Term structure modelling for multiple curves with stochastic discontinuities

Claudio Fontana, Zorana Grbac, Sandrine Gümbel and Thorsten Schmidt
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Zorana Grbac: UPCité - Université Paris Cité

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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.

Keywords: semimartingale; affine process; NAFLVR; large financial market; multiple yield curves; stochastic discontinuities; forward rate agreement; market models; Libor rate; HJM Model (search for similar items in EconPapers)
Date: 2020-04
Note: View the original document on HAL open archive server: https://hal.science/hal-03898927v1
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Published in Finance and Stochastics, 2020, 24 (2), pp.465-511. ⟨10.1007/s00780-020-00416-5⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03898927

DOI: 10.1007/s00780-020-00416-5

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