Option pricing for jump diffussion model with random volatility

A. Thavaneswaran and Jagbir Singh

Journal of Risk Finance, 2010, vol. 11, issue 5, 496-507

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.

Keywords: Options markets; Pricing; Mathematical modelling; Financial instruments; Kurtosis (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:eme:jrfpps:15265941011092077

DOI: 10.1108/15265941011092077

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