Semi-Analytical Option Pricing Under Double Heston Jump-Diffusion Hybrid Model

Abstract

We examine European call options in the jump-diffusion version of the Double Heston stochastic volatility model for the underlying price process to provide a more flexible model for the term structure of volatility. We assume, in addition, that the stochastic interest rate is governed by the Cox-- Ross -- Ingersoll (CIR) dynamics. The instantaneous volatilities are correlated with the dynamics of the stock price process, whereas the short-term rate is assumed to be independent of the dynamics of the price process and its volatility. The main result furnishes a semi-analytical formula for the price of the European call option in the hybrid call option/interest rates model. Numerical results show that the model implied volatilities are comparable for in-sample but outperform out-of-sample implied volatilities compared to the benchmark Heston model[1], and Double Heston volatility model put forward by Christoffersen et al., [2] for calls on the S&P 500 index.

Keywords

• finance
• double heston jump diffusion model
• l\'evy process
• affine processes
• calibration of stochastic volatility