Sequential Itô–Taylor expansions and characteristic functions of stochastic volatility models

Abstract

This study proposes a new approach to derive the characteristic function of a general stochastic volatility model by sequentially utilizing the Itô–Taylor expansions. In particular, our method applies to non‐affine stochastic volatility models with jumps, for which the corresponding characteristic functions do not have closed‐form expressions. Numerically inverting these characteristic functions can yield accurate probability density functions of stochastic volatility models to serve for various pricing and hedging purposes in quantitative finance. The proposed sequential Itô–Taylor expansion allows us to handle derivatives with medium to long maturities. Numerical experiments illustrate the accuracy and effectiveness of our approach.