Exploring the commodity market: pricing Asian options with stochastic convenience yields and jump diffusions, and the study of the trading-date seasonality

The main underlying theme of this PhD thesis is the study of the commodity market. We first begin by pricing Asian options based on the Schwartz (1997) model. Asian options have been widely used in the global commodity market for its unique feature of using the average price instead of the price at maturity to determine the payoff function. We attempt to price Asian options written on commodity related future contracts under the model of three stochastic factors, namely, the spot price, the convenience yield, and the interest rate. We obtain closed-form solutions of geometric average Asian options, which will serve as control variates to price arithmetic average Asian options by Monte Carlo simulation. Our results show significant improvements in terms of simulation accuracy. We also manipulate the parameters of the model to see how the options prices behave accordingly. Next, a jump diffusion process is introduced to the model. Although analytical solution is unobtainable, a new numerical method is found to price arithmetic average Asian options with jumps, which lead to observable accuracy improvements. During our journey to further explore the behaviour of the commodity futures prices, we found a new seasonality pattern. The traditional idea of seasonality in the future market relates to the maturity date of a future contract. However, we find a new seasonal pattern in the futures prices that relates to the trading dates. We decide to explore such phenomenon in three energy commodity markets, namely, natural gas, gasoline, and crude oil. To conduct our initial empirical research, we design the so-called backward curve, as opposite to the forward curve, to visually illustrate the pattern of the trading-date seasonality. We find that when the prices of a collection of future contracts with the same maturity month can be averaged over the different years, the seasonality of trading dates is obvious to observe. We also find an interesting change of behaviour in the natural gas futures prices. Then, we conduct multiple statistical tests to further confirm our findings, which include the Kruskal-Wallis test, the autocorrelation test, and the power spectrum test. The results show strong evidence to support the existence of the trading-date seasonality. In light of what we find in the second chapter, we decide to look further into the new seasonality that relates to the trading dates, by constructing a trading strategy that is designed specifically to profit from the new seasonal pattern in three commodity markets. The results show promising profit over the long run for all three commodities, with relatively low risks. Then, we establish a model based on the Sorensen (2002) model, with the introduction of an arbitrage factor to capture the trading-date seasonality. We calibrate the model using the Kalman filter in the state space form, and the results suggest that the vast majority of the parameters are highly statistically significant in explaining the movement of the futures prices in the three commodity markets