Base With A Poor Risk And Transaction Costs, Incomplete Markets In Options Pricing And Hedging Strategy

In this thesis, the pricing and hedging in incomplete markets with transaction cost and basis risk are examined. The Basis Risk model is assumed as the source of market incompleteness (Monoyios , 2004). In order to take transaction cost into account, a very appealing model for pricing European options in the presence of rehedging transaction costs presented by Davis, Panas, and Zariphopoulou (1993) and Hodges and Neuberger (1989) is employed to develop a hedging strategy and an option value for a more realistic and complex model. This model consists of a non-traded asset underlying the claim, and a correlated asset which is used for hedging purposes. A utility maximization approach assuming exponential utility is applied. The option value is given by the solution of a three-dimensional free boundary problem.However, the 'maximization of utility' and three-dimensional free boundary problem leads to the problem is computationally very time-consuming. Then an approximation approach raised by Whalley and Wilmott (1997) is taken to solve this problem. According to the method, this paper analyzes this problem in the realistic case of small transaction costs, applying ideas of asymptotic analysis. The problem is then reduced to an inhomogeneous diffusion equation in only three variables, the two different correlated asset price and time. The advantages of this approach are to increase the speed at which the optimal hedging strategy is calculated. Indeed, a simple analytical expression is found for the hedging strategy involving the correlation of the two assets. Finally, a Monte Carlo implementation is performed thus providing insight into the problem of hedging under a more realistic set of market assumptions.