Copula based dependence structure modelling with applications to financial markets

Abstract

Along with development of technology, financial markets are becoming more complex and fluctuations of financial time series have risen higher than before. There is abundant evidence showing that financial time series now exhibit some characteristics like fat tail, skewness and asymmetric dependence. These stylized features of financial variables challenge the traditional methods of financial time series modelling based on the assumption of normal distribution in three aspects. Firstly, distribution of univariate variable cannot be appropriately fitted by normal distribution. Secondly, the multivariate normal distribution is not able to capture the excess skewness and kurtosis of multivariate variables despite its simple tractability, which underestimates the dependence risks of financial multivariate variables. Finally, the linear correlation, used to depict the dependence between different variables, is also insufficient since the joint distribution of different financial time series is non-elliptical. To solve the above problems, we resort to copula to investigate the dependence structure of multivariate financial variables in this thesis. Firstly, this thesis applies the theory of copula in European electricity markets by investigating the dependence between electricity spot markets at the heart of Europe including France, Germany, Austria and Switzerland based on eleven different copulas with both time-invariant and time-varying parameters. The empirical results show that time-varying Student-t copula is the best model to fit the three sample data. A positive sign of upper and lower dependence indicates that spot electricity prices in France, Germany/Austria and Switzerland tend to move in the same direction. Also, the results indicate that the dependence between European electricity markets is time-varying and asymmetric, which means that traditional models such as Pearson’s correlation are inappropriate to measure the correlation between these markets. Secondly, this thesis estimates the Value-at-Risk (VaR) of an equally weighted portfolio of Onshore and Offshore RMB exchange rates based on copula models. The empirical results show that time-invariant Student-t copula is the best model to fit the sample data. Then we choose five best fitted constant models to forecast VaR of the portfolio. In this way, the proposed model can help business practitioners and government better track the risk evolutions and make better decisions. Thirdly, this thesis investigates the dependence among RMB exchange rates against US dollar (USD) the euro (EUR), Japanese yen (JPY) and South Korea’s won (KRW) based on vine copula and further forecast the portfolio risk based on VaR. The empirical results show that the D-vine copula performs better than other vine structures based on the AIC criteria. Moreover, according to the backtesting results, both D-vine and C-vine copulas are able to forecast the portfolio VaR accurately. However, the loss functions show that C-vine copula has better performance in forecasting VaR of the portfolio. To sum up, this thesis proposes use of copula to analyze the dependence structure of financial time series in different financial markets including European electricity markets and Chinese RMB exchange rate markets. These models provide effective solutions for practical problems in financial markets. The thesis expects to help business practitioners and individual investors better understand price movement and reduce their exposure to the identified financial risks.

Date of Award	2 Oct 2015
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Siu Wai William CHUNG (Supervisor) & Kin Keung LAI (Supervisor)