European Option Pricing and Hedging with Both Fixed and Proportional Transaction Costs

Abstract

In this paper we provide a systematic treatment of the utility based option pricing and hedging approach in markets with both fixed and proportional transaction costs: We extend the framework developed by Davis, Panas and Zariphopoulou (1993) and formulate the option pricing and hedging problem. We propose and implement a numerical procedure for computing option prices and corresponding optimal hedging strategies. We present a careful analysis of the optimal hedging strategy and elaborate on important differences between the exact hedging strategy and the asymptotic hedging strategy of Whaley and Wilmott (1994). We provide a simulation analysis in order to compare the performance of the utility based hedging strategy against the asymptotic strategy and some other common strategies.

Keywords: Option pricing, option hedging, transaction costs, stochastic impulse control, Markov chain approximation

JEL Classification: C61, G11, G13