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arXiv · 1810.09882

Term structure modeling for multiple curves with stochastic discontinuities

Claudio Fontana·Zorana Grbac·Sandrine Gümbel·Thorsten Schmidt
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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.

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Claudio Fontana, Zorana Grbac, Sandrine Gümbel, Thorsten Schmidt. 2018-10-23. Term structure modeling for multiple curves with stochastic discontinuities. https://arxiv.org/abs/1810.09882

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