Option pricing for jump diffussion model with random volatility

Abstract

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.

Citation

Thavaneswaran, A. and Singh, J. (2010), "Option pricing for jump diffussion model with random volatility", Journal of Risk Finance, Vol. 11 No. 5, pp. 496-507. https://doi.org/10.1108/15265941011092077