Option pricing for jump diffusion model with random volatility

Purpose – Option pricing based on Black-Scholes model is typically obtained under the assumption that the volatility of the return is a constant. The purpose of this paper is to develop a new method for pricing derivatives under the jump diffusion model with random volatility by viewing the call price as an expected value of a truncated lognormal distribution. Design/methodology/approach – Using Taylor series expansion the call price under random volatility is expressed as a function of kurtosis of the observed volatility process and applied to various class of GARCH models. Findings – A modified option pricing formula is developed for jump diffusion process model with random volatility. Originality/value – The main contribution of the paper is the development of a kurtosis-dependent option pricing formula for a jump diffusion model with random volatility.