Pricing models in the energy markets : a quantitative and qualitative approach

Abstract

This master’s thesis offers a comparative study on the performance of the two-factor models versus one-factor models when modeling energy related commodities. The models chosen for the study have been: on the two-factor side, the Schwartz-Smith model, and in the one-factor side, the Ornstein-Uhlenbeck model and the Geometric Brownian motion model. It is also studied the convenience of the medium-term performance of the Schwartz-Smith two-factor model, when projecting commodity prices to the future. The commodities studied in this master’s thesis have been: Brent oil, WTI oil, NBP natural gas, Henry Hub natural gas, API#2 coal index and Spanish, French and German electric power spot prices. The methodology employed in this study has been formed of three different analysis: in-sample analysis, out-sample analysis and real implementation. In the in-sample analysis models are adjusted with the 70% of the available dataset and compared between the in terms of log-likelihood scores and mean absolute errors. The out-sample analysis is devoted to analyze the performance of the Schwartz-Smith two-factor model, previously adjusted in the in-sample analysis, comparing it with the reserved 30% of the reserved observations of the spot price, employing Monte Carlo simulations. Finally, the he Schwartz-Smith two-factor model is adjusted for all commodities with the 100% of the dataset, and projected for a whole natural year employing Monte Carlo simulations. After that results obtained are analyzed in terms of last values and all values, computing statistical measures to compare with historical prices. Once all analysis were done, it could be observed how the Schwartz-Smith two-factor model scored the higher log-likelihood scores in all commodities, obtaining also, the lower mean absolute errors in most of the contracts studied for each commodity, so it can be stated that the Schwartz-Smith two-factor model performs best than any of the one-factor models in every commodity. On the future performance side, it can be concluded that the Schwartz-Smith two-factor model performs appropriately, identifying the past tendencies of the market and acting according to them. Related to electric power commodities, it can be seen how the Schwartz-Smith two-factor model has some difficulties when modeling their prices. The peculiarity of the electric power prices, combined with seasonal patterns that depend on many complex variables, makes the model not to adjust properly.