Pricing volatility swaps in the Heston’s stochastic volatility model with regime switching: A saddlepoint approximation method

Abstract

Pricing a volatility swap is a highly nonlinear problem. Explicit solutions of the prices of volatility swaps are notoriously difficult to find. In this paper, we consider a saddlepoint approximation method for the valuation of a volatility swap under the Heston’s stochastic volatility model with regime switching. All the values of key parameters in our model are supposed to depend on the states of a continuous time observable Markov chain process. We present a closed-form exact cumulant generating functions (CGFs) of the continuous realized variance. Additionally, an approximated CGF is given. Then we approximate the volatility swaps by the saddlepoint approximation formula which derived from the Fourier inversion representation. The numerical results suggest that the alternative saddlepoint approximation method (ASAP) and the approximated ASAP method could both produce fairly accurate results for the given range of maturities.