Probabilistic Representation of a Normal Generalized Inverse Gaussian Integral: Application to Option Pricing

Abstract

An analytical probabilistic integral representation for the European call option price in the Hurst-Platen-Rachev subordinated asset price model with generalized inverse Gaussian subordinator is obtained. For the limiting gamma mixing case, the representation yields simpler closed-form formulas for the European risk-neutral call option price in the exponential variance-gamma process by Madan, Carr and Chang. An elementary state-price deflator derivation of the Hurst-Platen-Rachev option pricing formula is also included.