Correlation and risk measurement modeling: A Markov-switching mixed Clayton copula approach

Correlation and risk measurement are important for reliability and safety evaluation of many practical systems. Clayton copula and 180 degrees rotated Clayton copula are suitable for measuring the lower-lower tail correlation and the upper-upper tail correlation reflecting positive correlation, respectively. The 90 degrees rotated Clayton copula and 270 degrees rotated Clayton copula are severally appropriate for measuring the lower-upper tail correlation and the upper-lower tail correlation reflecting negative correlation. In this paper, considering the possibility of variable correlation state transition under the condition of unfixed component copula function weight, a mixed Clayton copula function of Markov transformation is constructed by using the above four kinds of Clayton copula, and the marginal distributions of variables are modeled by combining ARMA (p, q) - GARCH (m, n) model, then the correlation and its corresponding risk measurement models are constructed based on mixed Clayton copula. Finally, the empirical results based on crude oil futures price and Chinese CSI 300 stock index futures price show that, compared with time-varying Normal copula, time-varying T copula and Markov-switching GRG copula, Markov-switching mixed-Clayton copula model can achieve better effect of parameter estimation. The calculation on the correlation and risk measurement further verifies the validity and reliability of the models.