Multiple curve Lévy forward price model allowing for negative interest rates

Ernst Eberlein, Christoph Gerhart and Zorana Grbac
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Zorana Grbac: UPCité - Université Paris Cité, LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité

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Abstract: In this paper we develop a framework for discretely compounding interest rates which is based on the forward price process approach. This approach has a number of advantages, in particular in the current market environment. Compared to the classical as well as the Lévy Libor market model, it allows in a natural way for negative interest rates and has superb calibration properties even in the presence of extremely low rates. Moreover, the measure changes along the tenor structure are simplified significantly. These properties make it an excellent base for a post-crisis multiple curve setup. Two variants for multiple curve constructions based on the multiplicative spreads are discussed. Time-inhomogeneous Lévy processes are used as driving processes. An explicit formula for the valuation of caps is derived using Fourier transform techniques. Relying on the valuation formula, we calibrate the two model variants to market data.

Date: 2019-03-12
Note: View the original document on HAL open archive server: https://hal.science/hal-03898912v1
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Published in Mathematical Finance, 2019, 30 (1), pp.167-195. ⟨10.1111/mafi.12210⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03898912

DOI: 10.1111/mafi.12210

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