Jacobi Stochastic Volatility factor for the Libor Market Model - Archive ouverte HAL Access content directly
Journal Articles Finance and Stochastics Year : 2022

Jacobi Stochastic Volatility factor for the Libor Market Model

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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.
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Dates and versions

hal-02468583 , version 1 (13-02-2020)
hal-02468583 , version 2 (07-12-2022)

Identifiers

  • HAL Id : hal-02468583 , version 2

Cite

Pierre-Edouard Arrouy, Bernard Lapeyre, Sophian Mehalla, Alexandre Boumezoued. Jacobi Stochastic Volatility factor for the Libor Market Model. Finance and Stochastics, 2022, 26, pp.771-823. ⟨hal-02468583v2⟩
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