Long-time large deviations for the multi-asset Wishart stochastic volatility model and option pricing - École des Ponts ParisTech Access content directly
Journal Articles (Review Article) SIAM Journal on Financial Mathematics Year : 2019

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

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.

Dates and versions

hal-01949485 , version 1 (10-12-2018)

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Aurélien Alfonsi, David Krief, Peter Tankov. Long-time large deviations for the multi-asset Wishart stochastic volatility model and option pricing. SIAM Journal on Financial Mathematics, 2019, ⟨10.1137/18M1197588⟩. ⟨hal-01949485⟩
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