Electronic Thesis and Dissertation Repository


Doctor of Philosophy


Statistics and Actuarial Sciences


Dr. Matt Davison


This thesis investigates quantitative techniques for trading strategies on two commodities, the difference of whose prices exhibits a long-term historical relationship known as mean-reversion. A portfolio of two commodity prices with very similar characteristics, the spread may be regarded as a distinct process from the underlying price processes so deserves to be modeled directly. To pave the way for modeling the spread processes, the fundamental concepts, notions, properties of commodity markets such as the forward prices, the futures prices, and convenience yields are described. Some popular commodity pricing models including both one and two factor models are reviewed. A new mean-reverting process to model the commodity spot prices is introduced. Some analytical results for this process are derived and its properties are analyzed. We compare the new one-factor model with a common existing one-factor model by applying these two models to price West Texas Intermediate (WTI) crude oil, and discuss its advantages and disadvantages. We investigate the recent behavioral change in the location spread process between WTI crude oil and Brent oil. The existing three major approaches to price a spread process namely cointegration, one-factor and two-factor models fail to fully capture these behavioral changes. We, therefore, extend the one-factor and two-factor spread models by including a compound Poisson process where jump sizes follow a double exponential distribution. We generalize the existing one-factor mean-reverting dynamics (Vasicek process) by replacing the constant diffusion term with a nonlinear term to price the spread process. Applying the new process to the empirical location spread between WTI and Brent crude oils dataset, it is shown how the generalized dynamics can rigorously capture the most important characteristics of the spread process namely high volatility, skewness and kurtosis. To consider the recent structural breaks in the location spread between WTI and Brent, we incorporate regime switching dynamics in the generalized model and Vasicek process by including two regimes. We also introduce a new mean-reverting random walk, derive its continuous time stochastic differential equation and obtain some analytical results about its solution. This new mean-reverting process is compared with the Vasicek process and its advantages discussed. We showed that this new model for spread dynamics is capable of capturing the possible skewness, kurtosis, and heavy tails in the transition density of the price spread process. Since the analytical transition density is unknown for this nonlinear stochastic process, the local linearization method is deployed to estimate the model parameters. We apply this method to empirical data for modeling the spread between WTI crude oil and West Texas Sour (WTS) crude oil. Finally, we apply the introduced trading strategies to empirical data for the location spread between WTI and Brent crude oils, analyze, and compare the profitability of the strategies. The optimal trading strategies for the spread dynamics in the cointegration approach and the one-factor mean-reverting process are discussed and applied to our considered empirical dataset. We suggest to use the stationary distribution to find optimal thresholds for log-term investment strategies when the spread dynamics is assumed to follow a Vasicek process. To incorporate essential features of a spread process such as skewness and kurtosis into the spread trading strategies, we extend the optimal trading strategies by considering optimal asymmetric thresholds.