Utility based option pricing with proportional transaction costs and diversification problems: an interior-point optimization approach

Abstract

The purpose of the present work is to examine the financial problem of finding the reservation purchase price of a European call option written on a risky security when there is proportional transaction costs in the market. Existing papers within this area have all simplified the analysis by considering only one risky security and assumed exponential utility functions. The goal of the present paper is to suggest an approach to compute the reservation price of an option in an economy with more than one risky security and where trade involves transaction costs. Furthermore, the new approach enables us to investigate to what extent the above mentioned simplifications affect the reservation prices. We consider an economy with a riskless security, two risky securities, and agents' with HARA utility functions. We suggest an approach to compute reservation prices using convex optimization. Unfortunately, the proposed optimization models become large in terms of the number constraints and variables. However, using a newly developed interior-point algorithm, we manage to solve problems of an interesting size. The major findings are: (i) the investor's reservation purchase price of a European call option is almost insensitive to the functional form of the utility function, but sensitive (only slightly) to the initial level of absolute risk aversion, and (ii) the presence of diversification opportunities does not affect the reservation price in any unique way.