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.
| Identifer | oai:union.ndltd.org:canterbury.ac.nz/oai:ir.canterbury.ac.nz:10092/4024 |
| Date | January 2010 |
| Creators | Zhao, Xin |
| Publisher | University of Canterbury. Mathematics and Statistics |
| Source Sets | University of Canterbury |
| Language | English |
| Detected Language | English |
| Type | Electronic thesis or dissertation, Text |
| Rights | Copyright Xin Zhao, http://library.canterbury.ac.nz/thesis/etheses_copyright.shtml |
| Relation | NZCU |
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