB9ath+t6c8Ty/4SC/+mcxaXHhfGv2WBbmjeb0zHiCAu0bdRsREsRtF07knpXFfFhyhHMnJQ2rlpKaZkICdcSNpxAR8lJjdSoEHzJo0BtjukXkVmANEAisMMYUi8i9QKExZiVwPnCfiBgsXTe3WJ+eAzwuIr1Yzgf83hjjuKEaatgyEyN56aYziQwNIi81Ztit8atmZ7B8XRn3r9nN3OzEYe1nT00z45Mi7f4Do5wvPy2GZ9cfoLunV38uPsCuPnpjzCpg1QnLftXn8WvAa/087xNg6ghrVE5yxvhRg280iNCgQJbNn8Qdr25lddEhlkwdM+R9lNS2MHNs/IhrUY6TlxrLse5e9h5uZfJoPXfi7fRPtRqxy2akkZ0cxQNv7R7y9Aqtx7qpqG/XoZUeJj/NMmWxjqf3DRr0asQCA4QfL5jM3sOtvP555eBP6GPvYetdpXTqA4+SlRhFeHCgXiHrIzTolUMszEvhtPRY/vJOCce67b/QZk+NLei1Re9JAgOEnDHRFOnIG5+gQa8cQkT4ycIpVDa08/ynB+1+XkmtZcTNOB1x43Hy02LZWdVEb6/9l7YYY6ht7mDzwXpWbq1i35FWJ1ao7OWoC6aUYk52ImdPGMXD75Vy5ekZRIYO/vYqqWnRETceKi/VMvLmYF0bmYmRgCXIj7Z2UlHfTnldGxX17VTUWz6X17dRWd/Ose4vztOMT4rk7WXn6RxGbqZBrxzqJwsnc9kjn7Dio33cdlH2oNuX1DYzPUNH3HiiPOuUxfesLEaE46He0fXlE+7xEcGkx0cwOSWaeTkppMeHkx4fTkV9O7/6ZzErt1Zy2Yz0/g6hXESDXjnUjLHxzM9NYfm6Mq45cxzxkSEDbtvW2U15XTvfmJUx4DbKfSalRJMWF87WigbS48OZmBTF+ZOSrEEeQUZCBGnx4UQN8J9bb6/hxc/KefDdUr42LVX/a3MjDXrlcHcsmMyiv6zjsQ/2cteSnAG321tr6b/VqQ88U0hQAB/97IJhX0wXECAsm5fN0uc28Y8tVVwxS1v17qJ/YpXDTR4dzWXT03j6k/0cauwYcDvb7Ig6mZnnGm7I28zPTSE/LYa/ri2hywNvYekvNOiVUyybP4leY/jr2pIBtympbSE4UMgcpSNufJWIsGzeJA4cbeONzUO7xkI5jga9coqMhAiunj2WlzeWc+Bo/0PsSmqaGZ8YpX23Pu7CKcmclh7Lg2tL6OzWVr076G+YcppbL5hIUKDw32/v6Xd9SW2LXijlB0SE2+dPoqK+nb9vrnB3OX5Jg145TXJMGDeck8XKrVXsrP7ypfTtnT2U17eRrf3zfuH8SUlMz4jjobWl2qp3Aw165VQ3nzuB6NAgHnjry7cc3Hu4BWN0xI2/EBF+NH8SlQ3tvFJYPvgTlENp0Cunio0I5vvnTeCdnbVsOlB3fLltxI1OZuY/5mYnUjAunoffK9Ubj7uYBr1yuhvOySQxKpQ/vrkbYyzzpthG3IzTETd+Q0RYNn8S1Y0dvLxRW/WupEGvnM52y8EN++pYV3IE+GLETbCOuPErZ08YxeysBB55X1v1rqS/Zcolrp49lvT4cO5fswtjDHtqWpio/fN+xzauvqbpGC9ssH+WUzUyGvTKJUKCAlg2bxJFlU288Xkl5fVtTNIRN37prAmjOGv8KB79YC/tndqqdwUNeuUyl1pvOXjPymKM0ZuN+LNl8ydxuPkYz2844O5S/IIGvXIZ2y0Hmzu6AR1a6c9mZyUwZ2Iij76/l7bObneX4/M06JVLLcxL4bSMOOuIm0h3l6PcaNn8bI62dvLcem3VO5sGvXIpEeEvV07noW/N1BE3fm7WuATOnZTE4+vKaD2mrXpn0t805XKZiZEszBvt7jKUB1g2L5u61k6eWb/f3aX4NA16pZTbzBgbz4VTklm+rozmji53l+OzNOiVUm51+7xsGtq6eOaT/e4uxWfZFfQiskhEdotIqYjc2c/6cSLyrohsE5H3RSS9z7rrRaTE+nG9I4tXSnm/aelxzMux3Ge4SVv1TjFo0ItIIPAwsBjIBa4WkdwTNvsT8KwxZhpwL3Cf9bkJwD3AGcBs4B4RiXdc+UopX3D7vGyaOrpZ8dE+d5fik+xp0c8GSo0xZcaYTuAl4JITtskF1lofv9dn/ULgbWNMnTGmHngbWDTyspVSviQ/LZaFeSk89dE+Gtu0Ve9o9gR9GtB3qrkK67K+tgKXWx9fBkSLyCg7n4uILBWRQhEpPHz4sL21K6V8yO3zJtHc0c1TH5W5u5wOKJMAABAfSURBVBSf46iTsXcA54nI58B5QCVg9yQWxpjlxpgCY0xBUlKSg0pSSnmTnDExLJk6mhUf76ehrdPd5fgUe4K+Esjo83W6ddlxxpgqY8zlxpgZwN3WZQ32PFcppWx+eNEkWju7eeJDbdU7kj1BvxHIFpEsEQkBrgJW9t1ARBJFxLavu4AV1sdrgAUiEm89CbvAukwppU4yeXQ0X5k6hqc/3k9dq7bqHWXQoDfGdAO3YgnoncArxphiEblXRC62bnY+sFtE9gApwO+sz60Dfovlj8VG4F7rMqWU6tft87Jp6+ph+Tpt1TuK2G7t5ikKCgpMYWGhu8tQSrnRD1/6nLd31LD+rouIDQ92dzleQUQ2GWMK+lunV8YqpTzO0nPH09bZw0uf6V2oHEGDXinlcfJSYzlr/Cie+WQ/XT297i7H62nQK6U80o1zsqhq7GB10SF3l+L1NOiVUh7pwinJZCVG8tRH+/C0c4neRoNeKeWRAgKE756TydbyBjYfrHd3OV5Ng14p5bG+Piud2PBgnvxQJzsbCQ16pZTHiggJ4ltnjGVN8SHK69rcXY7X0qBXSnm068/KJECEp/XGJMOmQa+U8mijY8P46rQxvLyxXG83OEwa9Eopj3fjnPG0HOvm5Y3lg2+sTqJBr5TyeFPTY5mdmcDfPt5Pt15ANWQa9Eopr3Dj3CwqG9p5a0eNu0vxOhr0SimvMC8nhbEJETyl95UdMg16pZRXCAwQbjgnk00H6vlcL6AaEg16pZTX+EZBBtFhQdqqHyINeqWU14gKDeLq2WNZXXSIyoZ2d5fjNTTolVJe5fqzMwF4Ri+gspsGvVLKq6TFhbM4fzQvfnaQlmPd7i7HK2jQK6W8zo1zsmju6ObVQr2Ayh4a9EoprzNjbDyzxsXzt4/309Orc9UPRoNeKeWVbpyTxcG6Nt7ZqRdQDUaDXinllRbkppAWF85TOlf9oDTolVJeKSgwgBvOyeSz/XVsq2hwdzkeTYNeKeW1rjw9g6hQvYBqMBr0SimvFR0WzDcLMvjPtmoONXa4uxyPpUGvlPJqN5yTSa8xPLN+v7tL8Vh2Bb2ILBKR3SJSKiJ39rN+rIi8JyKfi8g2EVliXZ4pIu0issX68ZijvwGllH/LSIhgYd5oXthwkLZOvYCqP4MGvYgEAg8Di4Fc4GoRyT1hs18ArxhjZgBXAY/0WbfXGDPd+nGzg+pWSqnjvjc3i8b2Lv6+qcLdpXgke1r0s4FSY0yZMaYTeAm45IRtDBBjfRwLVDmuRKWUOrWZY+M5LSOOFR/vp1cvoDqJPUGfBvS9zrjCuqyvXwPXiEgFsAq4rc+6LGuXzgciMre/A4jIUhEpFJHCw4cP21+9UkoBIsKNc7LYd6SVtbtq3V2Ox3HUydirgaeNMenAEuA5EQkAqoGx1i6dHwEviEjMiU82xiw3xhQYYwqSkpIcVJJSyp8szh9NamyYDrXshz1BXwlk9Pk63bqsrxuBVwCMMeuBMCDRGHPMGHPUunwTsBeYNNKilVLqRMGBAVx/dibry45SXNU45Od3dPVQ3djOwaNtTqjOvYLs2GYjkC0iWVgC/irgWydscxC4CHhaRHKwBP1hEUkC6owxPSIyHsgGyhxWvVJK9XHV7LH85d0SnvpwH/dcnEddayd1rceoa+360uejrZ3Ut3ZS19p5/HFrZ8/x/fxk4WRuuWCiG78Txxo06I0x3SJyK7AGCARWGGOKReReoNAYsxL4MfCEiCzDcmL2O8YYIyLnAveKSBfQC9xsjKlz2nejlPJrseGWC6ie/mQ/r39+YseDRWhQAKMiQ0iICiEhMpSsxEgSIkNJiAwmITKU93bX8t9v7+GMrAQKMhNc/B04hxjjWWeoCwoKTGFhobvLUEp5qaMtx3ju0wNEhQaREBlCfGSIJditHxEhp27fNnd0seTBD+nthVX/NZfYiGAXVT4yIrLJGFPQ7zoNeqWU+rIt5Q1c8egnzM9N4ZFvz0RE3F3SoE4V9DoFglJKnWB6Rhx3LJzM6qJDvPDZQXeXM2Ia9Eop1Y+lc8czNzuRe/+1gz01ze4uZ0Q06JVSqh8BAcID3zyN6LAgbn1hMx1dPYM/yUNp0Cul1ACSo8N44JvT2VPTwm//vcPd5QybBr1SSp3CeZOSWHrueJ7fcJA3i6rdXc6waNArpdQg7lgwmWnpsfz0tW1UNrS7u5wh06BXSqlBhAQF8OBVM+jpNfzwxc/p7ul1d0lDokGvlFJ2yEyM5HeXTaXwQD0Pri11dzlDokGvlFJ2unRGGpfPTOOhtSV8WnbU3eXYTYNeKaWG4LeX5DNuVCS3v7SF+tZOd5djFw16pZQagsjQIP569QyOth7jJ69tw9OmkemPBr1SSg1RflosP1s0hXd21vDs+gPuLmdQGvRKKTUMN87J4oLJSfxu1U52VDW5u5xT0qBXSqlhEBH+9I3TiA0P5rYXN9PW2e3ukgakQa+UUsM0KiqU/7lyOmVHWvnNSs+dIkGDXimlRuCciYn8n/Mm8HJhOf/aWuXucvqlQa+UUiO0bP4kZoyN4+evb6e8zvNuLq5Br5RSIxQcaJkiAYGbni2kqaPL3SV9iQa9Uko5QEZCBI98eyaltS3c8vxmujxoPhwNeqWUcpC52Un8v8un8mHJEe5+Y7vHXEx16tuhK6WUGpJvFmRQUdfGg2tLyYiP4LaLst1dkga9Uko52rL5kyivb+eBt/eQnhDOZTPS3VqPBr1SSjmYiPCHr0+jurGdn762jdEx4Zw1YZTb6tE+eqWUcoKQoAAev6aAcaMi+f5zhZTWNrutFruCXkQWichuESkVkTv7WT9WRN4Tkc9FZJuILOmz7i7r83aLyEJHFq+UUp4sNiKYv33ndEKCArl+xUZqmzvcUsegQS8igcDDwGIgF7haRHJP2OwXwCvGmBnAVcAj1ufmWr/OAxYBj1j3p5RSfiEjIYIV3ymgrrWTG58udMucOPa06GcDpcaYMmNMJ/AScMkJ2xggxvo4FrBdB3wJ8JIx5pgxZh9Qat2fUkr5jWnpcfz16hkUVzXyXy9+Tk+va4dd2hP0aUB5n68rrMv6+jVwjYhUAKuA24bwXERkqYgUikjh4cOH7SxdKaW8x7zcFH59cR7v7Kzl3n8Vu3SMvaNOxl4NPG2MSQeWAM+JiN37NsYsN8YUGGMKkpKSHFSSUkp5luvOyuSmuVk8s/4AT320z2XHtWd4ZSWQ0efrdOuyvm7E0gePMWa9iIQBiXY+Vyml/MZdi3OoqG/nd6t2khYXzuKpY5x+THta3RuBbBHJEpEQLCdXV56wzUHgIgARyQHCgMPW7a4SkVARyQKygc8cVbxSSnmbgADhz1dOZ0ZGHLe/vIVNB+qdf8zBNjDGdAO3AmuAnVhG1xSLyL0icrF1sx8DN4nIVuBF4DvGohh4BdgBvAncYozpccY3opRS3iIsOJAnritgdGwYNz1byP4jrU49nnjKpDs2BQUFprCw0N1lKKWU0+070srlj3xMXEQIf/8/Z5MQGTLsfYnIJmNMQX/r9MpYpZRyk6zESJ64roDKhnaWPltIR5dzOjw06JVSyo0KMhP48zenU3ignh+/upVeJ4yx10nNlFLKzb4ybQwV9VNo6+xBxPH716BXSikP8P3zJjht39p1o5RSPk6DXimlfJwGvVJK+TgNeqWU8nEa9Eop5eM06JVSysdp0CullI/ToFdKKR/ncZOaichh4MAIdpEIHHFQOY6kdQ2N1jU0WtfQ+GJd44wx/d65yeOCfqREpHCgGdzcSesaGq1raLSuofG3urTrRimlfJwGvVJK+ThfDPrl7i5gAFrX0GhdQ6N1DY1f1eVzffRKKaW+zBdb9EoppfrQoFdKKR/nlUEvIotEZLeIlIrInf2sDxWRl63rN4hIpgtqyhCR90Rkh4gUi8gP+9nmfBFpFJEt1o9fObuuPsfeLyLbrcc96e7rYvGg9TXbJiIzXVDT5D6vxRYRaRKR20/YxiWvmYisEJFaESnqsyxBRN4WkRLr5/gBnnu9dZsSEbneBXXdLyK7rD+nN0QkboDnnvJn7oS6fi0ilX1+VksGeO4pf3+dUNfLfWraLyJbBniuM1+vfvPBZe8xY4xXfQCBwF5gPBACbAVyT9jmB8Bj1sdXAS+7oK4xwEzr42hgTz91nQ/8202v234g8RTrlwCrAQHOBDa44ed6CMtFHy5/zYBzgZlAUZ9lfwTutD6+E/hDP89LAMqsn+Otj+OdXNcCIMj6+A/91WXPz9wJdf0auMOOn/Mpf38dXdcJ6x8AfuWG16vffHDVe8wbW/SzgVJjTJkxphN4CbjkhG0uAZ6xPn4NuEjEGXdi/IIxptoYs9n6uBnYCaQ585gOdgnwrLH4FIgTkTEuPP5FwF5jzEiuih42Y8w6oO6ExX3fR88Al/bz1IXA28aYOmNMPfA2sMiZdRlj3jLGdFu//BRId9TxRlKXnez5/XVKXdYM+CbwoqOOZ69T5INL3mPeGPRpQHmfrys4OVCPb2P9hWgERrmkOsDaVTQD2NDP6rNEZKuIrBaRPFfVBBjgLRHZJCJL+1lvz+vqTFcx8C+gu16zFGNMtfXxISCln23c/bp9F8t/Yv0Z7GfuDLdau5RWDNAN4c7Xay5QY4wpGWC9S16vE/LBJe8xbwx6jyYiUcDfgduNMU0nrN6MpWviNOCvwD9cWNocY8xMYDFwi4ic68Jjn5KIhAAXA6/2s9qdr9lxxvI/tEeNRRaRu4Fu4PkBNnH1z/xRYAIwHajG0k3iSa7m1K15p79ep8oHZ77HvDHoK4GMPl+nW5f1u42IBAGxwFFnFyYiwVh+iM8bY14/cb0xpskY02J9vAoIFpFEZ9dlPV6l9XMt8AaWf6H7sud1dZbFwGZjTM2JK9z5mgE1tu4r6+fafrZxy+smIt8Bvgp82xoQJ7HjZ+5QxpgaY0yPMaYXeGKA47nr9QoCLgdeHmgbZ79eA+SDS95j3hj0G4FsEcmytgSvAlaesM1KwHZm+gpg7UC/DI5i7f97CthpjPnvAbYZbTtXICKzsbz+rvgDFCki0bbHWE7mFZ2w2UrgOrE4E2js8y+lsw3Y0nLXa2bV9310PfDPfrZZAywQkXhrV8UC6zKnEZFFwE+Bi40xbQNsY8/P3NF19T2nc9kAx7Pn99cZ5gG7jDEV/a109ut1inxwzXvMGWeYnf2BZYTIHixn7++2LrsXyxsfIAxLN0Ap8Bkw3gU1zcHyb9c2YIv1YwlwM3CzdZtbgWIsIw0+Bc520es13nrMrdbj216zvrUJ8LD1Nd0OFLiotkgswR3bZ5nLXzMsf2iqgS4sfaA3Yjmv8y5QArwDJFi3LQCe7PPc71rfa6XADS6oqxRLn63tfWYbYZYKrDrVz9zJdT1nfe9swxJgY06sy/r1Sb+/zqzLuvxp23uqz7aufL0GygeXvMd0CgSllPJx3th1o5RSagg06JVSysdp0CullI/ToFdKKR+nQa+UUj5Og14ppXycBr1SSvm4/w/zIi+V7lKIKgAAAABJRU5ErkJggg==\n", 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\n", "text/plain": [ "
