Term structure modeling for multiple curves with stochastic discontinuities
Mathematical Finance
2020-04-28 v3 Probability
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.
Cite
@article{arxiv.1810.09882,
title = {Term structure modeling for multiple curves with stochastic discontinuities},
author = {Claudio Fontana and Zorana Grbac and Sandrine Gümbel and Thorsten Schmidt},
journal= {arXiv preprint arXiv:1810.09882},
year = {2020}
}