European option pricing and hedging with both fixed and proportional transaction costs

Abstract

In this paper we extend the utility based option pricing and hedging approach, pioneered by Hodges and Neuberger (1989) and further developed by Davis, Panas, and Zariphopoulou (1993), for the market where each transaction has a fixed cost component. We present a model, where investors have a CARA utility and finite time horizons, and derive some properties of reservation option prices. The model is then numerically solved for the case of European call options. We examine the e®ects on the reservation option prices and the corresponding optimal hedging strategies of varying the investor’s ARA and the drift of the risky asset. Our examination suggests distinguishing between two major types of investors behavior: the net investor and the net hedger, in relation to the pricing and hedging of options. The numerical results of option pricing and hedging for both of these types of investors are presented. We also try to reconcile our findings with such empirical pricing biases as the bid-ask spread, the volatility smile and the volatility term-structure.