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\n", 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\n", 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\n", 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\n", 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sF7T86mu5VDd28PgHOtzSVUprfe9mI4OZnBJNenz4oP30q4uqmTI6mvFJw3tt8qwjb3TKYv/gESdjRWSpiBSKSOHhw4eHtY+JyVE8ds0sljs45G1Oz0zgK9PG8Pi6vVQ16B16XGFPjW9PZtYfEWFeTgoflR6hvbP/i/VqmjooPFA/7NY8wOiYMEZFhugQSz/hiKCvBDL6fJ1uXTbQ8pMYY5YbYwqMMQVJSUnDLmRB3minhLzNXYunYAz8frUOt3SFkpoWvxlx09f83BSOdffyUemRfte/WXQIYxh2/zxY/qBYTshqi94fOCLoVwLXWUffnAk0GmOqgTXAAhGJt56EXWBd5rXS4yNYeu54Vm6tYtOBoV2qrobOdlcpfxhx09fsrASiw4IG7L75z/ZqspOjmDjCawvyUmPYU9PMsW6d5sPX2TO88kVgPTBZRCpE5EYRuVlEbrZusgooA0qBJ4AfABhj6oDfAhutH/dal3m1m8+bQEpMKL/51w56e9073LKyoZ2H3yulqcM3L2UvqWnxq/55m+DAAM6blMS7u2pOeo/VNnewcX/diLptbPJTY+nuNcengVa+K2iwDYwxVw+y3gC3DLBuBbBieKV5psjQIH62aAo/emUrr39eyRWz0l1eQ1dPL3/7eB9/fruE9q4eOrp6+PGCyS6vw5ka27s41NThk7cPtMf83BT+va2aLRUNzBz7xajkNcU11m4bBwT98ROyjcfnqVe+ySNOxnqbS6encVpGHH98cxetx1w73HLzwXq+9teP+H+rdnHWhFGcPWEUz316wOeGfZYen/rA/1r0AOdPSiYwQE7qvlm1rZoJSZEOmfsnIz6C6NAgvULWD2jQD0NAgHDP13KpbT7Go+/vdckxG9u6uPuN7Xz90U9oaOvisWtm8tT1Bfxo/iQa2rp4tbDCJXW4SkmNbTIz/2zRx0YEMzsz4UuzWR5pOcaGfUdZMnUMIiM/bxEQIDplsZ/QoB+mmWPjuXR6Kss/LKO8rs1pxzHG8M8tlVz03+/z4mcH+e45Wbzz4/NYlG/5ZS/ITGDm2Die/KiMHjefM3CkktoWwoIDSI/3rxE3fc3LTWFPTQsHj1reX2uKD9HroG4bm7zUWHZWN/nUe0edTIN+BH62eAoB4rzhlvuOtHLtU5/xw5e2kBYXzspb5/DLr+YSFfrlUytLzx1PeV07bxYdckod7mCb+sDfRtz0Nc82yZm1Vb96+yGyEiOZMtpx/+Xkp8XQ0dVL2WE9IevLNOhHYExsODefN4H/bK9mQ9lRh+33WHcP//POHhb+zzq2ljfw20vyeP0H5wx4wmx+7mgyR0WwfN1en5l4rbS2hUl+MDXxqYwbFUl2chTv7KyhrrWT9WVHWTJ1tEO6bWxs7yntvvFtg466Uaf2/XMn8MrGcr73TCHTMmLJHRNDzpgYclNjmJAURXDg0P6WflJ6hF/8o4iyI6187bRUfvmVHJJjwk75nMAA4ca54/nlP4rYuL+e2VkJI/mW3K6po4vqxg4m+vjNRuwxLzeF5evKeLWwnJ5ew+IhTkk8mPGJkYQGBVBc2cRlMxy6a+VBNOhHKDwkkOXXFfC/nx5gR3UTz64/wDHrDZ5DAgPITomyBL/tD8CYGGIjgk/az5GWY/zuPzt54/NKxo2K4Jnvzua8SfZfJXzFzHT+/PYelq/b6/VBbxtx4+8terDcjOTR9/fyl3dLGDcqgrzUGIfuPygwgJwxekLW12nQO0B+Wiy///o0ALp7etl3pJUd1U3sqG5iZ3Uz7++u5bVNX4yKSYsLP97qzx0TzZGWTu5fs5u2zm5uu3Ait1wwcchTOYSHBHLtmeP4y7sllNa2ePXUvrYRN75+n1h7TM+IIzEqhCMtnSzOd8xomxPlpcawcmsVxhin7F+5nwa9gwUFBpCdEk12SjSXTP9iss7a5g52Vjezo6qJndY/Amt31WAb7HDm+AT+76VTRxTQ1501jsc+2MuTH5Yd/8PjjUpqbCNu7L8Pqq8KDBAunJLMK4UVI5rb5lTy02J5fsNByuvah3TvWeU9NOhdJDk6jOTosC91x7R39rCnppnWzm7OGj9qxK2pUVGhXDErnVcLK/jRgkkkR5+6b99T7altYUJSFIF+POKmr++fN4FxoyKZ6qSrV/P73ENWg9436agbNwoPCeS0jDjOnpDosH+Zvzd3PF29vTy3/oBD9ucOpTXNfnuhVH8mJEVxywUTndatMml0FEEBolMW+zANeh+TlRjJgtwUr50Wobmji6rGDq8+x+BtQoMCyU6J1imLfZgGvQ9aeu54r50W4fiIG23Ru1R+agzFVY0+cx2G+jINeh80a1wCs8bF8+RHZXT39Lq7nCGxTZnrr5OZuUteagxHWjqpbT7m7lKUE2jQ+6ib5lqmRVhTfOp7j3qaPTXNhAYFkJGgJwVd6fgVspXaT++LNOh91PzcFK+cFqFER9y4Rc6YGETQKYt9lAa9jwoMEL43dzxbKxr5bJ/33NirpKbZIXOtq6GJDA0iKzFSW/Q+SoPeh10xK52EyBCe+LDM3aXYxTbixl/vKuVu+amx2qL3URr0PiwsOJDrzhrHOztrKa1tdnc5g/L3u0q5W15qDJUN7dS3drq7FOVgGvQ+7tozxxEaFMCTH+5zdymDKtGhlW5lOyGrrXrfo0Hv42zTIry+uZLa5g53l3NKJTrixq1sM2PqFbK+R4PeD9imRXj2E8+eFkFH3LhXXEQIaXHhFGmL3udo0PuBvtMitB7z3GkRSmpadGpiN8tPi6FYR974HA16P7H03Ak0tnfxamG5u0vpV8uxbiob2rV/3s3yUmPZd7SVFg9uEKih06D3E7PGxTNrXDxPfbzPI6dFsI240cnM3Cs/LQZjYGe1dt/4Eg16P7L0XMu0CG8WH3J3KSex3VVKW/TudXxueu2+8Sl2Bb2ILBKR3SJSKiJ39rN+nIi8KyLbROR9EUnvs65HRLZYP1Y6sng1NPNyUshKjOSJdWUeNy1CSW0LIUEBjNURN26VHBNGYlSoDrH0MYMGvYgEAg8Di4Fc4GoRyT1hsz8BzxpjpgH3Avf1WddujJlu/bjYQXWrYQgMEG6ck8XWikY2DGNaBGMMJTXNPLS2hEse/pjf/WeHw2orqWnWETceIj8tRlv0PsaeFv1soNQYU2aM6QReAi45YZtcYK318Xv9rFce4vi0COvsmxaht9ew+WA9963eyYUPfMD8P6/jT2/toaaxgyc/2seuQ45p+e2padErYj1EfmospbUtdHT1uLsU5SD2BH0a0HeoRoV1WV9bgcutjy8DokVklPXrMBEpFJFPReTS/g4gIkut2xQePnx4COWrobJNi/DuroGnRejs7mXdnsPc/cZ2zrzvXS5/5BOe+nAf6fHh/PbSfD696yLW3H4uUaFB/GnN7hHX1Hp8xI0GvSfIS42hu9ewp8bzp81Q9nHUzcHvAB4Ske8A64BKwNYcGGeMqRSR8cBaEdlujNnb98nGmOXAcoCCggLP6jz2Qdedlcmj7+/liXX7+MMV0wBL2H6w5zBrig+xdlctzR3dhAcHcv7kJBbkpXDh5BRiI4K/tJ+bz5vA/Wt2s+lAHbPGJQy7ni9G3OiJWE/wxdz0TUxLj3NzNcoR7An6SiCjz9fp1mXHGWOqsLboRSQK+LoxpsG6rtL6uUxE3gdmAF8KeuVaCZEhfKMgnVc2VpCXFsMHuw/zYekROrt7iY8IZlHeaBbkjWZudiJhwYED7ueGczL528f7+eObu3lp6ZnDvnn1F3PcaIveE6THhxMTFqRTIfgQe4J+I5AtIllYAv4q4Ft9NxCRRKDOGNML3AWssC6PB9qMMces25wD/NGB9ath+t6c8Ty/4SC/+mcxaXHhfGv2WBbmjeb0zHiCAu0bdRsREsRtF07knpXFfFhyhHMnJQ2rlpKaZkICdcSNpxAR8lJjdSoEHzJo0BtjukXkVmANEAisMMYUi8i9QKExZiVwPnCfiBgsXTe3WJ+eAzwuIr1Yzgf83hjjuKEaatgyEyN56aYziQwNIi81Ztit8atmZ7B8XRn3r9nN3OzEYe1nT00z45Mi7f4Do5wvPy2GZ9cfoLunV38uPsCuPnpjzCpg1QnLftXn8WvAa/087xNg6ghrVE5yxvhRg280iNCgQJbNn8Qdr25lddEhlkwdM+R9lNS2MHNs/IhrUY6TlxrLse5e9h5uZfJoPXfi7fRPtRqxy2akkZ0cxQNv7R7y9Aqtx7qpqG/XoZUeJj/NMmWxjqf3DRr0asQCA4QfL5jM3sOtvP555eBP6GPvYetdpXTqA4+SlRhFeHCgXiHrIzTolUMszEvhtPRY/vJOCce67b/QZk+NLei1Re9JAgOEnDHRFOnIG5+gQa8cQkT4ycIpVDa08/ynB+1+XkmtZcTNOB1x43Hy02LZWdVEb6/9l7YYY6ht7mDzwXpWbq1i35FWJ1ao7OWoC6aUYk52ImdPGMXD75Vy5ekZRIYO/vYqqWnRETceKi/VMvLmYF0bmYmRgCXIj7Z2UlHfTnldGxX17VTUWz6X17dRWd/Ose4vztOMT4rk7WXn6RxGbqZBrxzqJwsnc9kjn7Dio33cdlH2oNuX1DYzPUNH3HiiPOuUxfesLEaE46He0fXlE+7xEcGkx0cwOSWaeTkppMeHkx4fTkV9O7/6ZzErt1Zy2Yz0/g6hXESDXjnUjLHxzM9NYfm6Mq45cxzxkSEDbtvW2U15XTvfmJUx4DbKfSalRJMWF87WigbS48OZmBTF+ZOSrEEeQUZCBGnx4UQN8J9bb6/hxc/KefDdUr42LVX/a3MjDXrlcHcsmMyiv6zjsQ/2cteSnAG321tr6b/VqQ88U0hQAB/97IJhX0wXECAsm5fN0uc28Y8tVVwxS1v17qJ/YpXDTR4dzWXT03j6k/0cauwYcDvb7Ig6mZnnGm7I28zPTSE/LYa/ri2hywNvYekvNOiVUyybP4leY/jr2pIBtympbSE4UMgcpSNufJWIsGzeJA4cbeONzUO7xkI5jga9coqMhAiunj2WlzeWc+Bo/0PsSmqaGZ8YpX23Pu7CKcmclh7Lg2tL6OzWVr076G+YcppbL5hIUKDw32/v6Xd9SW2LXijlB0SE2+dPoqK+nb9vrnB3OX5Jg145TXJMGDeck8XKrVXsrP7ypfTtnT2U17eRrf3zfuH8SUlMz4jjobWl2qp3Aw165VQ3nzuB6NAgHnjry7cc3Hu4BWN0xI2/EBF+NH8SlQ3tvFJYPvgTlENp0Cunio0I5vvnTeCdnbVsOlB3fLltxI1OZuY/5mYnUjAunoffK9Ubj7uYBr1yuhvOySQxKpQ/vrkbYyzzpthG3IzTETd+Q0RYNn8S1Y0dvLxRW/WupEGvnM52y8EN++pYV3IE+GLETbCOuPErZ08YxeysBB55X1v1rqS/Zcolrp49lvT4cO5fswtjDHtqWpio/fN+xzauvqbpGC9ssH+WUzUyGvTKJUKCAlg2bxJFlU288Xkl5fVtTNIRN37prAmjOGv8KB79YC/tndqqdwUNeuUyl1pvOXjPymKM0ZuN+LNl8ydxuPkYz2844O5S/IIGvXIZ2y0Hmzu6AR1a6c9mZyUwZ2Iij76/l7bObneX4/M06JVLLcxL4bSMOOuIm0h3l6PcaNn8bI62dvLcem3VO5sGvXIpEeEvV07noW/N1BE3fm7WuATOnZTE4+vKaD2mrXpn0t805XKZiZEszBvt7jKUB1g2L5u61k6eWb/f3aX4NA16pZTbzBgbz4VTklm+rozmji53l+OzNOiVUm51+7xsGtq6eOaT/e4uxWfZFfQiskhEdotIqYjc2c/6cSLyrohsE5H3RSS9z7rrRaTE+nG9I4tXSnm/aelxzMux3Ge4SVv1TjFo0ItIIPAwsBjIBa4WkdwTNvsT8KwxZhpwL3Cf9bkJwD3AGcBs4B4RiXdc+UopX3D7vGyaOrpZ8dE+d5fik+xp0c8GSo0xZcaYTuAl4JITtskF1lofv9dn/ULgbWNMnTGmHngbWDTyspVSviQ/LZaFeSk89dE+Gtu0Ve9o9gR9GtB3qrkK67K+tgKXWx9fBkSLyCg7n4uILBWRQhEpPHz4sL21K6V8yO3zJtHc0c1TH5W5u5wOKJMAABAfSURBVBSf46iTsXcA54nI58B5QCVg9yQWxpjlxpgCY0xBUlKSg0pSSnmTnDExLJk6mhUf76ehrdPd5fgUe4K+Esjo83W6ddlxxpgqY8zlxpgZwN3WZQ32PFcppWx+eNEkWju7eeJDbdU7kj1BvxHIFpEsEQkBrgJW9t1ARBJFxLavu4AV1sdrgAUiEm89CbvAukwppU4yeXQ0X5k6hqc/3k9dq7bqHWXQoDfGdAO3YgnoncArxphiEblXRC62bnY+sFtE9gApwO+sz60Dfovlj8VG4F7rMqWU6tft87Jp6+ph+Tpt1TuK2G7t5ikKCgpMYWGhu8tQSrnRD1/6nLd31LD+rouIDQ92dzleQUQ2GWMK+lunV8YqpTzO0nPH09bZw0uf6V2oHEGDXinlcfJSYzlr/Cie+WQ/XT297i7H62nQK6U80o1zsqhq7GB10SF3l+L1NOiVUh7pwinJZCVG8tRH+/C0c4neRoNeKeWRAgKE756TydbyBjYfrHd3OV5Ng14p5bG+Piud2PBgnvxQJzsbCQ16pZTHiggJ4ltnjGVN8SHK69rcXY7X0qBXSnm068/KJECEp/XGJMOmQa+U8mijY8P46rQxvLyxXG83OEwa9Eopj3fjnPG0HOvm5Y3lg2+sTqJBr5TyeFPTY5mdmcDfPt5Pt15ANWQa9Eopr3Dj3CwqG9p5a0eNu0vxOhr0SimvMC8nhbEJETyl95UdMg16pZRXCAwQbjgnk00H6vlcL6AaEg16pZTX+EZBBtFhQdqqHyINeqWU14gKDeLq2WNZXXSIyoZ2d5fjNTTolVJe5fqzMwF4Ri+gspsGvVLKq6TFhbM4fzQvfnaQlmPd7i7HK2jQK6W8zo1zsmju6ObVQr2Ayh4a9EoprzNjbDyzxsXzt4/309Orc9UPRoNeKeWVbpyTxcG6Nt7ZqRdQDUaDXinllRbkppAWF85TOlf9oDTolVJeKSgwgBvOyeSz/XVsq2hwdzkeTYNeKeW1rjw9g6hQvYBqMBr0SimvFR0WzDcLMvjPtmoONXa4uxyPpUGvlPJqN5yTSa8xPLN+v7tL8Vh2Bb2ILBKR3SJSKiJ39rN+rIi8JyKfi8g2EVliXZ4pIu0issX68ZijvwGllH/LSIhgYd5oXthwkLZOvYCqP4MGvYgEAg8Di4Fc4GoRyT1hs18ArxhjZgBXAY/0WbfXGDPd+nGzg+pWSqnjvjc3i8b2Lv6+qcLdpXgke1r0s4FSY0yZMaYTeAm45IRtDBBjfRwLVDmuRKWUOrWZY+M5LSOOFR/vp1cvoDqJPUGfBvS9zrjCuqyvXwPXiEgFsAq4rc+6LGuXzgciMre/A4jIUhEpFJHCw4cP21+9UkoBIsKNc7LYd6SVtbtq3V2Ox3HUydirgaeNMenAEuA5EQkAqoGx1i6dHwEviEjMiU82xiw3xhQYYwqSkpIcVJJSyp8szh9NamyYDrXshz1BXwlk9Pk63bqsrxuBVwCMMeuBMCDRGHPMGHPUunwTsBeYNNKilVLqRMGBAVx/dibry45SXNU45Od3dPVQ3djOwaNtTqjOvYLs2GYjkC0iWVgC/irgWydscxC4CHhaRHKwBP1hEUkC6owxPSIyHsgGyhxWvVJK9XHV7LH85d0SnvpwH/dcnEddayd1rceoa+360uejrZ3Ut3ZS19p5/HFrZ8/x/fxk4WRuuWCiG78Txxo06I0x3SJyK7AGCARWGGOKReReoNAYsxL4MfCEiCzDcmL2O8YYIyLnAveKSBfQC9xsjKlz2nejlPJrseGWC6ie/mQ/r39+YseDRWhQAKMiQ0iICiEhMpSsxEgSIkNJiAwmITKU93bX8t9v7+GMrAQKMhNc/B04hxjjWWeoCwoKTGFhobvLUEp5qaMtx3ju0wNEhQaREBlCfGSIJditHxEhp27fNnd0seTBD+nthVX/NZfYiGAXVT4yIrLJGFPQ7zoNeqWU+rIt5Q1c8egnzM9N4ZFvz0RE3F3SoE4V9DoFglJKnWB6Rhx3LJzM6qJDvPDZQXeXM2Ia9Eop1Y+lc8czNzuRe/+1gz01ze4uZ0Q06JVSqh8BAcID3zyN6LAgbn1hMx1dPYM/yUNp0Cul1ACSo8N44JvT2VPTwm//vcPd5QybBr1SSp3CeZOSWHrueJ7fcJA3i6rdXc6waNArpdQg7lgwmWnpsfz0tW1UNrS7u5wh06BXSqlBhAQF8OBVM+jpNfzwxc/p7ul1d0lDokGvlFJ2yEyM5HeXTaXwQD0Pri11dzlDokGvlFJ2unRGGpfPTOOhtSV8WnbU3eXYTYNeKaWG4LeX5DNuVCS3v7SF+tZOd5djFw16pZQagsjQIP569QyOth7jJ69tw9OmkemPBr1SSg1RflosP1s0hXd21vDs+gPuLmdQGvRKKTUMN87J4oLJSfxu1U52VDW5u5xT0qBXSqlhEBH+9I3TiA0P5rYXN9PW2e3ukgakQa+UUsM0KiqU/7lyOmVHWvnNSs+dIkGDXimlRuCciYn8n/Mm8HJhOf/aWuXucvqlQa+UUiO0bP4kZoyN4+evb6e8zvNuLq5Br5RSIxQcaJkiAYGbni2kqaPL3SV9iQa9Uko5QEZCBI98eyaltS3c8vxmujxoPhwNeqWUcpC52Un8v8un8mHJEe5+Y7vHXEx16tuhK6WUGpJvFmRQUdfGg2tLyYiP4LaLst1dkga9Uko52rL5kyivb+eBt/eQnhDOZTPS3VqPBr1SSjmYiPCHr0+jurGdn762jdEx4Zw1YZTb6tE+eqWUcoKQoAAev6aAcaMi+f5zhZTWNrutFruCXkQWichuESkVkTv7WT9WRN4Tkc9FZJuILOmz7i7r83aLyEJHFq+UUp4sNiKYv33ndEKCArl+xUZqmzvcUsegQS8igcDDwGIgF7haRHJP2OwXwCvGmBnAVcAj1ufmWr/OAxYBj1j3p5RSfiEjIYIV3ymgrrWTG58udMucOPa06GcDpcaYMmNMJ/AScMkJ2xggxvo4FrBdB3wJ8JIx5pgxZh9Qat2fUkr5jWnpcfz16hkUVzXyXy9+Tk+va4dd2hP0aUB5n68rrMv6+jVwjYhUAKuA24bwXERkqYgUikjh4cOH7SxdKaW8x7zcFH59cR7v7Kzl3n8Vu3SMvaNOxl4NPG2MSQeWAM+JiN37NsYsN8YUGGMKkpKSHFSSUkp5luvOyuSmuVk8s/4AT320z2XHtWd4ZSWQ0efrdOuyvm7E0gePMWa9iIQBiXY+Vyml/MZdi3OoqG/nd6t2khYXzuKpY5x+THta3RuBbBHJEpEQLCdXV56wzUHgIgARyQHCgMPW7a4SkVARyQKygc8cVbxSSnmbgADhz1dOZ0ZGHLe/vIVNB+qdf8zBNjDGdAO3AmuAnVhG1xSLyL0icrF1sx8DN4nIVuBF4DvGohh4BdgBvAncYozpccY3opRS3iIsOJAnritgdGwYNz1byP4jrU49nnjKpDs2BQUFprCw0N1lKKWU0+070srlj3xMXEQIf/8/Z5MQGTLsfYnIJmNMQX/r9MpYpZRyk6zESJ64roDKhnaWPltIR5dzOjw06JVSyo0KMhP48zenU3ignh+/upVeJ4yx10nNlFLKzb4ybQwV9VNo6+xBxPH716BXSikP8P3zJjht39p1o5RSPk6DXimlfJwGvVJK+TgNeqWU8nEa9Eop5eM06JVSysdp0CullI/ToFdKKR/ncZOaichh4MAIdpEIHHFQOY6kdQ2N1jU0WtfQ+GJd44wx/d65yeOCfqREpHCgGdzcSesaGq1raLSuofG3urTrRimlfJwGvVJK+ThfDPrl7i5gAFrX0GhdQ6N1DY1f1eVzffRKKaW+zBdb9EoppfrQoFdKKR/nlUEvIotEZLeIlIrInf2sDxWRl63rN4hIpgtqyhCR90Rkh4gUi8gP+9nmfBFpFJEt1o9fObuuPsfeLyLbrcc96e7rYvGg9TXbJiIzXVDT5D6vxRYRaRKR20/YxiWvmYisEJFaESnqsyxBRN4WkRLr5/gBnnu9dZsSEbneBXXdLyK7rD+nN0QkboDnnvJn7oS6fi0ilX1+VksGeO4pf3+dUNfLfWraLyJbBniuM1+vfvPBZe8xY4xXfQCBwF5gPBACbAVyT9jmB8Bj1sdXAS+7oK4xwEzr42hgTz91nQ/8202v234g8RTrlwCrAQHOBDa44ed6CMtFHy5/zYBzgZlAUZ9lfwTutD6+E/hDP89LAMqsn+Otj+OdXNcCIMj6+A/91WXPz9wJdf0auMOOn/Mpf38dXdcJ6x8AfuWG16vffHDVe8wbW/SzgVJjTJkxphN4CbjkhG0uAZ6xPn4NuEjEGXdi/IIxptoYs9n6uBnYCaQ585gOdgnwrLH4FIgTkTEuPP5FwF5jzEiuih42Y8w6oO6ExX3fR88Al/bz1IXA28aYOmNMPfA2sMiZdRlj3jLGdFu//BRId9TxRlKXnez5/XVKXdYM+CbwoqOOZ69T5INL3mPeGPRpQHmfrys4OVCPb2P9hWgERrmkOsDaVTQD2NDP6rNEZKuIrBaRPFfVBBjgLRHZJCJL+1lvz+vqTFcx8C+gu16zFGNMtfXxISCln23c/bp9F8t/Yv0Z7GfuDLdau5RWDNAN4c7Xay5QY4wpGWC9S16vE/LBJe8xbwx6jyYiUcDfgduNMU0nrN6MpWviNOCvwD9cWNocY8xMYDFwi4ic68Jjn5KIhAAXA6/2s9qdr9lxxvI/tEeNRRaRu4Fu4PkBNnH1z/xRYAIwHajG0k3iSa7m1K15p79ep8oHZ77HvDHoK4GMPl+nW5f1u42IBAGxwFFnFyYiwVh+iM8bY14/cb0xpskY02J9vAoIFpFEZ9dlPV6l9XMt8AaWf6H7sud1dZbFwGZjTM2JK9z5mgE1tu4r6+fafrZxy+smIt8Bvgp82xoQJ7HjZ+5QxpgaY0yPMaYXeGKA47nr9QoCLgdeHmgbZ79eA+SDS95j3hj0G4FsEcmytgSvAlaesM1KwHZm+gpg7UC/DI5i7f97CthpjPnvAbYZbTtXICKzsbz+rvgDFCki0bbHWE7mFZ2w2UrgOrE4E2js8y+lsw3Y0nLXa2bV9310PfDPfrZZAywQkXhrV8UC6zKnEZFFwE+Bi40xbQNsY8/P3NF19T2nc9kAx7Pn99cZ5gG7jDEV/a109ut1inxwzXvMGWeYnf2BZYTIHixn7++2LrsXyxsfIAxLN0Ap8Bkw3gU1zcHyb9c2YIv1YwlwM3CzdZtbgWIsIw0+Bc520es13nrMrdbj216zvrUJ8LD1Nd0OFLiotkgswR3bZ5nLXzMsf2iqgS4sfaA3Yjmv8y5QArwDJFi3LQCe7PPc71rfa6XADS6oqxRLn63tfWYbYZYKrDrVz9zJdT1nfe9swxJgY06sy/r1Sb+/zqzLuvxp23uqz7aufL0GygeXvMd0CgSllPJx3th1o5RSagg06JVSysdp0CullI/ToFdKKR+nQa+UUj5Og14ppXycBr1SSvm4/w/zIi+V7lKIKgAAAABJRU5ErkJggg==\n", 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wTcV8YFpBOlUNpzlY599xgiVbqkm1d+ArPaJrF0KNBoIA+OasQmpPtfC/fm4VvL/rKHN+u4KlW6p5YHYRr3x9+nn7L980MRdj4PXNh/xal97CsZDM6/UDu16HmEQYOQ+2vgRtZ3xTQS9NtdcT+LN7qLG5lQ9313DLpHwyEmO0RRCCNBAEwEWD05hRmMH/fOifVkFjcysP/nMLX/7LOvrHx/DaPZdy38zCs5uedzY0M5EJ+Sm8FibdQ2cXknkzPtDRDruWQuFsKP4yNDfA7jd9VEPvjMhOIjU+2q8b1SzbcYSW9g6uH59DYVYSe3Q1c8jRQBAg98+0WgWPLN7OugN1NLf6ZgH1yr3HmPu7j3hx/UHuvnIYi79xKWPzLrxo6qZJeWw/dILSMPhmV1LuWEjmxYyhg2vhVA2MugGGXgVJub2meygiQpgyxL/jBEu2VJOX2o/Jg1Ipyk6k7EijzhwKMRoIAqR4SBo3T8rjxfWVfO5Pqxj78Nvc+MTHPLJ4O4s2VXGwrsmtP67TLe08sng7t/95DTFREbz0tel8d+5IYqN6zqw6b3wukRESFq2Ckop6RmQnebe6e9cSiIyB4bMhIhIm3Apl70Jj75h9Na0gjfLaJr+M+xxvauWj0hquH5+DiFCYncSplnaqGk77/FoqeDT3QQD99l8n8tD1o9hY0cDGinpKKup5Yd1B/mJnKs1IjGXSoFQmD+rP5EGpjM9PpV/M+R/sG8rr+Y+XNrP/2Cm+NH0I35070mm57mQmxXLp8Axe23iIb80eQUSE7zbo6U06OgybDjYwb3yu5ycxBnYutloCccnWsYm3w8e/gS0vwqX3+aayXji7nmB/LfMnOt3Ow2Nvbz9Ma7th3vgcAIrsMafSIyfJ79/3s7gqiwaCAMtIjGX26Gxmj84GoK29g91HGimpaGBjeT0bDzawbMcRACIjhFE5SUwe1J9JdmB4eUMl//PhXnJS+vGPO6cxfXiGR/W4eVIu/++FzWyoqGfKkDSf/ft6kzJfLCQ7vBUaKuDyb396LKMQ8qfCpr/D9G+AD3e688To3GQSY6NYu7/O54Hg9S2HGJQWzzi7u7EoOxGA0qONXDUyy6fXUsGjgSDIoiIjGJObwpjclLPJw+pOtbCxop6NFQ2UVNTzzw2V56xO/tfigXx/3iiv8ubMGT2AftHbeG1jVcgGgpJyHywk2/k6SASMuO7c4xNvhyXfhEMlkHeRF7X0XmSEUDykv8/HCepOtbByby1fvXzo2am3qfExZCbFskenkIYUDQS9UFpCDDNHZTNzlNVqaO8w7DnSyKaDDQxOj2f6MM9aAZ0lxEYxZ0w2S7dW8/ANY4iJCr3hopKKeu8Xku1aAoOmQ0KX93zMzfDWg9agcZADAVjdQx/s3sWxk2fISIz1yTnf2naY9g7D9Xa3kENRdmJYTDQIJ6H31x+CrC6iZG6bOsgnQcDhpol5NDS18uEe9/eA7gs2VjR4t5Csdi8c3QGj5p3/XL9Ue03By9Aa/MV504Zarbp1PmwVLNlyiKEZCYzOST7neGFWEqVHT9LRoTOHQoUGgjB2WWEG6QkxvLYx9GYP+WQh2c7XrZ8jr3f+/KTPW2sK9gR/TcG4vBT6RUf6rHuopvEMq/fVMs+eLdRZYXYiTTpzKKRoIAhj0ZERzBufw7s7j4RcRlKfLCTbtQRyJkLqIOfPF1wByXm9Yk1BdGQEFw3uz2ofZSJ9c1s1HQbmTTh/xtXZmUNHtXsoVGggCHPzJ+WFZEbSkvJ6IrxZSHaiGirXOe8WcuhlawqmFqSx+0gjDU0tXp9ryZZqirITz37od1aUZR3TAePQoYEgzE0amBqSGUlLKuop8mYh2a4l1s+RN1y43ITbwXTA5uc9u44PTStIwxhYd6Deq/McOdHMugN1XD/O+fqLlPhospJiNedQCNFAEOY6ZyQ9ciL4g56+4FhI5nW3UHohZI64cLmM4TBwmtU9FOS0CxMGphITFeH1RjVLt1RjDMybkNNtmaLsJM1CGkI0EKizGUkXbwqNjKSfLiTzMBA01cH+j6xuIVdmHE28HY7thqoSz67nI3HRkUwcmMraA94NGC/ZcohROckMy0zstkxhdiJlOnMoZGggUCGXkfTsQjJPVxTveRtMu5VkzhVjboaoOGulcZBdXJDGtqrjNHo4+F/VcJqSioazKSW6U5SdxOlWnTkUKjQQKCC0MpKWVNTTPz6aAk8Xku1aYs0Gyp3sWvm4FCtobAv+moJpQ9PpMLC+3LNxgqVbrFZhz4HAai3oOEFo8CoQiEiaiCwTkVL7p9O2uIgssMuUisgC+1i8iCwVkV0isl1EHvOmLso7oZSRtKSigUmD+nu2kKzllDULaOT17uUQmvh5aD4Ou99w/5o+NGlQKlER4vFGNUu3VDMuL4XB6RcOosN15lBI8bZF8CCw3BhTCCy3H59DRNKAh4FpwFTg4U4B41fGmJHAJOBSEbnWy/ooDzkyki7adKhP9/seb2ql7OhJJnk6bbRsObQ1u94t5FBwOSTnB31NQXxMFOPzUzwaMK6obWJz5fEeWwMAKf2iyU6ODYkWpPI+EMwHFtr3FwI3OSlzDbDMGFNnjKkHlgFzjTFNxpj3AYwxLUAJkO9lfZQXbp6US2X9aTZUeDf9MJg2HvQy0dyuJdAvzcov5A7HmoK9y601CEE0bWg6WyqPu70b3pKtVrdQ19xC3SnKTmKPLioLCd4GgmxjjOO3/jCQ7aRMHnCw0+NK+9hZIpIK3IDVqnBKRO4SkfUisr6mJjRz4wSblZE0sk+nnCipaPB8IVlbC+x+C0ZcC5EerD+YaK8p2BLcNQVTC9Jo6zBsrGhw63VLNlczaVCqy/sMFGYl6cyhENFjIBCRd0Vkm5Pb/M7ljLW9ltu/ESISBfwf8LgxZl935YwxTxljio0xxZmZme5eRrmgc0bSlraOYFfHIxu9WUh24CM4c9z9biGH9GEw8OKgrykoHtyfCMGt7qF9NSfZUX3CrU18irITaW7t4GB9kyfVVL1Ij4HAGDPLGDPWyW0RcEREcgDsn0ednKIKGNjpcb59zOEpoNQY8zvP/xnKV/pyRtKODsOmCi8Wku1aAtEJ1m5knpp4OxzbA1UbPD+Hl5Liohmbl8JqNwaMl26xGvbXj3OtWwigMFsHjEOFt11Di4EF9v0FwCInZd4G5ohIf3uQeI59DBH5MZACfNPLeigf6csZSUuPnqTxjIcLyTo6YNdSKJwF0XGeV2LMzRDVL+hrCqYOSWPTwQaaW9tdKr9kSzVThvRnQIrr//ZCnUIaMrwNBI8Bs0WkFJhlP0ZEikXkaQBjTB3wI2CdfXvUGFMnIvnAQ8BooERENonInV7WR3mpc0ZSTxclBcvGCi8WklWug5NHYNSN3lUiLhlG3whb/xnUNQXThqbT0tbB5oM9jxOUHmlk95FGt/d2To6LJiclTmcOhQCvAoExptYYM9MYU2h3IdXZx9cbY+7sVO5ZY8xw+/acfazSGCPGmFHGmIn27Wnv/jnKF/pqRlKvFpLtXAwR0VA42/uKTLzdGmvYvdT7c3loypD+iODS/gSvb6kmQuDacQPcvk5htrVJjerbdGWxOo8jI2lfW1zm8UIyY6zxgaFXWquEvTUk+GsKUuNjGJGd1OPCMmMMS7YcYlpBOllJ7neJFWVZOYfadeZQn6aBQJ2nL2YkdSwk86hb6Mh2qD9w4b0H3BERARNvg73vwYngJfK7eGg6G8rraW3vfgbYzupG9tWcumCm0Qspyk7iTFsHB+t05lBfpoFAOdXXMpKeXUjmyUDxztcBgRHX+a5CE24L+j4FUwvSON3azpbK492WWbr1EJERwtwx7ncLAQzXAeOQoIFAOdXXMpJ6tZBs1xIYdAkkZvmuQunDrHMGcU3B1AJrQ/vuuoesbqFqpg9LJz0x1qNrFGZZgUDHCfo2DQSqW/Mn9p2MpBsr6hkxIJkEdxeS1e2DI9t81y3U2cTbobYUKtf7/twuyEiMZXhWImv2O19Ytq3qBOW1TS7lFupOUlw0uSlx2iLo4zQQqG7dMKFvZCQ9u5DMk/GBnY4tKf0QCMbcDNHxQV1TMLUgjfUH6mlzMk6wZMshoiKEazzsFnIozE7SRWV9nAYC1a2+kpHUq4Vku5bAgPHQf7DvKxabZK1L2PYKtPpgA5fm43DKvayi0wrSOHmmjZ3V535jd3QLzSjMIDU+xqtqFWUnsrdGZw71ZRoI1AX1hYykJXbdJrnbImg8DAfXep5byBWONQW7vFhTcHgbLL4PfjUCnp3j1kunFaQDnNc9tPFgA1UNp7nezUVkzhRmJ9HS1kF57Smvz6WCQwOBuqC+kJG0pNzDhWS7lgLGP91CDkNmQMpA99cUtLfB9tfguevgT5fClhchfTjUlsGpYy6fZkBKHIPT41m979wB46VbqomJjGDOGGcJg91TpDmH+jwNBOqCfJGR1BhD2dGTPPvxft7dccTHNbRaBB4tJNu1BNKGQdYon9fprIgIayrp3vfguAvB9GQNrPgl/H48vLQAjh+E2Y/CAztg7s+sMtWb3arCtII01h2oO9u919FhWLqlmsuLMkmOi3b3X3Qex8yhMt2boM/SQKB65ElG0pNn2nhn+2EeenUrM37xPrN+8yGPLtnB1/9RwoFjvutCaGhqYW/NKfcHik/Xw/4V1mwhT7a0dMfE2wBz4X0KqjbAK1+F346G934MGYVw6//BfZvg0vshPg0GjLPKuh0I0jl+upXd9syeDRX1HD7RzA0eLiLrKiE2irzUftoi6MM8SNquws1lhRmkJcTw2qYqZo923pVgjGHX4UY+2F3Dh3uOWjNVOgwJMZFMH57B164YxpjcZL74zFp+sGgbf/3KVM/2FO5io51Uze2B4j3vQEeb90nmXJE21NrxbNM/4LIHPg08bWes7p+1T0HVeohJhMkLYOq/Q+aI88/TLxX6D3E7EDjWE6zZV8uonGSWbD5EbFQEM0d53y3kUJSdqFNI+zANBKpH0ZER3DA+h+fXHaSxuZUkuzvheFMrH5XV8OHuGj7cU8PRxjMAjByQxJ0zhnJFUSYXDe5PTNSnDc9vzx3BDxdtZ/HmQ8yfmOf0eu7YWF7v2UKyXa9DUg7kTva6Di6Z9HlYdI+V5TQlH9Y/Bxueg1M1Vt//tb+wupDiki98npwJbgeCgWnx5KX2Y+2BOr5wyRDe2HaYq0dmebZ5TzcKs5P4pKyWtvYOoiK1o6Gv0UCgXDJ/Uh4LV5Xz1Ip9REdG8OGeGjZW1NNhIDkuihlFmVxh37KTu09e9vlpg/nnhkp+tGQHVxZlkRLvXR/1xoMN7i8ka2mC0netD+eIAH1ojZ4Pb3wbXr4DGg9BRzsUXQNT77I2wnG1HjkTYMciON1gtRBcNLUgjY9Ka1izv5aaxjMu70vsqsKsRFraOyiva2JYZqJPz638TwOBcokjI+kf3itDBMbnpXDvVcO5YkQWE/JTXP4WGBkh/OTmcdz4xMf8/O1d/PTmcR7XybGQ7MaJbk6B3PsetJ3277TRrmKTrKmkW1+CaV+DKXdYXUbuyplg/Ty8FQpmuPyyaQVpvLqxiseXl9IvOpKrR/ownQafzhwqPdKogaAP0kCgXCIiPHn7ZPbWnOSy4Rke56YBGJuXwlcuLeDpj/fzmcn5XOTh1pIeLyTbtQTiUmHwpR5d12PX/Qqu/aV3rZABdiCo3uxeIBhqrSdYva+OeeNziI/x4E+/tRlam6yB6y6GZzmSz51k7lj3T62CSzvzlMvG5qUwf2KeV0HA4f/NLiI3JY6HXt16wTTJF+JYSObWHsXtrbD7DRhxLUR6P3XSLSLed0UlZkJyntvjBEPS48lMsv7f3N2J7Kzlj8KfZjhNopcQG0V+/346YNxHaSBQQZEQG8UjN45h1+FGnvl4v0fnKCmvJy0hhiHp8a6/6MDHVqqGQHYL+ZoHA8YiwvRh6STFRnHliEzPrrt/BZyotBL1OVGUnUSpTiHtkzQQqKCZM2YAs0dn87t393i0sUlJRT2TBqa6Nw115+tWIrhhV7t9vV4jZwIc2wMt7q3H+MG80bx893TioiPdv+aZk3B0u3W/m2yqhdmJ7Dt20uMWngoeDQQqqP7rxjFEiPDDRZ7rlckAACAASURBVNswbuTtP7uQzJ1uoY4OK63E8FkQ3c+D2vYSORMAY+UgckNGYiwjBiR5ds1DG62NdsCaAutEUVYSre2G8lrdrayv0UCggio3tR8PzC7i/d01vLntsMuvcywkcyvRXNUGOHm4b3cLwaczh9zsHvJK5Vrr54Bxn97vovPMIdW3aCBQQfel6UMYnZPMf72+ncbmVpdec3YhWb4bgWDnYoiIgkL3Mnj2Okk5kJAZ4ECw3lr4VniN1RJpOf9b//CsREQ0+VxfpIFABV1UZAQ/vWUcRxvP8Ot39rj0mpIKDxaS7fvA2j7SjYVYvZKIRwPGHjPG6g7Kn2LdTDtUbzqvWL+YSGvmkCaf63O8CgQikiYiy0Sk1P7ptMNWRBbYZUpFZIGT5xeLiHsdniqkTByYyhcuHszCVQfYbHf7dKe9w7DpoJs7kjWfsLakDPTaAX/JmQA1O625/f7WUG6lwsgvtm5wwXEC7Rrqe7xtETwILDfGFALL7cfnEJE04GFgGjAVeLhzwBCRWwBtSyr+45oRZCbG8p+vbnW6taJD6dFGTrq7kKxyrTXYOehiH9S0F8iZYCXNO7rD/9dyzBLKnwIJGdC/oNtAUJidxP5jp3TmUB/jbSCYDyy07y8EbnJS5hpgmTGmzhhTDywD5gKISCLwAPBjL+uhQkByXDQP3zCG7YdOsHBVebflSsrtjKPuzBgqXwUSaX2YhYJADhhXrrOm3GaNsR7nT4GD65wuLCvKTqS13fg01bjyP28DQbYxptq+fxhwltc2DzjY6XGlfQzgR8CvgR7nm4nIXSKyXkTW19S4nhdf9S3XjRvAlSMy+c07u6k+7nyf35IKDxaSVayyPjxjQyQPTupgiEsJXCDInQyR9nhM/hRr9tWJ8zfa0d3K+qYeA4GIvCsi25zc5ncuZ6xJ4C5PBBeRicAwY8yrrpQ3xjxljCk2xhRnZnq4MlL1eiLCj+aPpd0YHlm83WkZtxeStZ2xpo4OusSHNQ0yERgwHg5v8e91WpuhesunYwMAA+1WlZPuoWGZjplDOk7Ql/QYCIwxs4wxY53cFgFHRCQHwP551MkpqoCBnR7n28cuAYpF5ADwMVAkIh94989RoWBgWjz3zyzi7e1HWNZla8uGphb2ubuQ7NAmaGuGwSEUCMBq4RzeZuVP8pfDW6Cj9dwuteyxEBXndIVxv5hIBqXFU6ozh/oUb7uGFgOOWUALgEVOyrwNzBGR/vYg8RzgbWPMH40xucaYIcBlwB5jzJVe1keFiDtnFDAiO4mHF23j1Jm2s8c9WkhWsdL6GUotAoCcidB+xko34S+Ob/2dWwSR0ZA7CQ46X1hWmKU5h/oabwPBY8BsESkFZtmPEZFiEXkawBhThzUWsM6+PWofU6pb0ZER/PSWsRw63szv3v30g86jhWTlqyC90JrxEkoCMWB8cC2kDIKkAecezy+2rtt25ryXFGUnsv/YKVradOZQX+FVIDDG1BpjZhpjCu0upDr7+HpjzJ2dyj1rjBlu355zcp4DxhjNYq7OcdHgNG6bOpBnPznA9kPHAWsh2Uh3FpJ1dMDB1aHXLQSQPgyiE/wbCCrXn9sacMifYrVGnOQ7KspOoq3DcKBWZw71FbqyWPVq3507kv7x0fznq9tobe+wFpINdqM1ULPTSjs9aLr/KhksEZFW7h9/BYITh6y0086m3OZ3P2D86SY1Ok7QV2ggUL1aanwM379+NJsPNvDI4u3uLyQrt8cHQrFFAHaqiS1Wy8fXOi8k6yo519ogp5tAEKE5h/oUDQSq15s/MZfLhmfw9zUVAO4FgorVVpK21MF+ql2Q5UyA1lNQt9f3565cB5ExkDPe+fP5xU4DQVy0PXNIWwR9hgYC1euJCD+6aSwxURGkJcQw2NWFZMZYC8kGXWLNuw9F/hwwrlxvnT+qm61J86dYeYhOnj9rvDA7SbuG+hANBKpPKMhI4BefGc+3rxnh+kKyhgpr9evgEBwfcMgcAZGxTrOBeqW91dqM5kIpOfKnWj+drCcoyk7kQG0TZ9rafVsv5RcaCFSfcdOkPG6bOsj1F1Sstn6GSqI5ZyKjIXuM71sER7ZD22nnM4YccsZDRLTT7qGi7CTaOwz7NedQn6CBQIWuipUQmwJZo4NdE/9y7E3gxlafPTq7kOwCLYLofvaOZecHgsIszTnUl2ggUKGrfBUMmmZNswxlOROsKbIN3WdsdVvlekjMhpSBFy6XPwWqSqC97ZzDQzMTiBAo03GCPkEDgQpNp2rh2O7Q7hZy8MeAceVa60O+p/GY/CnWrKWaneccjouOZEh6grYI+ggNBCo0HXSMD4TwQLFD1mhrL2ZfBYJTtVC378LjAw4X2LGsMDtRt63sIzQQqNBUvtKaTZM3Odg18b/oOMgc6btAUHWBhWRd9R8C8RlOZw4VZiVRrjOH+gQNBCo0VayCvIu6nwMfanImWOm2fTFgXLnO2s0td1LPZUWsgNFNi6C9w7CvRmcO9XYaCFToaTllfTsOh/EBh5wJ0HQMGqt7LtuTynXWlNSYBNfK5xdbqbBP159z+NPdyrR7qLfTQKBCT+V6a2P3UF5I1pWvBow72qFyg3t7OzvKVm045/DQzAQiI0T3JugDNBCo0FOxChAYODXYNQmc7LGAeB8Iju2Blkb3AkHeZJCI88YJYqMiGZwery2CPkADgQo9FausD8a4lGDXJHBiEyGj0PtA4MpCsvOunWTNXHKyY1lRVhKlR7VF0NtpIFChpb0NDq4L3bTTF+JYYeyNynUQl2pteuOO/GJrtlGXdNhF2YmU156iuVVnDvVmGghUaDm82VrgFGr7E7siZ4KVZO/UMc/PcXCdawvJusqfYq1uri0753BhdhIdBp051MtpIFCh5WyiuTANBOB5q6D5ONTscq9byKGbHcscM4dKdWFZr6aBQIWW8pXWIqfknGDXJPAG2BvIeBoIqkoAAwM9CATphVaCvy6BYEhGPJERogPGvZwGAhU6jLFaBOGQVsKZfqlWEPQ0EFSuB8RaiOeuiAjIv8jpzKEh6fGac6iX00DgjpNHz1s0o3qR2jJrUVU4DhQ7eDNgXLnO2ujG09lW+VPg6HY4c+6HflF2km5b2ctpIHBVexs8PQue/3ywa6K649ioPhzHBxxyJkD9fjjd4N7rjLECgSuJ5rqTPwVMh7WzWSeF2UmU1zXpzKFezKtAICJpIrJMRErtn053FReRBXaZUhFZ0Ol4jIg8JSJ7RGSXiHzGm/r41Y7XrHzv5Z9YMytU71OxChIyIX14sGsSPI4B48Nb3Xtd3T44XefZQLGDo0vpvAHjRIyBMl1P0Gt52yJ4EFhujCkEltuPzyEiacDDwDRgKvBwp4DxEHDUGFMEjAY+9LI+/mEMfPJ7SBtmzbFe+ftg10g5U77Syi8UqhvVu2KAhzOHKt3IONqd+DRr0FhnDvU53gaC+cBC+/5C4CYnZa4Blhlj6owx9cAyYK793FeAnwEYYzqMMV5MgPaj/Svg8Ba49H6YcgfsXAK1e4NdK9XZiUNWiy2cu4UAEjMhOc+DQLAOYhKtdNbecGQi7ZQFdUh6AlERogPGvZi3gSDbGONId3gYyHZSJg842OlxJZAnIqn24x+JSImIvCQizl4PgIjcJSLrRWR9TU2Nl9V208rHISELxv8rTL3L2jB81ZOBrYO6sIpV1s9wDwTg2YBx5TorZ5C323rmF8OpmnO2zYyJiqAgI0EHjHuxHgOBiLwrItuc3OZ3LmeMMYA7ydCjgHxgpTFmMrAK+FV3hY0xTxljio0xxZmZmW5cxktHtkPZuzDtLmsDkKQBVkDY9HfvVnAq3ypfBdEJn86lD2cDxtvJ41xczdvSBEe2edct5HB2Ydm500iLsjXnUG/WYyAwxswyxox1clsEHBGRHAD751Enp6gCOu+AnW8fqwWagFfs4y8BvW87qZV/sD5giu/49Nj0b0BbM6z9c/Dqpc5VsdpaCBUZFeyaBF/OBMDA4W2ula/eZKXtzvdBttas0RAdf944QWF2IhV1TZxu0ZlDvZG3XUOLAccsoAXAIidl3gbmiEh/e5B4DvC23YJ4HbjSLjcT2OFlfXzreBVsfQkmf8EaCHPIHAFFc2Hdn61vUyq4TjdY32jDdSFZV+6mmjibcdSLqaMOkVGQO/n8QJCVhDGwt0ZbBb2Rt4HgMWC2iJQCs+zHiEixiDwNYIypA34ErLNvj9rHAL4LPCIiW4AvAN/ysj6+teZP1rzoi+8+/7np90FTLWz+R+Drpc51cC1gwnshWWfJudY+wu4Egv4FkJDhm+vnF0P1FmhtPnuoKDsR0N3Keiuv2tHGmFqsb/Jdj68H7uz0+FngWSflyoHLvamD3zSfgA1/gdE3Wcv2uxo83Zo3vfIJuOjL3g+yKc9VrIKIKMjzwTfaUCDi+oCxMda6mAIf/hnmT4GOVmumnb050JCMBKIjXZ85ZIyh9lQLhxpOc6ihmUMNp6k+fpqMxFi+eoWbKbJVj7RDtTslC+HMCWs8wBkRq1Xw0gLYtRRG3xjY+qlPVayCnIkQEx/smvQeOROs2W6tzdYkh+6cqIKTh30zUOzQOROpHQiiI8+dOXTqTBvVx09T5fiQb7DuVx8/bX34H2+mpe3cvQ2iIoS2DsPYvBQuHe6j1osCNBA4194Kq/8IQ2ZYU+q6M+oGq7Ww8nHrfjgvZAqW1mZrr9xpXw12TXqXnAnWAPDRHRf+Hfbl+IBDUjakDrK67C655+zhwuwklm0/woT/eofjp1vPeUmEQHZyHDkpcYzNS+GaMQPISYkjN7Xf2Vt8TCQzf/0hP3tzJ4vvuYyICP178xUNBM5s+6f1TWne7y5cLiISLrkX3vgPa9aK9lEH3qGN0N6iA8VddR4wvmAgWA9Rcfaexz6UPwUq1pxz6LYpg2hp62BAchw5qXHk2R/wOSlxZCfHER3Z85Dlt68ZwTdf2MTrWw4xf2Keb+scxjQQdGUMfPI4ZI6Cwtk9l5/4eXj/p9Y0Uw0EgVfhSDR3cXDr0dv0H2LtD9DTOEHlOqtbLSrGt9fPn2J/oTpkDV4DlxVmcFmhd106N07I5c8f7eMXb+1m7tgBxEbp2JwvaPbRrva+Z6XSnf4N17p6YuJhyp2w+w04Vur/+qlzla+y0iJ0nt6r7AHj8RcOBG0tcGiTZxvR9KSbhWXeiogQvnftKKoaTvO3VeU9v0C5RANBVysfh8QBMO6zrr9m6l0QFWu1ClTgdLRb/dCaVsK5nAnWyvj2VufPH94K7Wd8O1DsMGAcRMact57AFy4rzODyokz+8F4Zx5u6+bcpt2gg6Kx6M+z7AC7+mvXB7qrETJhwG2x+3tq8RgXG0R1w5rgGgu7kTLQ+6Gt2O3/+7ECxHwJBVKwViHzcInB4cO5ITjS38t8flvnl/OFGA0FnK5+wMjBe9GX3X3vJvdag5dqnfF8v5Vy5nWhOx2acO7s3wRbnz1euszKV2n34Ppc/xR7M9/239tG5ydwyKZ/nPjlAVcNpn58/3GggcGg4aA1uXfQla+9Xd2UMh5HXw7qnXU/2pbxTsRKS862piup86cOsPFndjRN4uyNZT/KLoe201T3lBw/MKQLg1+900+JRLtNA4LD6j9bPaV/z/BzT77P2NN74v76pk+re2Y3qdbZQtyIirb56Z4Hg5FErVbQ/uoUcOi8s84O81H58+dIhvLqxih2HTvjlGuFCAwFYSctKFsLYz0DqwJ7Ld2fQNBg4zdqroL3Nd/VT56s/AI3V2i3Uk5wJVt6fjnNX6fpkR7KepAyExGy/BQKAr185nJR+0Tz21i6/XSMcaCAA2PActJzsPp2EO6Z/w/qmtXOx9+dS3Tu7EY0uJLugnPHQegrquuyoV7nOys/kGEfwB5FPdyzzk5R+0dx71XBW7Knho9IAb1gVQjQQtJ2B1X+CoVdafzTeGnGdtbfxysfP2a5P+VjFKmv/aG+3Vgx13aWkrlxndRtF9/Pv9fOnQN0+OFXrt0t84ZLB5Pfvx2Nv7qKjQ//mPKGBYOtLVtKt6ff55nwRkTD9Xmu2RPknvjmnOl/5Kmt8IEJ/hS8oc6Q1n79606fHOtqhqsQ3G9H0xNH1VOWfaaQAsVGRfPuaEWw/dILFmw/57TqhLLz/ioyxFoFlj4NhV/vuvBNus/LBf/K4786pPnWyBmpLdf2AKyKjIXvMuS2Cozus7iJ/jg845E4EifRr9xDADeNzGZuXzC/f3k1zq+6C5q7wDgSly6Bml+vpJFwV3c9abVz6NhzVQSyfO7ja+jlYxwdc4tibwNFV6Y+Mo92JSbACkZ8DQUSE8J+aesJj4R0IVj5uLagZe4vvzz3lTojqp2kn/KF8lZUxM2disGvSN+RMgObj1iQGsGYMxWc433DJH/KnQOUGq0vKj6YPz+DKEZk88b6mnnBX+AaCqhI48JG1DWVktO/Pn5AOk/4NtrwAjYd9f/5wVrHS2o3M1xkzQ1XXAePKddaHc6D2z8ifAi2NcGyP3y/1XUfqiQ809YQ7wjcQrPwDxCbD5AX+u8YlXwfTbu19rHzjzElrXryuH3Bd1hirn756s7Xg8diewHQLOfh5YVlno3KS+czkfJ5beYDK+ia/Xy9UhGcgqD8AO16z0knEJfvvOmlDrZ3L1j0LZ3TTbp+oXGcFV11R7LroOMgaZQWCqg3WsUAMFDukD7Om+h5cG5DLPTC7CAF+847/WyChIjwDwar/tr4hXXy3/681/T4rQ2bJ3/x/rXBQsQokIjBTH0NJzgRr74GD66z370K7lvna2YVl/ptC2lluaj++clkBr26qYvuh4wG5Zl8XfoGgqQ42/g3Gfc5/WRc7yy+2Vr+u/m+/ZGEMO+UrrYVQ/mzJhaKcCdB0DHa+DlmjITYpsNcfONWaodccmA/mu68cRmq/aB57U2ftuSL8AsH6Z6C1yTfpJFx16X1w/CBsfy1w1wxF7a3Wt0pNK+E+x4Dx0e2BHR9wyC8GjDVJIwCS46K59+pCPio9xoo9mnqiJ14FAhFJE5FlIlJq/+zfTbkFdplSEVnQ6fhtIrJVRLaIyFsi4t2Gpj1pbYY1T8HwWZA92q+XOkfhNZBRpGknvFW92UprrOMD7sseC9izhAI5PuCQd5F1/QB1DwH828WDGJjWj59p6okeebt5/YPAcmPMYyLyoP34u50LiEga8DBgfyVgg4gsBhqB3wOjjTHHROQXwL3AI17WqXtbXoBTR32XTsJVERHWxjWv32clo8sNYP9sKCl9x/qpC8ncF5sIGYX2jKEgBIK4FMgcAeUfQ8OtAblkLPDDGck8vGg7b6+M5dqxOQG5rt+l5Pt86q+3gWA+cKV9fyHwAV0CAXANsMwYUwcgIsuAucDLWF9REkSkFkgG/Df5t6PDmjKaMwEKLvfbZbo1/l/h/Z/Ai18M/LVDSfpwSMwKdi36ptzJcKoG0guDc/2BU6Hkr/C7sQG75Gxgdhzwrn0LBQ8dsWaC+ZC3gSDbGFNt3z8MZDspkwcc7PS4EsgzxrSKyN3AVuAUUArc092FROQu4C6AQYM82JFKBK77pZV6N1ALaTqLjoN/e8VKRqc8F8jZLqFm9qNWQsRgJeq76vvWfh0B7h4tqznJ/6zYx7xxA7iiKAS+RER4+7F9vh7PKCLvAgOcPPVQ5wfGGCMiLv8Pi0g0cDcwCdgH/AH4HvBjZ+WNMU8BTwEUFxe7/5skAsOucvtlPjVgrHVTKhiSsq1bMK8/6d8CftnhwLFDa/nGrnpW3HgVqfG6Ir2rHr8aGGNmGWPGOrktAo6ISA6A/fOok1NUAZ23/cq3j020z7/XGGOAFwHt/FVK+dyD147i5Jk2nnxfU084420bcTHgmAW0AFjkpMzbwBwR6W/PKppjH6sCRotIpl1uNrDTy/oopdR5RgxI4rMX5fOXlQcoPaKr/LvyNhA8BswWkVJglv0YESkWkacB7EHiHwHr7Nujxpg6Y8wh4L+AFSKyBauF8FMv66OUUk59d+5IkuKi+fbLW2jX6aTnENMH57UXFxeb9esDNx9ZKRUaFm2q4v7nN/H960dx54yhwa5OwInIBmPMeSsKw29lsVIqbN04IZdZo7L41Tu7OXDsVLCr02toIFBKhQ0R4cc3jSM6IoIHX9miK45tGgiUUmFlQEoc3583itX76vi/dRXBrk6voIFAKRV2/qV4IJcNz+Bnb+ziUMPpYFcn6DQQKKXCjojws1vG0d5h+M9Xt9IXJ834kgYCpVRYGpgWz3fmjuCD3TW8urEq2NUJKg0ESqmwteCSIVw0uD+PLtlBTeOZYFcnaDQQKKXCVkSE8PPPjKeppZ2HF28LdnWCRgOBUiqsDc9K5JuzCnlj62He3Frd8wtCkAYCpVTYu2vGUMbmJfODRdtpaGoJdnUCTgOBUirsRUVG8IvPTKChqYVHl+wIdnUCTgOBUkoBo3OTufvKYbxSUsX7u51l1A9dGgiUUsp279XDKcxK5KFXttLY3Brs6gSMBgKllLLFRkXyi8+O5/CJZh57c1ewqxMwGgiUUqqTSYP685VLC/j7mgpW7a0NdnUCQgOBUkp18a05IxicHs+Dr2zhdEt7sKvjdxoIlFKqi34xkTx2y3jKa5v4zbLdwa6O32kgUEopJy4Zls7t0wbxzMf72VhRH+zq+JUGAqWU6sb3rh1JdnIc33l5C2faQreLSAOBUkp1Iykump/ePI7Soyd58r2yYFfHb6KCXQGllOrNrhqZxS2T8vjvD/Yyd2wOo3OTnZbr6DCcaeugubWd5rZ2mlvt+63W/TNt7aQnxDIuPyXA/4KeaSBQSqke/GDeaFaU1rDgubVkJ8dyprXjnA/7M60dtLR3uHSu26cN4gfXj6ZfTKSfa+06DQRKKdWD/gkxPH7bJP74wV6iIoS46Ej7FkFsVCSx0RHERX167OxP+1hsVASx0ZG8s/0w/7NiH2v21fL4bZMYk9s7WgfizRZtIpIGvAAMAQ4A/2KMOW94XUTeAi4GPjbGzOt0vAB4HkgHNgBfMMb0mPqvuLjYrF+/3uN6K6VUsHxSdowHXtxE/alWvjN3BF+5tICICAnItUVkgzGmuOtxbweLHwSWG2MKgeX2Y2d+CXzByfGfA781xgwH6oE7vKyPUkr1apcOz+Ct+y/nyhGZ/HjpThY8t5ajJ5qDWidvA8F8YKF9fyFwk7NCxpjlQGPnYyIiwNXAyz29XimlQkn/hBj+5wsX8ZObx7LuQB1zf/8Ry3ceCVp9vA0E2cYYx5Y+h4FsN16bDjQYY9rsx5VAXneFReQuEVkvIutramo8q61SSvUSIsLnpw1myTcuY0ByHHcsXM8PF22juTXw6xV6DAQi8q6IbHNym9+5nLEGGzwfcOiBMeYpY0yxMaY4MzPTX5dRSqmAGp6VxKv3TOfOywr466pybnziY3ZWnwhoHXoMBMaYWcaYsU5ui4AjIpIDYP90ZzeHWiBVRBwzl/KBKnf/AUop1dfFRkXy/Xmj+etXplLf1Mr8Jz/h2Y/3481kHnd42zW0GFhg318ALHL1hXYL4n3gs568XimlQs3lRZm8df8MZgzP4NElO/jSc+uoaTzj9+t6GwgeA2aLSCkwy36MiBSLyNOOQiLyEfASMFNEKkXkGvup7wIPiEgZ1pjBM17WRyml+rT0xFieXlDMj+aPYfW+Wq79/Qre3+XfrTO9WkcQLLqOQCkVDvYcaeS+/9vIrsONfGn6EB68diRx0Z6vSPbXOgKllFJ+UpSdxGv3XMqXLx3CX1Ye4KYnP+GIH9YcaIoJpZTqxeKiI3n4hjFcXpTJ82srSE+I8fk1NBAopVQfcNWILK4akeWXc2vXkFJKhTkNBEopFeY0ECilVJjTQKCUUmFOA4FSSoU5DQRKKRXmNBAopVSY00CglFJhrk/mGhKRGqDcw5dnAMd8WB1f0/p5R+vnHa2fd3p7/QYbY87b0KVPBgJviMh6Z0mXegutn3e0ft7R+nmnt9evO9o1pJRSYU4DgVJKhblwDARPBbsCPdD6eUfr5x2tn3d6e/2cCrsxAqWUUucKxxaBUkqpTjQQKKVUmAvZQCAic0Vkt4iUiciDTp6PFZEX7OfXiMiQANZtoIi8LyI7RGS7iNzvpMyVInJcRDbZtx8Gqn729Q+IyFb72udtEC2Wx+33b4uITA5g3UZ0el82icgJEflmlzIBff9E5FkROSoi2zodSxORZSJSav/s381rF9hlSkVkQQDr90sR2WX//70qIqndvPaCvwt+rN8jIlLV6f/wum5ee8G/dT/W74VOdTsgIpu6ea3f3z+vGWNC7gZEAnuBoUAMsBkY3aXM14E/2fdvBV4IYP1ygMn2/SRgj5P6XQksCeJ7eADIuMDz1wFvAgJcDKwJ4v/1YayFMkF7/4DLgcnAtk7HfgE8aN9/EPi5k9elAfvsn/3t+/0DVL85QJR9/+fO6ufK74If6/cI8B8u/P9f8G/dX/Xr8vyvgR8G6/3z9haqLYKpQJkxZp8xpgV4Hpjfpcx8YKF9/2VgpohIICpnjKk2xpTY9xuBnUBeIK7tQ/OBvxrLaiBVRHKCUI+ZwF5jjKcrzX3CGLMCqOtyuPPv2ELgJicvvQZYZoypM8bUA8uAuYGonzHmHWNMm/1wNZDv6+u6qpv3zxWu/K177UL1sz83/gX4P19fN1BCNRDkAQc7Pa7k/A/as2XsP4bjQHpAateJ3SU1CVjj5OlLRGSziLwpImMCWjEwwDsiskFE7nLyvCvvcSDcSvd/gMF8/wCyjTHV9v3DQLaTMr3lffwKVgvPmZ5+F/zpXrvr6tluutZ6w/s3AzhijCnt5vlgvn8uCdVA0CeISCLwT+CbxpgTXZ4uwerumAD8AXgtwNW7zBgzGbgWuEdELg/w9XskIjHAjcBLTp4O9vt3DmP1EfTKudoi8hDQBvy9myLB+l34IzAMmAhUY3W/9Ea3ceHWQK//WwrVQFAF6iQsBgAAAg5JREFUDOz0ON8+5rSMiEQBKUBtQGpnXTMaKwj83RjzStfnjTEnjDEn7ftvANEikhGo+hljquyfR4FXsZrgnbnyHvvbtUCJMeZI1yeC/f7Zjji6y+yfR52UCer7KCJfAuYBn7eD1Xlc+F3wC2PMEWNMuzGmA/hzN9cN9vsXBdwCvNBdmWC9f+4I1UCwDigUkQL7W+OtwOIuZRYDjhkanwXe6+4PwdfsPsVngJ3GmN90U2aAY8xCRKZi/V8FJFCJSIKIJDnuYw0qbutSbDHwRXv20MXA8U7dIIHS7TexYL5/nXT+HVsALHJS5m1gjoj0t7s+5tjH/E5E5gLfAW40xjR1U8aV3wV/1a/zmNPN3VzXlb91f5oF7DLGVDp7Mpjvn1uCPVrtrxvWrJY9WDMKHrKPPYr1Sw8Qh9WlUAasBYYGsG6XYXUTbAE22bfrgK8BX7PL3Atsx5oFsRqYHsD6DbWvu9mug+P961w/AZ6039+tQHGA/38TsD7YUzodC9r7hxWQqoFWrH7qO7DGnJYDpcC7QJpdthh4utNrv2L/HpYBXw5g/cqw+tcdv4OOWXS5wBsX+l0IUP3+Zv9ubcH6cM/pWj/78Xl/64Gon338L47fuU5lA/7+eXvTFBNKKRXmQrVrSCmllIs0ECilVJjTQKCUUmFOA4FSSoU5DQRKKRXmNBAopVSY00CglFJh7v8D8fZtlCGpAvgAAAAASUVORK5CYII=\n", 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\n", 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\n", 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" } } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "for i in range(10):\n", " model_hedge.fit(x=xtrain,y=ytrain, epochs=1,verbose=True)\n", " helper = model_hedge.predict(xtest)\n", " for j in range(2*N):\n", " pricetrajectory = np.exp(np.cumsum(np.array([0]+[xtest[2+k][0][0] for k in range(N)])))\n", " hedgetrajectory = [helper[0,2*k] for k in range(N)]\n", " payofftrajectory = [helper[0,2*k+1] for k in range(N)]\n", " plt.plot(pricetrajectory)\n", " plt.show()\n", " plt.plot(hedgetrajectory)\n", " plt.plot(payofftrajectory)\n", " plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "pT0uyCPBH6hM" }, "source": [ "This provides us with a precise view on hedging and the machine learning way to construct hedging strategies." ] }, { "cell_type": "markdown", "metadata": { "id": "9y5a4oJnH6hN" }, "source": [ "# Fixed income markets -- basic notions" ] }, { "cell_type": "markdown", "metadata": { "id": "sC_7FtwjH6hN" }, "source": [ "Prices of zero-coupon bonds (ZCB) with maturity $ T $ are denoted by $P(t,T)$. Interest rates are governed by a market of (default free) zero-coupon bonds modeled by stochastic processes \n", "$ {(P(t,T))}_{0 \\leq t \\leq T} $ for $ T \\geq 0 $. We assume the normalization $ P(T,T)=1 $." ] }, { "cell_type": "markdown", "metadata": { "id": "k1_IXgjmH6hN" }, "source": [ "$T$ denotes the maturity of the bond, $P(t,T)$ its price at a time $t$ before maturity $T$." ] }, { "cell_type": "markdown", "metadata": { "id": "W3LSgcFaH6hO" }, "source": [ "The yield\n", "$$\n", "Y(t,T) = - \\frac{1}{T-t} \\log P(t,T)\n", "$$\n", "describes the compound interest rate p.a. for maturity $T$." ] }, { "cell_type": "markdown", "metadata": { "id": "A4TX1bpnH6hO" }, "source": [ "The curve $f$ is called the forward rate curve of the bond market\n", "\\begin{align*}\n", "P(t,T) & =\\exp(-\\int_{t}^{T}f(t,s)ds)\n", "\\end{align*}\n", "for $0\\leq t\\leq T$." ] }, { "cell_type": "markdown", "metadata": { "id": "wfqDNuXZH6hO" }, "source": [ "Let us understand a bit the dynamics of yield curves and forward rate curves at this point:" ] }, { "cell_type": "markdown", "metadata": { "id": "ZNb7_fHOH6hO" }, "source": [ "### We are now applying our principles from the first general part to this large market. We use extensively that we can choose the asset $S^0$ for our convenience. In different market situations we can have different ways of discounting. We shall see two: discounting by the bank account process and discounting by a (forward) bond $ P(t,T^*) $. " ] }, { "cell_type": "markdown", "metadata": { "id": "Hl-2CfbXH6hP" }, "source": [ "The short rate process is given through $R_{t}=f(t,t)$ for $t\\geq0$ defining the \"bank account process\"\n", "$$\n", "(B(t))_{t \\geq 0}:=(\\exp(\\int_{0}^{t}R_{s}ds))_{t \\geq 0}.\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "id": "pqga3tI3H6hP" }, "source": [ "Consider now $ P(t,T) $ as price of a contract which promises $ 1 $ at time $ T $ and do the discounting with $ S^0 $ equal the bank account process." ] }, { "cell_type": "markdown", "metadata": { "id": "fbS7u8-QH6hP" }, "source": [ "No arbitrage is then guaranteed if on the filtered probability space $ (\\Omega,\\mathcal{F},Q) $ with filtration\n", "$ {(\\mathcal{F}_t)}_{t \\geq 0} $,\n", "$$\n", "E(\\exp(-\\int_t^T R_s ds)|\\mathcal{F}_t) = P(t,T)\n", "$$\n", "holds true for $ 0 \\leq t \\leq T $ for some equivalent (martingale) measure $ Q $." ] }, { "cell_type": "markdown", "metadata": { "id": "SoP8ZqajH6hP" }, "source": [ "This is a useful and important approach but not feasible for many market situations. There it is better to take another discounting unit." ] }, { "cell_type": "markdown", "metadata": { "id": "D8I32Y3cH6hQ" }, "source": [ "Consider a bond market $(P(t,T))_{t \\leq T}$ with $P(T,T) = 1$ and $P(t,T) > 0$. Let $t \\leq T \\leq T^{\\ast}$. We define the simple forward rate through\n", "\\begin{align*}\n", "F(t;T,T^{\\ast}) := \\frac{1}{T^{\\ast} - T} \\bigg( \\frac{P(t,T)}{P(t,T^{\\ast})} - 1 \\bigg).\n", "\\end{align*}\n", "and the simple spot rate through\n", "\\begin{align*}\n", "F(t,T) := F(t;t,T).\n", "\\end{align*}" ] }, { "cell_type": "markdown", "metadata": { "id": "wqbALC7CH6hQ" }, "source": [ "Apparently $P(t,T^{\\ast}) F(t;T,T^{\\ast})$ is first a traded portfolio (long in the $T$ bond and short in the $T^*$ bond) and the fair value at time $t$ of a contract paying $F(T,T^{\\ast})$ at time $T^{\\ast}$, since $ P(T^*,T^*) = 1 $.\n", "\n", "Indeed, note that\n", "\\begin{align*}\n", "P(t,T^{\\ast}) F(t;T,T^{\\ast}) &= \\frac{P(t,T) - P(t,T^{\\ast})}{T^{\\ast} - T},\n", "\\\\ F(T,T^{\\ast}) &= \\frac{1}{T^{\\ast} - T} \\bigg( \\frac{1}{P(T,T^{\\ast})} - 1 \\bigg).\n", "\\end{align*}\n", "Fair value means that we can build a portfolio at time $ t $ and at price $ \\frac{P(t,T) - P(t,T^{\\ast})}{T^{\\ast} - T} $ yielding $ F(T,T^{\\ast}) $ at time $ T^{\\ast} $:\n", "\n", "-> Holding a ZCB with maturity $ T $ at time $ t $ has value $ P(t,T) $, being additionally short in a ZCB with maturity $ T^{\\ast} $ amounts all together to $P(t,T) - P(t,T^{\\ast})$.\n", "\n", "-> at time $T$ we have to rebalance the portfolio by buying with the maturing ZCB another bond with maturity $ T^{\\ast} $, precisely an amount $ 1/P(T,T^{\\ast}) $. \n", "\n", "-> at time $ T^{\\ast} $ we receive $ 1/P(T,T^{\\ast}) - 1 $." ] }, { "cell_type": "markdown", "metadata": { "id": "AOkXdjnYH6hR" }, "source": [ "In this setup it is of course much better to take $ S^0 $ the $ T^*$ bond and to have $ X_t = F(t,T,T^*) $ as discounted price with respect to $ S^0 $. We can use all models for discounted prices like the binomial model or the Black-Scholes model for this situation.