Extreme value modelling with application in finance and neonatal research
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
Modelling the tails of distributions is important in many fields, such as environmental science, hydrology, insurance, engineering and finance, where the risk of unusually large or small events are of interest. This thesis applies extreme value models in neonatal and finance studies and develops novel extreme value modelling for financial applications, to overcome issues associated with the dependence induced by volatility clustering and threshold choice. The instability of preterm infants stimulates the interests in estimating the underlying variability of the physiology measurements typically taken on neonatal intensive care patients. The stochastic volatility model (SVM), fitted using Bayesian inference and a particle filter to capture the on-line latent volatility of oxygen concentration, is used in estimating the variability of medical measurements of preterm infants to highlight instabilities resulting from their under-developed biological systems. Alternative volatility estimators are considered to evaluate the performance of the SVM estimates, the results of which suggest that the stochastic volatility model provides a good estimator of the variability of the oxygen concentration data and therefore may be used to estimate the instantaneous latent volatility for the physiological measurements of preterm infants. The classical extreme value distribution, generalized pareto distribution (GPD), with the peaks-over-threshold (POT) method to ameliorate the impact of dependence in the extremes to infer the extreme quantile of the SVM based variability estimates. Financial returns typically show clusters of observations in the tails, often termed “volatility clustering” which creates challenges when applying extreme value models, since classical extreme value theory assume independence of underlying process. Explicit modelling on GARCH-type dependence behaviour of extremes is developed by implementing GARCH conditional variance structure via the extreme value model parameters. With the combination of GEV and GARCH models, both simulation and empirical results show that the combined model is better suited to explain the extreme quantiles. Another important benefit of the proposed model is that, as a one stage model, it is advantageous in making inferences and accounting for all uncertainties much easier than the traditional two stage approach for capturing this dependence. To tackle the challenge threshold choice in extreme value modelling and the generally asymmetric distribution of financial data, a two tail GPD mixture model is proposed with Bayesian inference to capture both upper and lower tail behaviours simultaneously. The proposed two tail GPD mixture modelling approach can estimate both thresholds, along with other model parameters, and can therefore account for the uncertainty associated with the threshold choice in latter inferences. The two tail GPD mixture model provides a very flexible model for capturing all forms of tail behaviour, potentially allowing for asymmetry in the distribution of two tails, and is demonstrated to be more applicable in financial applications than the one tail GPD mixture models previously proposed in the literature. A new Value-at-Risk (VaR) estimation method is then constructed by adopting the proposed mixture model and two-stage method: where volatility estimation using a latent volatility model (or realized volatility) followed by the two tail GPD mixture model applied to independent innovations to overcome the key issues of dependence, and to account for the uncertainty associated with threshold choice. The proposed method is applied in forecasting VaR for empirical return data during the current financial crisis period.