Applications Of Copula Methods In Financial Risk Management

Financial risk management is playing an increasingly important role in helping individuals, financial institutions, or even countries avoid risks and achieve a secure investment environment. It is defined as a process of assessing and managing the financial risks facing an investor by reducing exposure to the identified risks. Measuring financial risks accurately and then making efficient investment decisions may provide an investor with competitive advantages and considerable profits. The measurement of financial risks is actually constricted by the real-life financial variables. However, abundant evidence shows that financial variables usually exhibit fat tails, skewness, and asymmetric dependence. These stylized features of financial variables challenge the traditional methods of financial risk management based on normally-distributed hypothesis from three aspects. First, the distribution of univariate variable cannot be sufficiently fitted by univariate normal distribution, or alternative elliptical distributions. Second, normal distribution of multivariate variables cannot capture their excess kurtosis and skewness despite simple tractability. Therefore, it can underestimate dependency risks of multivariate financial variables. Last, linear correlation, usually used to describe the dependency of different variables in traditional portfolio risk management, is also not enough when the joint distribution of different variables is non-elliptical. To solve these problems this dissertation resorts to a promising method based on copulas combined with GARCH and Realized Volatility models to investigate risks of multivariate financial variables.The main achievements of this dissertation are threefold. Firstly, copulas combined with GARCH and Realized Volatility models are used to construct the multivariate distributions, and then to estimate portfolio risks in financial markets. The results show that models based on copulas to fit financial data perform better than the traditional models. Secondly, different marginal models, such as GARCH and Realized Volatility models, have significant effect on the portfolio Value at Risk. Finally, there exists significant skewness in marginal distribution, as well as in dependence structure. Therefore, the skewed Student-t distribution is better fitted to seleceted datasets than the normal or Student-t distributions. Structurally, this dissertation is organized as follows. Chapter one emphasizes the importance of portfolio financial risk management, and illustrates well-known methods of measuring financial risks-Value at Risk. Chapter2introduces the background knowledge of dependence and the theory of copulas. In the case of financial time series, the dissertation considers time-invariant and time-varying copula models. Parameter estimation and model selection of copulas are also explained in this chapter. Modelling of marginal distributions is presented in Chapter3. GARCH and Realized Volatility models are fitted to the marginal distributions of financial variables of interest, respectively. Chapter4illustrates ways to use the constructed model based on copulas to forecast Value at Risk by Monte Carlo Simulation. To evaluate the performance of different constructed models, backtesting techniques are applied. Empirical results are detailedly presented in Chapter4. Finally, conclusions and suggestions are outlined in Chapter5.