Modeling the dependence between stock index and exchange returns with copula-extreme value theory based semiparametric approaches and their applications in risk management.

摘要

Measuring Value-at-Risk (VaR) is an important function in financial risk management. One of the most popular methods of computing VaR is the Monte Carlo simulation, which focuses on utilizing an appropriate approach to estimate the dependence between returns of financial assets. However, the existence of fat-tailed, skewed distributions and non-linear relationships of financial asset returns makes conventional Pearson product-moment coefficient approach incongruous. To overcome this difficulty, the current research applies the extreme value theory (EVT) in order to model the tails of the return distributions and copula functions to build the joint distribution of returns. More specifically, in the copula-EVT-based methodologies, the marginal distributions of asset returns are modeled using a semiparameter approach in which the distribution center is modeled by a nonparameter empirical distribution and the distribution tails are modeled by the generalized Pareto distribution (GPD) with parameters; furthermore, three copula functions---Gaussian, Gumbel, and Clayton---are applied to model the general, upper-tail, and lower-tail dependencies.;To test the advantages of these approaches, six Asian countries were selected based on their different stock index and foreign exchange return distribution shapes, and backtestings were conducted to examine the Monte Carlo VaRs simulated from the correlation coefficients estimated by the Pearson product-moment coefficient, the Gaussian copula, the Gaussian copula-EVT, the Gumbel copula, the Gumbel copula-EVT, the Clayton copula, and the Clayton copula-EVT. The results suggest that the Clayton copula-EVT has the best performance regardless of the shapes of the return distributions.