Utility Based Option Evaluation with Proportional Transaction Costs

Abstract

We examine the problem of finding investors' reservation prices of European contingent claims in a continuous time finite horizon economy with proportional transaction costs. We derive analytically numerous properties of reservation prices reflecting their dependency on the size of the option position, the risk aversion, and the initial wealth. For the special case of HARA utility functions, we consider the so-called marginal reservation prices, i.e. unit reservation prices of infinitesimal positions of the contingent claim, and prove that these are independent of the initial wealth and the parameters of the utility function, except for the exponent. Furthermore, we present numerical examples suggesting that the marginal reservation prices are, for reasonable parameter values, insensitive to the drift of the underlying security and the exponent of the HARA utility function.