Utility-indifference pricing of European options with proportional transaction costs

Abstract

Pricing options in a market with transaction costs is an important research topic in quantitative finance. There are basically two categories of approaches to deal with transaction costs. One is discrete hedging strategies under the Black–Scholes framework, another is utility indifference approaches. Hedging approaches are easy to implement, but preference-independent, whereas utility indifference approaches incorporate risk preferences, in general involving lengthy calculations. In a market with transaction costs, trading stocks involves risk so investors’ risk preferences must be taken into consideration. In this paper, we price European options with proportional transaction costs using a utility indifference approach which updates the fraction of one’s total wealth in the risky asset at regular intervals. Our HJB equation for the portfolio without option is two-dimensional instead of three-dimensional as in standard utility indifference approaches. Since the HJB equations could only be solved by a numerical method, our approach provides saving of computing time. Results from our numerical experiments via the finite difference method are presented to illustrate the effects of key option parameters on option prices.