Alpha-stable, normal inverse Gaussian and multi-factor models for spot and futures modelling in natural gas.

摘要

In this thesis, we aim to find suitable models for modelling the natural gas futures curve as well as modelling the gas spot prices. We begin introducing natural gas storages, which are key drivers of the futures, spot prices and other derivatives associated with the industry. This also gives us an intuition on the necessity for "convenience yield" in gas models.;We also introduce Levy processes to capture spot dynamics and try to model the futures curve based on the availability of the futures price via the Characteristic Function. We consider OU and CIR type processes with Levy processes instead of Wiener Processes as the noise driving term. The processes used are alpha-stable Levy processes as well as the normal inverse gaussian (NIG) Process.;Two different methods of calibration are used, one of them is an estimator based on finding the Empirical Characteristic Function (ECF) of the observations and making use of the availability of the characteristic function of Levy processes to directly find the minimum of the parameters. We also use MLE to estimate the parameters, and we can see the advantages and disadvantages of the two estimation methods.;We then look at the implication of the parameters estimated on the futures curve and also go ahead to calculate the risk neutral measure of the futures curve.;We then begin reviewing the literature in natural gas and energy's, spot and futures modelling. A two factor spot model based on Xu [14] is introduced, as well as a new technique, where the underlying futures curve is stripped off at every stage by linear regression. This approach allows us to strictly model the underlying curve, the parameters are estimated by maximum likelihood estimation (MLE).