A Utility Based European Option Pricing Model With Transaction Costs

As the cornerstone of the theory of the derivatives, option pricing models play an important role in the thriving global derivatives market. But the classical theory, Black-Scholes model and its revisions, can not take transaction costs and the risk aversion of investors into account, therefore fails in some degree at its application in the real market. The rapid development of the derivatives market calls for a new theory that can handle these two important factors above.In this paper, an efficient model is developed to price European options in the presence of proportional transaction costs, basing the pricing model of Davis. We build a market model, import utility functions, and compare the conditions of utility maximization in order to find the regions of different investor s optimal strategy, using the Hamilton-Jacobi-Bellman equation (HJB equation).Through comparing the utility maximization in different regions with Hyperbolic Absolute Risk Aversion (HARA) functions, we find the equations which include the solutions of option reservation prices.The exciting feature of this model is that the reservation purchase price of option is a decreasing function of the level of risk aversion, and the reservation write price is an increasing function of the level of risk aversion.