Jacobi Stochastic Volatility factor for the Libor Market Model

Pierre-Edouard Arrouy (), Alexandre Boumezoued (), Bernard Lapeyre () and Sophian Mehalla
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Pierre-Edouard Arrouy: Recherche et Développement, Milliman Paris - Milliman France
Alexandre Boumezoued: Recherche et Développement, Milliman Paris - Milliman France
Bernard Lapeyre: CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École nationale des ponts et chaussées, MATHRISK - Mathematical Risk Handling - UPEM - Université Paris-Est Marne-la-Vallée - ENPC - École nationale des ponts et chaussées - Centre Inria de Paris - Inria - Institut National de Recherche en Informatique et en Automatique
Sophian Mehalla: CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École nationale des ponts et chaussées, MATHRISK - Mathematical Risk Handling - UPEM - Université Paris-Est Marne-la-Vallée - ENPC - École nationale des ponts et chaussées - Centre Inria de Paris - Inria - Institut National de Recherche en Informatique et en Automatique, Recherche et Développement, Milliman Paris - Milliman France

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Abstract: We propose a new method to efficiently price swap rates derivatives under the LIBOR Market Model with Stochastic Volatility and Displaced Diffusion (DDSVLMM). This method uses polynomial processes combined with Gram-Charlier expansion techniques. The standard pricing method for this model relies on dynamics freezing to recover an Heston-type model for which analytical formulas are available. This approach is time consuming and efficient approximations based on Gram-Charlier expansions have been recently proposed. In this article, we first discuss the fact that for a class of stochastic volatility model, including the Heston one, the classical sufficient condition ensuring the convergence of the Gram-Charlier series can not be satisfied. Then, we propose an approximating model based on Jacobi process for which we can prove the stability of the Gram-Charlier expansion. For this approximation, we have been able to prove a strong convergence toward the original model; moreover, we give an estimate of the convergence rate. We also prove a new result on the convergence of the Gram-Charlier series when the volatility factor is not bounded from below. We finally illustrate our convergence results with numerical examples.

Keywords: Stochastic Volatility; Jacobi dynamics; Polynomial processes; Gram-Charlier expansions; LIBOR Market Model (search for similar items in EconPapers)
Date: 2022-09
New Economics Papers: this item is included in nep-rmg
Note: View the original document on HAL open archive server: https://hal.science/hal-02468583v2
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Citations: View citations in EconPapers (1)

Published in Finance and Stochastics, 2022, 26 (4), pp.771-823. ⟨10.1007/s00780-022-00488-5⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-02468583

DOI: 10.1007/s00780-022-00488-5

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