2Laboratoire de Probabilités, Statistique et Modélisation,
Université Paris Diderot,
avenue de France, 75205, Paris, France
(email: grbac@math.univ-paris-diderot.fr)
3University of Freiburg, Department of Mathematical Stochastics, Ernst-Zermelo-Str. 1, 79104 Freiburg, Germany
(email: sandrine.guembel@stochastik.uni-freiburg.de)
4Freiburg Institute of Advanced Studies (FRIAS), Germany,
University of Strasbourg Institute for Advanced Study (USIAS), France and
University of Freiburg, Department of Mathematical Stochastics, Ernst-Zermelo-Str. 1, 79104 Freiburg, Germany
(email: thorsten.schmidt@stochastik.uni-freiburg.de)
Abstract
We develop a general term structure framework taking stochastic discontinuities explicitly into account. Stochastic discontinuities are a key feature in interest rate markets, as for example the jumps of the term structures in correspondence to monetary policy meetings of the ECB show. We provide a general analysis of multiple curve markets under minimal assumptions in an extended HJM framework and provide a fundamental theorem of asset pricing based on NAFLVR. The approach with stochastic discontinuities permits to embed market models directly, unifying seemingly different modeling philosophies. We also develop a tractable class of models, based on affine semimartingales, going beyond the requirement of stochastic continuity.