Estimating Value At Risk

Abstract

Significantly driven by JP Morgan's RiskMetrics system with EWMA (exponentially weighted moving average) forecasting technique, value-at-risk (VaR) has turned to be a popular measure of the degree of various risks in financial risk management. In this paper we propose a new approach termed skewed-EWMA to forecast the changing volatility and formulate an adaptively efficient procedure to estimate the VaR. Differently from the JP Morgan's standard-EWMA, which is derived from a Gaussian distribution, and the Guermat and Harris (2001)'s robust-EWMA, from a Laplace distribution, we motivate and derive our skewed-EWMA procedure from an asymmetric Laplace distribution, where both skewness and heavy tails in return distribution and the time-varying nature of them in practice are taken into account. An EWMA-based procedure that adaptively adjusts the shape parameter controlling the skewness and kurtosis in the distribution is suggested. Backtesting results show that our proposed skewed-EWMA method offers a viable improvement in forecasting VaR.