Pricing and Hedging using Hedge Monte-Carlo Method

Abstract: In this master’s thesis The Hedge Monte-Carlo method (HMC) is evaluated. The HMC method is used to price financial derivatives and at the same time obtain optimal hedge portfolios. The optimal hedge is of great importance as it enables risk management in option trading. The advantage of this method is also that different types of options with features like path-dependent and early exercise can be priced. The evaluation is based on the quality of the price and hedge estimates of European options. To further evaluate the performance of the method the price process of the underlying asset followed initially a Geometric Brownian Motion process (GBM) and then the Normal Inverse Gaussian process (NIG). Several different scenarios are considered in the evaluation of retrieving good prices and hedges, i.e. different times to maturity, initial stock prices and variances. Results shows that the method is very promising when considering the quality of the price and as for the quality of the hedge good levels are obtained for GBM when the option is in the money. A desirable feature as the probability of exercise of an in the money option is very high. For options where the underlying asset follows NIG acceptable levels on the hedging errors were difficult to obtain. As the performance of the method is measured on both good prices and good hedges, the NIG process isn’t as suitable as the GBM process when the HMC method i used.