Applications of Copula Theory and Regime Switching in Finance

There is well-documented evidence that the dependence structure of financial assets is often characterized by considerable time variation. Financial markets are repeatedly subjected to episodes of rapid growth and dramatic decline of asset prices, and the recent financial crisis reinforced the need to model extreme events and sudden changes in the behaviour of financial assets. In particular, financial returns have been shown to exhibit stronger tail dependence during financial downturn. That is, extreme negative events are highly correlated and tend to cluster together. Traditional static models, such as the multivariate Normal distribution, are unable to capture these characteristics of the dependence structure, which resulted in copula models attracting attention and becoming popular over the last decade. Copulas provide greater flexibility by allowing the dependence structure to be modelled separately from marginal distributions. Furthermore, a rich class of higher dimensional copulas with various types of asymmetric tail dependence can be constructed through the use of vine copulas. The objective of this research work is take into account the time-varying dependence structure by combining copula theory with regime switching models that exhibit Markov property. In this class of models the dependence structure is assumed to switch between regimes according to a hidden state variable, with the purpose of accurately describing the behaviour of financial time series. Furthermore, the goal is to extend this class of models to higher dimensions where complex dependence characteristics are also present. Applications of these models are not restricted to finance and can be useful in any context where the dependence structure amongst random variables changes over time.