Orthogonal polynomial expansions for the valuation of options under the stochastic volatility models with stochastic correlation

Abstract

This work provides a new method for pricing options under the generalized stochastic volatility models with Jacobi stochastic correlation. Our method is based on the observation that the generalized models belong to the class of polynomial diffusions and therefore the option prices can be efficiently computed via orthogonal polynomial expansions. We take the Heston and Schöbel-Zhu models with stochastic correlation as two specific examples and are able to derive the analytical formulas for the option prices. We also illustrate the accuracy of the proposed method through a number of numerical experiments.

Keywords

• Orthogonal polynomial expansions
• Polynomial diffusions
• Stochastic correlation
• Jacobi process
• Stochastic volatility