A vine copula–GARCH approach to corporate exposure management

Christopher M. Wells, Ahmad Farhat, Christopher Richardson and T. Ryan Deering

Abstract

We apply vine copulas with generalized autoregressive conditional heteroscedasticity (GARCH) marginals to the problem of capturing asset dependence and tail dynamics for currency and commodity exposures commonly found in portfolios of global corporates. This approach permits a more realistic description of both the pairwise dependence of asset prices and the large movements of a given asset, ie, fat tails. We compare the cashflow-at-risk, expected tail loss, backtest performance and optimal hedging order for this approach to both the traditional Gaussian model and the analogous t-copula fit for a pair of hypothetical corporate portfolios. Our results suggest that, while more traditional models may be adequate to capture either tail behavior or dependence adequately for a given portfolio at a given time, vine–GARCH models more consistently capture both dependence and tail risks and thus offer a more reliable estimate of the risk held in a portfolio and better hedge performance. In particular, the likelihood of so-called black swan events is much more accurately predicted. Finally, we introduce a set of diagnostics used to measure the relative quality of the developed models for the purposes of model selection, and validate our choice of measures against the results of backtesting.