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Term structure modeling for multiple curves with stochastic discontinuities

Claudio Fontana, Zorana Grbac, Sandrine G\"umbel and 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.

Date: 2018-10, Revised 2019-12
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Published in Finance and Stochastics, 24: 465-511, 2020

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