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

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 derive some properties of reservation option prices. We suggest and implement discretization schemes for computing the reservation option prices. The numerical results of option pricing and hedging are presented for the case of European call options and the investors with different levels of ARA. We also try to reconcile our findings with such empirical pricing bias as the volatility smile.