Long-time large deviations for the multi-asset Wishart stochastic volatility model and option pricing

TL;DR

This paper establishes a large deviations principle for multi-asset Wishart stochastic volatility models, extending the Heston model to multiple assets, and applies it to approximate basket option implied volatility and improve Monte Carlo simulations.

Contribution

It introduces a large deviations framework for multidimensional Wishart stochastic volatility models and applies it to option pricing and simulation efficiency.

Findings

Large deviations principle proven for Wishart models

Asymptotic approximation for basket option implied volatility

Development of an optimal importance sampling algorithm

Abstract

We prove a large deviations principle for the class of multidimensional affine stochastic volatility models considered in (Gourieroux, C. and Sufana, R., J. Bus. Econ. Stat., 28(3), 2010), where the volatility matrix is modelled by a Wishart process. This class extends the very popular Heston model to the multivariate setting, thus allowing to model the joint behaviour of a basket of stocks or several interest rates. We then use the large deviation principle to obtain an asymptotic approximation for the implied volatility of basket options and to develop an asymptotically optimal importance sampling algorithm, to reduce the number of simulations when using Monte-Carlo methods to price derivatives.