Dr. Pavel Shevchenko

Title: A generalized grouped t-copula with multiple parameters of degrees of freedom and analysis of tail dependence in currency carry trades. Joint work with Gareth Peters, Matthew Ames, Guillaume Bagnarosa and Xiaolin Luo

Abstract: The t-copula is a popular dependence structure often used in risk management as it allows for modelling the tail dependence between risks and it is simple to simulate and calibrate. The use of a standard t-copula is often criticized due to its restriction of having a single parameter for the degrees of freedom (dof) that may limit its capability to model the tail dependence structure in a multivariate case. To overcome this problem, the grouped t-copula was proposed in the literature, where risks are grouped a priori in such a way that each group has a standard t-copula with its specific dof parameter. To avoid a priori grouping, which is often difficult in practice, recently we proposed a generalized grouped t-copula, where each group consists of one risk factor. We present characteristics, simulation and calibration procedures for the generalized t-copula, including Markov chain Monte Carlo method for estimation and Bayesian model selection. This generalized grouped t-copula is significantly different from the standard t-copula in terms of risk measures such as tail dependence, value-at-risk and expected shortfall. Using historical data of foreign exchange (FX) rates as a case study, we found that Bayesian model choice criteria overwhelmingly favor the generalized t-copula when compared to the grouped and standard t-copulas. We demonstrate the impact of model choice on the conditional Value-at-Risk for portfolios of major FX rates. In addition, using this and other copula models, we analyse tail dependence in baskets of high and low interest rate currencies used for carry trade investment strategies