\n", "\n", "In the sequel we apply the binomial tree model with one timestep with a simple forward rate process and the foward bond starting at $0.9$ and terminating at $1$. Here discounting matters what you can see in the difference between the first (format time / numeraire / foward rate time $T^*$ bond) and second tree (format time / simple forward rate)." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "id": "3MUu6doJH6hR", "outputId": "5f8f6bfa-e628-440e-e6a5-24b3245a2bc4", "colab": { "base_uri": "https://localhost:8080/", "height": 172 } }, "outputs": [ { "output_type": "execute_result", "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "execution_count": 14 } ], "source": [ "import numpy as np\n", "from itertools import product\n", "\n", "\n", "# EUROPEAN\n", "F0 = 0.04\n", "u = 2\n", "d = 0.5\n", "payoffE = lambda F: np.maximum(F-F0,0.)\n", "\n", "timesteps = 1\n", "bin = set((0,1))\n", "trajectories = set(product(bin, repeat = timesteps))\n", "\n", "\n", "import pygraphviz as PG\n", "from IPython.display import Image\n", "binomialtreeforward = PG.AGraph(directed=True, strict=True)\n", "binomialtreeforward.edge_attr.update(len='2.0',color='blue')\n", "binomialtreeforward.node_attr.update(color='red')\n", "binomialtreeforwarddiscounted = PG.AGraph(directed=True, strict=True)\n", "binomialtreeforwarddiscounted.edge_attr.update(len='2.0',color='blue')\n", "binomialtreeforwarddiscounted.node_attr.update(color='red')\n", "binomialtreebackward = PG.AGraph(directed=True, strict=True)\n", "binomialtreebackward.edge_attr.update(len='2.0',color='blue')\n", "binomialtreebackward.node_attr.update(color='red')\n", "process = {(omega,0):F0 for omega in trajectories}\n", "numeraire = {(omega,0):0.9 for omega in trajectories}\n", "discountedprocess = {(omega,0):F0 for omega in trajectories}\n", "\n", "#construct process by forward steps\n", "for time in range(1,timesteps+1):\n", " for omega in trajectories:\n", " shelper = process[(omega,time-1)]*u**(omega[time-1])*d**(1.-omega[time-1])\n", " process.update({(omega,time):shelper})\n", " \n", "for time in range(1,timesteps+1):\n", " for omega in trajectories:\n", " #shelper = process[(omega,time-1)]*u**(omega[time-1])*d**(1.-omega[time-1])\n", " numeraire.update({(omega,time):1.0})\n", " \n", "for time in range(1,timesteps+1):\n", " for omega in trajectories:\n", " binomialtreeforward.add_edge('%d / %f / %f'% (time-1,numeraire[(omega,time-1)],process[(omega,time-1)]),\n", " '%d / %f / %f'% (time,numeraire[(omega,time)],process[(omega,time)]))\n", "\n", "#for time in range(1,timesteps+1):\n", "# for omega in trajectories:\n", "# binomialtreeforward.add_edge('%d, %d'% (time-1,numeraire[(omega,time-1)]),'%d, %d'% (time,numeraire[(omega,time)]))\n", "\n", "Image(binomialtreeforward.draw(format='png',prog='dot')) " ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "id": "iF294x6oH6hR", "outputId": "ce670b4b-df5b-4592-89b8-06adc5ddfcd5", "colab": { "base_uri": "https://localhost:8080/", "height": 172 } }, "outputs": [ { "output_type": "execute_result", "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "execution_count": 15 } ], "source": [ "for time in range(0,timesteps+1):\n", " for omega in trajectories:\n", " shelper = process[(omega,time)]/numeraire[(omega,time)]\n", " discountedprocess.update({(omega,time):shelper})\n", " \n", "for time in range(1,timesteps+1):\n", " for omega in trajectories:\n", " binomialtreeforwarddiscounted.add_edge('%d / %f'% (time-1,discountedprocess[(omega,time-1)]),'%d / %f'% (time,discountedprocess[(omega,time)]))\n", "\n", "#for time in range(1,timesteps+1):\n", "# for omega in trajectories:\n", "# binomialtreeforward.add_edge('%d, %d'% (time-1,numeraire[(omega,time-1)]),'%d, %d'% (time,numeraire[(omega,time)]))\n", "\n", "\n", "Image(binomialtreeforwarddiscounted.draw(format='png',prog='dot')) " ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "id": "znIzWsbeH6hS" }, "outputs": [], "source": [ "def condprob(omega,time): \n", " omegahelperu = list(omega)\n", " omegahelperd = list(omega)\n", " omegahelperu[time]=1\n", " omegahelperd[time]=0\n", " omegahelperu = tuple(omegahelperu)\n", " omegahelperd = tuple(omegahelperd)\n", " return (discountedprocess[(omega,time)]-discountedprocess[(omegahelperd,time+1)])/(discountedprocess[(omegahelperu,time+1)]-discountedprocess[(omegahelperd,time+1)])" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "id": "rfcRmU-8H6hS", "outputId": "e6cd63c7-c33e-4f1b-b8ad-cd609fd3d9d5", "colab": { "base_uri": "https://localhost:8080/", "height": 172 } }, "outputs": [ { "output_type": "execute_result", "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "execution_count": 17 } ], "source": [ "processbackward = {(omega,timesteps):(payoffE(process[(omega,timesteps)])/numeraire[(omega,timesteps)]) for omega in trajectories}\n", "#backwardssteps: European\n", "for time in reversed(range(0,timesteps)):\n", " for omega in trajectories:\n", " shelper=0 \n", " omegahelperu = list(omega)\n", " omegahelperd = list(omega)\n", " omegahelperu[time]=1\n", " omegahelperd[time]=0\n", " omegahelperu = tuple(omegahelperu)\n", " omegahelperd = tuple(omegahelperd)\n", " shelper = processbackward[(omegahelperu,time+1)]*condprob(omega,time)+processbackward[(omegahelperd,time+1)]*(1-condprob(omega,time))\n", " processbackward.update({(omega,time):shelper})\n", "\n", "for time in range(1,timesteps+1):\n", " for omega in trajectories:\n", " binomialtreebackward.add_edge('%d / %f / %f'% (time-1,discountedprocess[(omega,time-1)],processbackward[(omega,time-1)]),'%d / %f / %f'% (time,discountedprocess[(omega,time)],processbackward[(omega,time)]))\n", "\n", "Image(binomialtreebackward.draw(format='png',prog='dot')) " ] }, { "cell_type": "markdown", "metadata": { "id": "0cHccwhRH6hS" }, "source": [ "In order to get prices back one has to multiply this tree with the corresponding numeraire prices, hence the actual caplet price will be $ 0.016296 * 0.9 $." ] }, { "cell_type": "markdown", "metadata": { "id": "CK8n14XsH6hS" }, "source": [ "## Caps" ] }, { "cell_type": "markdown", "metadata": { "id": "fHLqlaikH6hT" }, "source": [ "In the sequel, we fix a number of future dates \n", "\\begin{align*}\n", "T_0 < T_1 < \\ldots < T_n \n", "\\end{align*}\n", "with $T_i - T_{i-1} \\equiv \\delta$.\n", "\n", "Fix a rate $\\kappa > 0$. At time $T_i$ the holder of the cap receives\n", "\\begin{align*}\n", "\\delta (F(T_{i-1},T_i) - \\kappa)^+.\n", "\\end{align*}\n", "Let $t \\leq T_0$. We write\n", "\\begin{align*}\n", "{\\rm Cpl}(t;T_{i-1},T_i), \\quad i=1,\\ldots,n\n", "\\end{align*}\n", "for the time $t$ price of the $i$th caplet, and\n", "\\begin{align*}\n", "{\\rm Cp}(t) = \\sum_{i=1}^n {\\rm Cpl}(t;T_{i-1},T_i)\n", "\\end{align*}\n", "for the time $t$ price of the cap." ] }, { "cell_type": "markdown", "metadata": { "id": "d1u2R5pbH6hT" }, "source": [ "## Floors " ] }, { "cell_type": "markdown", "metadata": { "id": "ZIN9mX-5H6hU" }, "source": [ "At time $T_i$ the holder of the floor receives\n", "\\begin{align*}\n", "\\delta (\\kappa - F(T_{i-1},T_i))^+.