Contact
About me
Research
Teaching
Conferences
Grants
The Press

Prof. Dr. Erich Walter Farkas
Home
Thesis Supervision

Past Thesis Supervision
 Students who are planning to write a Bachelor or Master thesis under my direction and with my team are advised to contact me well ahead of time. In more concrete terms, this means approximately one semester ahead of the planned starting date.
 An interesting material on how to write a thesis can be found at the home page of Prof. Martin Schweizer, follow this Link.
Possible Topics

In the area of Quantitative Finance
These topics are more appropriate for students having a solid background in quantitative techniques and finance.
 Cointegration in commodity markets
Cointegration is a longrun relationship where a linear combination of two or more nonstationary time series is stationary. In particular, evidence of cointegration is found in commodity markets. In general, a cointegrated system has an Error Correction Model (ECM) representation that allows for capturing the dynamics of the shortrun deviations from the longrun (cointegration) relations. Several Gaussian continuoustime models have been developed in the literature to account for cointegration in commodity markets and to price commodity derivatives. Interesting themes for a thesis are: a) continuous time modeling of a cointegrated system of commodities including features such as stochastic volatility in the shortrun equations, jumps in the shortrun equations, structural breaks in the longrun equations, stochastic switching of regimes in the longrun equations; b) pricing methods for spread/basket options or for structured products on cointegrated commodities; c) development of strategies for hedging exposures on a commodity using other cointegrated commodities; d) portfolio management of cointegrated commodities.
 Duan, J.C. and Pliska, S. R. (2004). Option valuation with cointegrated asset prices. Journal of Economic Dynamics and Control, 28(4):727754.
 Farkas, W., E. Gourier, R. Huitema and C. Necula (2014). A TwoFactor Cointegrated Commodity Price Model with an Application to Spread Option Pricing. working paper.
 Nakajima, K. and Ohashi, K. (2012). A cointegrated commodity pricing model. Journal of Futures Markets, 32(11):9951033.
 Paschke, R. and Prokopczuk, M. (2009). Integrating multiple commodities in a model of stochastic price dynamics. Journal of Energy Markets, 2(3):4782.
 Expansionbased methods for pricing derivative products
Expansionbased methods are employed in quantitative finance in order to obtain modified option pricing formulas that account for deviations from the assumption of Gaussian logreturns in the classic BlackScholesMerton model. The idea consists in expanding the density function of the riskneutral probability measure around the Gaussian probability density function, using a set of orthogonal polynomials. One such approach showing promising results is the GaussHermite expansion, based on the set of "physicist" Hermite polynomials. The GaussHermite expansion also allows for obtaining closed form option pricing formulas. Interesting themes for a thesis are: a) conducting an empirical analysis of the pricing and hedging performance of existing expansionbased methods; b) investigating the properties of expansion methods based on other sets of orthogonal polynomials; c) extending the GaussHermite expansion method to price derivatives on multiple underlying; d) using expansionbased methods to obtain closed form option pricing methods for nonaffine stochastic volatility models.
 Corrado, C. J., and T. Su. (1996). S&P 500 index option tests of Jarrow and Rudd's approximate option valuation formula. Journal of Futures Markets, 16, 611629.
 Corrado, C. J., and T. Su. (1997). Implied volatility skews and stock index skewness and kurtosis implied by S&P 500 index option prices. Journal of Derivatives, 4, 819.
 Jurczenko, E., B. Maillet, and B. Negrea. (2002). Revisited multimoment approximate option pricing models: A general comparison (Discussion Paper of the LSEFMG, No. 430).
 Necula, C., G., Drimus, and W., Farkas. (2013). A General Closed Form Option Pricing Formula, Link.
 Microfoundations of stochastic volatility models
A popular approach for modeling volatility consists in using exogenous stochastic volatility models. In this respect, one departs from the central hypothesis of the BlackScholesMerton model, concerning a constant level of volatility, by specifying exogenously a dynamics (in general, affine) of the underlying and its instantaneous variance. However, there are, at micro level, various sources, such as the heterogeneity of traders (in beliefs, in preferences or in behavior) and their interaction generating herding phenomena that could influence the dynamics of volatility. It is, therefore, much more appealing to investigate the implications of such microfoundations that could lead, in a partial or general equilibrium framework, to an endogenously determined (in general, nonaffine) dynamics of the underlyingvolatility system. Interesting themes for a thesis are: a) conducting an empirical analysis of the option pricing performance of existing nonaffine stochastic volatility models; b) modeling heterogeneity and interaction in financial markets; c) modeling the dynamics of heterogeneity in beliefs; d) analyzing the implications of the heterogeneity and interaction of traders on the dynamics of volatility.
 Alfarano, S., T. Lux, and F. Wagner (2008). Timevariation of higher moments in a financial market with heterogeneous agents: An analytical approach. Journal of Economic Dynamics and Control, 32(1):101136.
 Follmer, H. and M. Schweizer (1993). A microeconomic approach to diffusion models for stock prices. Mathematical Finance, 3, 123.
 Horst, U. (2005). Financial price fluctuation in a stock market model with many interacting agents. Economic Theory, 25, 917932.
 Kaeck, A., and C. Alexander (2012) Volatility dynamics for the S&P 500 Further evidence from nonaffine, multifactor jump diffusions, Journal of Banking & Finance, 36, 31103121

In the area of Mathematical Finance / Quantitative Methods for Risk Management These topics are more appropriate for students having a solid mathematical background.
 Risk Measures
We are interested in studying measures to quantify the amount of
capital that a financial institution should be required to raise and use
for regulatory purposes. The theory of risk measures has been having a
considerable influence on the debate about regulatory capital as witnessed
by the current solvency regimes, such as the Basel regimes for banks and
Solvency II and the Swiss Solvency Test for insurance companies.
Possible topics include:
 Risk measures in the absence of riskfree securities
 Liquidityadjusted risk measures
 Risk functionals based on utility profiles
 Risk measures under model uncertainty
 Risk measures in a dynamic setting
 Valuation/Pricing
A key requirement for financial agents is the ability to value financial
assets. Risk measures can be fruitfully used for valuation and pricing
purposes, from the single instrument level to the company level.
Possible topics include:
 Multiasset risk measures
 Good deal valuation based on acceptability criteria
 Valuation in CAPMlike equilibrium models
 Capital Allocation
Once asset valuation has been performed, financial agents face the
problem of portfolio selection. Risk measures typically appear as
constraints in the corresponding optimization programs.
Possible topics include:
 Optimal risk sharing
 Differentiability properties of risk measures
 Convex duality and optimization applied to portfolio selection
In this context we recommend the reading of the following papers and a preliminary contact also with Ludovic Mathys:

Farkas, W., P. KochMedina, C. Munari (2014). Beyond cashadditive risk measures: when changing the numeraire fails. Finance and Stochastics, 18(1):145173,
[Link to the Journal]
[NCCR FinRisk]
[SSRN]
[arXiv]
 Farkas, W., P. KochMedina, C. Munari (2014). Capital requirements with defaultable securities. Insurance: Mathematics and Economics, 55, 5867,
[Link to the Journal]
[NCCR FinRisk]
[SSRN]
[arXiv]

Farkas, W., P. KochMedina, C. Munari (2015). Measuring risk with multiple eligible assets. Mathematics and Financial Economics, 9 (1), 327,
[Link to the Journal]
[SSRN]
[arXiv]
