Longtime large deviations for the multiasset 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 MonteCarlo methods to price derivatives.
 Publication:

arXiv eprints
 Pub Date:
 June 2018
 arXiv:
 arXiv:1806.06883
 Bibcode:
 2018arXiv180606883A
 Keywords:

 Quantitative Finance  Pricing of Securities;
 Quantitative Finance  Mathematical Finance;
 60F10;
 91G20;
 91G60