Pricing and Hedging of Variable Annuities With Path-dependent Guarantee in Wishart Stochastic Volatility Models

Abstract

This paper presents the pricing of a path-dependent guaranteed minimum maturity benefit in the Wishart multidimensional stochastic volatility model and the Wishart affine stochastic correlation model. We derive a closed-form solution for the option price in these two models, requiring only the computation of a one-dimensional integration. Thanks to the remarkable analytical properties of these models, we also compute all sensitivities of the option price to the model parameters. An implementation illustrates the results, confirms that pricing is fast and accurate, and provides a framework for pricing and risk management of this product in Wishart stochastic volatility models.