Numerical Option Pricing under Levy Process with Minimal Martingle Measure

Abstract

The classic Black Scholes option pricing model assumes that the returns follows Brownian Motions, but return processes may have discontinuous definitely or infi nitely many positive or negative jumps, leading to non-normal distributions.In such scenario, we can consider the Levy process as one of the suitable process for pricing contingent claims of a stock. But because jumps of random sizes, the market is incomplete and there is not an unique martingale measure. In such case its difficult to compute the option values both analytically and numerically because the price process distribution is unknown.Here, we study numerical approach for pricing options with an equivalent martingale measure as per Follmer Schweizer minimal measure which has minimum risk.We calculate the call price with sensitivities numerically by Inverse Laplace Transform techniques like Gaver Stehfest.