A Mean-Reverting Stochastic Volatility Option-Pricing Model With An Analytic Solution

Abstract

The five essays in this dissertation are all concerned with how commodity price uncertainty affects the valuation of real and financial assets. Focusing on the stochastic process approximating the price process of the commodity, a time-inhomogeneous mean reverting process is suggested and used in the valuation of a pulp mill. Also an analytic approximation and a parameter estimation procedure to a stochastic volatility option-pricing model are developed. Generally, the large valuation differences and hedging errors that occur for different assumptions about the price process indicate the importance of an appropriately specified price process. The dissertation provides examples of this. The question of whether commodity prices are mean reverting or follow a random walk is also studied. Using a large database with close to 300 different commodities, econometric tests favour a random walk. There are very few exceptions. However, when applied to an option pricing model, the time-inhomogeneous mean reverting process gives smaller hedging errors than the traditional Black-Scholes model based on a random walk. The results are therefore inconclusive, although mean reversion seems more predominant than econometric tests reveal.