| Abstract [eng] |
This thesis investigates measures of concordance, namely Kendall’s tau, Spearman’s rho, and Blomqvist’s beta, and their relationship with copula theory, with applications to dependence modeling in financial markets. Measures of concordance provide a nonparametric framework for assessing the dependence between random variables independently of their marginal distributions, which makes them particularly suitable for financial data that often exhibit nonlinear dependence structures. The theoretical part of the thesis is based on Sklar’s theorem, which allows a joint distribution function to be decomposed into marginal distribution functions and a copula, as well as on Scarsini’s axioms, which characterize the class of concordance measures. The empirical part of the study analyzes five years of daily closing price data for ten selected companies and indices: Microsoft(MSFT), S\&P 500(SP500), SAP(SAP), Nasdaq(NDAQ), Apple(AAPL), SAPGF(SAPGF), Nestlé(NSRGY), the German DAX index(DAX), the iShares MSCI France ETF(EWQ), and AstraZeneca(AZN). The data were obtained from the publicly available financial platform \href{https://stocknear.com}{stocknear.com}. The price series are transformed into logarithmic returns, concordance measures are computed, and dependence structures are modeled using Gaussian, Student’s t, Clayton, and Gumbel copulas. Monte Carlo simulations show that Kendall’s $\tau$ reliably reproduces the theoretical dependence structure across different copula families, while the Gaussian and Student’s t copulas provide the best fit to empirical financial market data. The Student’s t copula exhibits strong tail dependence and generates higher portfolio risk for the same values of Kendall’s tau. The results indicate that Kendall’s tau is the most stable and informative empirical measure of dependence, while Spearman’s rho typically attains larger values and Blomqvist’s beta the smallest ones. Portfolio risk analysis reveals that the portfolio standard deviation increases monotonically with Kendall’s tau, with a more pronounced growth in the case of the Student’s t copula due to tail dependence effects. The thesis concludes that measures of concordance and copula models provide a solid mathematical foundation for advanced financial risk modeling and can be effectively applied to portfolio optimization and stress testing. |
