Inhomogeneous Dependency Modelling with Time Varying Copulae

Abstract

Value-at-Risk (VaR) of a portfolio is determined by the multivariate distribution of risk factor increments. The RiskMetrics approach, a widely used methodology for VaR estimation, is based on the assumption of multivariate normality. This paper performs a better method for VaR estimation. The distribution of returns is modelled by copulae with adaptively estimated time varying parameters. The copula approach frees the modelling from the usual normality assumptions resulting in multivariate distributions that better describe the empirical characteristics of financial returns. The adaptive estimation is based on the assumption of local homogeneity: for every time point there exists an interval of time homogeneity in which the copula parameter can be well approximated by a constant. This interval is recovered from the data using local change point analysis. For a stock portfolio, copulae with time varying parameters are estimated and the VaR simulated accordingly. Backtesting underlines the improved performance of adaptive time varying copulae.