Multivariate DCC GARCH and Dynamic Copula models for VaR analysis

he diploma thesis deals with financial time series volatility models. The aim of the work is to firstly describe in detail two approaches to model the time series volatility, verify them and then use both approaches in an empirical study. The first approach is based on dynamic conditional correlation general- ized autoregressive conditional heteroskedasticity models compared to the second approach, which are copula functions. The copula functions approach is then fur- ther divided into copula function with constat parameters and copula functions with dynamic parameters. The models are used for CVaR portfolio optimiza- tion problem and results are compared with the classical approach of portfolio optimization theory based on unconditional estimates. Resulting portfolios were compared using four metrics that reflect realized portfolio returns and combina- tion of realized portfolio returns and risk. The results showed that using copula functions when optimizing portfolio by minimizing CVaR of portfolio expecting minimum return surpassed the classical approach and DCC GARCH approach.