Essays on stochastic models of the US natural gas market

Abstract

The evolution of commodity markets calls for advanced models to capture and analyze complex properties of the markets. This dissertation focuses on a large sector: the US natural gas market, and consists of three papers where three stochastic models are proposed to investigate the distinct characteristics of the market. Model parameters are estimated by maximizing the likelihood functions with the aid of the Kalman filter and the Kim filter.

The first paper explores the multi-factor structure and risk premiums implied from the natural gas spot and futures. The model features a two-short-term/one-long-term structure, time-varying risk premiums and a seasonal risk premium. We find that three factors and the seasonal risk premium are needed to accurately describe the term structure of the natural gas futures. The coefficients for the time-varying risk premiums are significant. We also reveal a negative correlation between the seasonal risk premium and the uncertainty of the natural gas total consumption.

The second paper deals with the changing slope of the natural gas futures long-end curve. We develop a Markov regime-switching model with a regime-dependent drift term under the equivalent martingale measure. The model has two factors and three regimes to capture three basic cases of the changing slope. The estimation results show that the model is able to produce a downward/flat/upward slope in each regime and classifies the regime status generally consistent with the observation. Through detailed model comparisons, we find that models without the regimes or the two factors lead to poor results.

The third paper considers the variance dynamics of the natural gas futures returns. We directly model and estimate the variance dynamics. The model incorporates two variance factors, the Samuelson effect and seasonality. The estimation is implemented using a dataset of synthesized variance swap rates on the futures across the term-structure dimension. The rates are computed by integrating prices of relevant futures options across the strike dimension. The results indicate the existence of the Samuelson effect, seasonal variance and a negative variance risk premium. In addition, the two-factor setup exhibits its advantage along the term-structure dimension.