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

Authors : Rehez AHLİP, Laurence A F PARK, Ante PRODAN

Pages : 138-152

Doi:10.33187/jmsm.432019

View : 19 | Download : 12

Publication Date : 2018-12-30

Article Type : Research Paper

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 insert ignore into journalissuearticles values(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