Numerical Simulation for an Optimal Fixed Ratio of Investment in Hedged Portfolio of Commodities and Their Futures Under Schwartz Pricing Model

Abstract

In this thesis, we are interested in a portfolio maximization problem and a numerical method solving for the optimal investment solution associated with our problem. Accordingly, we first present a specific kind of portfolio model which consisted of only two assets, one is a commodity asset, and another one is a futures contract written on this commodity. Through out this study, we assume that the behavior of commodity price in a perfect market is described by the Schwartz two-factor pricing model. In additions, by no-arbitrage assumption, the close-form formula of fair price can be used to derive an instantaneous futures price. In the first part of this study we formulate the portfolio model by considering the generating of portfolio incomes. We give an emphasize on a tradeoff between a proportion of commodities and commodity futures in the portfolio. In order to solve this problem, we employ Monte Carlo technique to simulate the process generating the return on our portfolio model and to approximate the fixed ratio solution of an investment that maximizes the portfolio final wealth. Some numerical examples are given to illustrate the procedure and additional applications are suggested.