Financial data can exhibit many characteristics, some include asymmetry, nonlinearity, high dimensionality and time-varying dependence. Each of these poses their own unique challenges in financial modelling.
The thesis aims to better handle financial data by proposing a mixture of copulas model consisting of Gaussian and Archimedean copulas. The Gaussian copula has been used in areas of finance and economics in activities such as pricing and structuring of financial derivatives and portfolio applications. However, the Gaussian copula does not address the issue of asymmetry, which motivates the idea of mixing the Gaussian copula with other copulas that can handle asymmetric dependence. One class of such copulas are the Archimedean copulas, which are able to emit lower and upper tail dependence, that is, the rare events occuring in the tails.
Provided in the thesis is the model specifications of the mixture of copulas model and a proposed estimation strategy to handle an application in higher dimensions. The model is applied to the financial stock return data representing the recent Chinese stock market crash in the year 2015. Specifically, the daily returns of the 50 largest firms by market capitalization on the Shanghai Stock Exchange are used as an illustration.