\n", "\\end{align*}\n", "Let $t \\leq T_0$. We write\n", "\\begin{align*}\n", "{\\rm Fll}(t;T_{i-1},T_i), \\quad i=1,\\ldots,n\n", "\\end{align*}\n", "for the time $t$ price of the $i$th floorlet, and\n", "\\begin{align*}\n", "{\\rm Fl}(t) = \\sum_{i=1}^n {\\rm Fll}(t;T_{i-1},T_i)\n", "\\end{align*}\n", "for the time $t$ price of the floor." ] }, { "cell_type": "markdown", "metadata": { "id": "7SVn1fgzH6hU" }, "source": [ "## Swaps" ] }, { "cell_type": "markdown", "metadata": { "id": "zAto8qOKH6hV" }, "source": [ "Fix a rate $K$ and a nominal $N$. The cash flow of a payer swap at $T_i$ is\n", "\\begin{align*}\n", "(F(T_{i-1},T_i) - K) \\delta N.\n", "\\end{align*}\n", "The total value $\\Pi_p(t)$ of the payer swap at time $t \\leq T_0$ is\n", "\\begin{align*}\n", "\\Pi_p(t) = N \\bigg( P(t,T_0) - P(t,T_n) - K \\delta \\sum_{i=1}^n P(t,T_i) \\bigg).\n", "\\end{align*}\n", "The value of a receiver swap at $t \\leq T_0$ is\n", "\\begin{align*}\n", "\\Pi_r(t) = -\\Pi_p(t).\n", "\\end{align*}\n", "The swap rate $R_{\\rm swap}(t)$ is the fixed rate $K$ which gives $\\Pi_p(t) = \\Pi_r(t) = 0$. Hence\n", "\\begin{align*}\n", "R_{\\rm swap}(t) = \\frac{P(t,T_0) - P(t,T_n)}{\\delta \\sum_{i=1}^n P(t,T_i)}, \\quad t \\in [0,T_0].\n", "\\end{align*}" ] }, { "cell_type": "markdown", "metadata": { "id": "E9SN74gQH6hV" }, "source": [ "## Swaptions" ] }, { "cell_type": "markdown", "metadata": { "id": "KNVoH_sQH6hV" }, "source": [ "A payer (receiver) swaption is an option to enter a payer (receiver) swap at $T_0$.\n", "The payoff of a payer swaption at $T_0$ is\n", "\\begin{align*}\n", "N \\delta (R_{\\rm swap}(T_0) - K)^+ \\sum_{i=1}^n P(T_0,T_i),\n", "\\end{align*}\n", "and of a receiver swaption\n", "\\begin{align*}\n", "N \\delta (K - R_{\\rm swap}(T_0))^+ \\sum_{i=1}^n P(T_0,T_i).\n", "\\end{align*}" ] }, { "cell_type": "markdown", "metadata": { "id": "QkgFQMuxH6hW" }, "source": [ "## Spot measure" ] }, { "cell_type": "markdown", "metadata": { "id": "_auJSD5EH6hW" }, "source": [ "From now on, let $P$ be a martingale measure in the bond market $(P(t,T))_{t \\leq T}$, i.e. for each $T > 0$ the discounted bond price process\n", "\\begin{align*}\n", "\\frac{P(t,T)}{B(t)}\n", "\\end{align*}\n", "is a martingale. This leads to the following fundamental formula of interest rate theory\n", "$$\n", "P(t,T) = E(\\exp(-\\int_t^T R_s ds)) | \\mathcal{F}_t )\n", "$$\n", "for $ 0 \\leq t \\leq T $." ] }, { "cell_type": "markdown", "metadata": { "id": "7HfXt0cOH6hW" }, "source": [ "## Forward measures" ] }, { "cell_type": "markdown", "metadata": { "id": "B9Q0jKqaH6hX" }, "source": [ "For $T^{\\ast} > 0$ define the \\emph{$T^{\\ast}$-forward measure} ${P}^{T^{\\ast}} $ such that for any $T > 0$ the discounted bond price process\n", "\\begin{align*}\n", "\\frac{P(t,T)}{P(t,T^{\\ast})}, \\quad t \\in [0,T]\n", "\\end{align*}\n", "is a ${P}^{T^{\\ast}}$-martingale.\n", "\n", "\n", "For any $T < T^{\\ast}$ the simple forward rate\n", "\\begin{align*}\n", "F(t;T,T^{\\ast}) = \\frac{1}{T^{\\ast} - T} \\bigg( \\frac{P(t,T)}{P(t,T^{\\ast})} - 1 \\bigg)\n", "\\end{align*}\n", "is a $\\mathbb{P}^{T^{\\ast}}$-martingale.\n", "\n", "For any time derivative $X \\in \\mathcal{F}_{T^*}$ paid at $ T^* $ we have that the fair value via ``martingale pricing'' is given through\n", "\\begin{align*}\n", "P(t,T^*) \\mathbb{E}^{T^*}[X | \\mathcal{F}_t].\n", "\\end{align*}\n", "The fair price of the $i$th caplet is therefore given by\n", "\\begin{align*}\n", "{\\rm Cpl}(t;T_{i-1},T_i) = \\delta P(t,T_i) \\mathbb{E}^{T_i} [ (F(T_{i-1},T_i) - \\kappa)^+ | \\mathcal{F}_t].\n", "\\end{align*}\n", "By the martingale property we obtain therefore\n", "\\begin{align*}\n", "\\mathbb{E}^{T_i}[F(T_{i-1},T_i) | \\mathcal{F}_t] = F(t;T_{i-1},T_i),\n", "\\end{align*}\n", "what was proved by trading arguments before." ] }, { "cell_type": "markdown", "metadata": { "id": "0W90M8OcH6hX" }, "source": [ "## Black's formula" ] }, { "cell_type": "markdown", "metadata": { "id": "ekb4Wk2YH6hX" }, "source": [ "Let $X \\sim N(\\mu,\\sigma^2)$ and $K \\in \\mathbb{R}_{> 0}$. Then we have\n", "\\begin{align*}\n", "\\mathbb{E}[ (e^X - K)^+ ] &= e^{\\mu + \\frac{\\sigma^2}{2}} \\Phi \\bigg( -\\frac{\\log K - (\\mu + \\sigma^2)}{\\sigma} \\bigg)\n", "- K \\Phi \\bigg( -\\frac{\\log K - \\mu}{\\sigma} \\bigg),\n", "\\\\ \\mathbb{E}[ (K - e^X)^+ ] &= K \\Phi \\bigg( \\frac{\\log K - \\mu}{\\sigma} \\bigg) - e^{\\mu + \\frac{\\sigma^2}{2}} \\Phi \\bigg( \\frac{\\log K - (\\mu + \\sigma^2)}{\\sigma} \\bigg).\n", "\\end{align*}" ] }, { "cell_type": "markdown", "metadata": { "id": "CYfsYhmbH6hX" }, "source": [ "## Black's formula for caps and floors" ] }, { "cell_type": "markdown", "metadata": { "id": "tx2fpG2tH6hY" }, "source": [ "\n", "Let $t \\leq T_0$. From our previous results we know that \n", "\\begin{align*}\n", "{\\rm Cpl}(t;T_{i-1},T_i) &= \\delta P(t,T_i) \\mathbb{E}_t^{{T_i}} [ (F(T_{i-1},T_i) - \\kappa)^+ ],\n", "\\\\ {\\rm Fll}(t;T_{i-1},T_i) &= \\delta P(t,T_i) \\mathbb{E}_t^{{T_i}} [ (\\kappa - F(T_{i-1},T_i))^+ ],\n", "\\end{align*}\n", "and that $F(t;T_{i-1},T_i)$ is an $P^{T_i}$-martingale.\n", "\n", "We assume that under ${P}^{T_i}$ the forward rate $F(t;T_{i-1},T_i)$ is an exponential Brownian motion\n", "\\begin{align*}\n", "F(t;T_{i-1},T_i) & = F(s;T_{i-1},T_i) \\\\\n", "& \\exp \\bigg( -\\frac{1}{2} \\int_s^t \\lambda(u,T_{i-1})^2 du + \\int_s^t \\lambda(u,T_{i-1}) dW_u^{T_i} \\bigg)\n", "\\end{align*}\n", "for $s \\leq t \\leq T_{i-1}$,\n", "with a function $\\lambda(u,T_{i-1})$. \n", "\n", "We define the variance $\\sigma^2(t)$ as\n", "\\begin{align*}\n", "\\sigma^2(t) := \\frac{1}{T_{i-1} - t} \\int_t^{T_{i-1}} \\lambda(s,T_{i-1})^2 ds.\n", "\\end{align*}\n", "The $P^{T_i}$-distribution of $\\log F(T_{i-1},T_i)$ conditional on $\\mathcal{F}_t$ is\n", "$N(\\mu,\\sigma^2)$ with\n", "\\begin{align*}\n", "\\mu &= \\log F(t;T_{i-1},T_i) - \\frac{\\sigma^2(t)}{2} (T_{i-1} - t),\n", "\\\\ \\sigma^2 &= \\sigma^2(t) (T_{i-1} - t).\n", "\\end{align*}\n", "In particular\n", "\\begin{align*}\n", "\\mu + \\frac{\\sigma^2}{2} &= \\log F(t;T_{i-1},T_i),\n", "\\\\ \\mu + \\sigma^2 &= \\log F(t;T_{i-1},T_i) + \\frac{\\sigma^2(t)}{2} (T_{i-1} - t).\n", "\\end{align*}\n", "\n", "We have\n", "\\begin{align*}\n", "{\\rm Cpl}(t;T_{i-1},T_i) &= \\delta P(t,T_i) (F(t;T_{i-1},T_i) \\Phi(d_1(i;t)) - \\kappa \\Phi(d_2(i;t))),\n", "\\\\ {\\rm Fll}(t;T_{i-1},T_i) &= \\delta P(t,T_i) ( \\kappa \\Phi(-d_2(i;t)) - F(t;T_{i-1},T_i) \\Phi(-d_1(i;t)) ),\n", "\\end{align*}\n", "where\n", "\\begin{align*}\n", "d_{1,2}(i;t) = \\frac{\\log \\big( \\frac{F(t;T_{i-1},T_i)}{\\kappa} \\big) \\pm \\frac{1}{2} \\sigma(t)^2 (T_{i-1} - t)}{\\sigma(t) \\sqrt{T_{i-1} - t}}.\n", "\\end{align*}" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "mttsBAWcH6hY" }, "outputs": [], "source": [ "" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "hRVV5dgcH6hY" }, "outputs": [], "source": [ "" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.8" }, "colab": { "name": "CAS_interest_rates_202112.ipynb", "provenance": [] } }, "nbformat": 4, "nbformat_minor": 0 }