A New Approach to Minimal Variance Hedging of European Options (Part 2: The Pure-Jump Case)

Abstract

This paper addresses the following question: How can a financial institution, which has issued a European option, optimally hedge the payoff of this option by investing into the underlying stock and into the option itself? Here, optimality is measured in terms of minimal variance and the associated optimal hedging portfolio is derived by a sufficient stochastic maximum principle. We further obtain a pricing formula for general European options by an application of Fourier transform methods and deduce the time dynamics of the stochastic option price process. We finally apply our theoretical results to several practical examples.