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: Milliman R&D
Alexandre Boumezoued: Milliman R&D
Bernard Lapeyre: École des Ponts ParisTech
Sophian Mehalla: Milliman R&D

Finance and Stochastics, 2022, vol. 26, issue 4, No 3, 823 pages

Abstract: Abstract We propose a new method to efficiently price swap rate derivatives under the LIBOR market model with stochastic volatility and displaced diffusion. This method applies series expansion techniques built around Gaussian (Gram–Charlier) or Gaussian mixture densities to polynomial processes. The standard pricing method for the considered model relies on dynamics freezing to recover a Heston-type model for which analytical formulas are available. This approach is time-consuming, and efficient approximations based on Gram–Charlier expansions have been proposed recently. 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 Gram–Charlier series is not satisfied. Then we propose an approximating model based on a Jacobi process for which we can prove the stability of Gram–Charlier-type expansions. For this approximation, we have been able to prove a strong convergence towards 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; Expansion series; Gram–Charlier expansion; Polynomial processes; LIBOR market model; 60J60; 60G99; 91G30; 91G60 (search for similar items in EconPapers)
JEL-codes: C02 C63 C65 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00780-022-00488-5

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