Electronic Thesis and Dissertation Repository

Degree

Doctor of Philosophy

Program

Statistics and Actuarial Sciences

Supervisor

Mamon, Rogemar.

Abstract

The liberalisation of regional and global commodity markets over the last several decades resulted in certain commodity price behaviours that require new modelling and estimation approaches. Such new approaches have important implications to the valuation and utilisation of commodity derivatives. Derivatives are becoming increasingly crucial for market participants in hedging their exposure to volatile price swings and in managing risks associated with derivative trading. The modelling of commodity-based variables is an integral part of risk management and optimal-investment strategies for commodity-linked portfolios. The characteristics of commodity price evolution cannot be captured sufficiently by one-state driven models even with the inclusion of multiple factors. This inspires the adoption of regime-switching methods to rectify the one-state multi-factor modelling inadequacies. In this research, we aim to employ higher-order hidden Markov models (HOHMMs) in order to take advantage of the latent information in the observed process recorded in the past. This hugely enhances and complements the regime-switching features of our approach in describing certain variables that virtually determine the value of some commodity derivatives such as contracts dependent on temperature, electricity spot price, and fish-price dynamics. Our push for the utility of the change-of-probability-measure technique facilitates the derivation of recursive filtering algorithms. This then establishes a self-tuning dynamic estimation procedure. Both the data-fitting and forecasting performances of various model settings are investigated.

This research work emerged from four related projects detailed as follows. (i) We start with an HMM to model the behaviour of daily average temperatures (DATs) geared towards the analysis of weather derivatives. (ii) The model in (i) is extended naturally by showcasing the capacity of an HOHMM-based approach to simultaneously describe the DATs’ salient properties of mean reversion, seasonality, memory and stochasticity. (iii) An HOHMM-driven jump process augments the HOHMM-based de-seasonalised temperature process to capture price spikes, and the ensuing filtering algorithms under this modelling framework are constructed to provide optimal parameter estimates. (iv) Finally, a multi-dimensional HOHMM-modulated set up is built for futures price-curve dynamics pertinent to financial product valuation and risk management in the aquaculture sector. We examine the performance of this new modelling set up by considering goodness-of-fit and out-of-sample forecasting metrics with a detailed numerical demonstration using a multivariate dataset compiled by the Fish Pool ASA.

This research offers a collection of more flexible stochastic modelling approaches for pricing and risk analysis of certain commodity derivatives on weather, electricity and fish prices. The novelty of our techniques is the powerful capability to automate the parameter estimation. Consequently, we contribute to the development of financial tools that aid in selecting the appropriate and optimal model on the basis of some information criteria and within current technological advancements in which continuous flow of observed data are now readily accessible in real time.

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