A two-stage approach to allowing time-varying volatility and heavytailed distribution for value-at-risk estimation

Abstract

This study proposes a two-stage approach for estimating Value-at-Risk (VaR) that can simultaneously reflect two stylized facts displayed by most asset return series: stochastic volatility and the heavy-tailedness of conditional return distribution over short horizons. The proposed method combines the power exponentially weighted moving average (EWMA) model to estimate the conditional volatility and extreme value theory (EVT) to estimate the tail of the innovation distribution. In particular, for minimizing bias in the estimation procedure, this study uses the kurtosis coefficients calculation in a reverse way to estimate the power parameter of the power EWMA estimator. Moreover, this study makes minimal assumptions about the underlying innovation distribution and concentrates on modeling its tail using the non-parametric Hill estimator for the shape parameter of the extreme value distribution. To validate the proposed method, this study conducted an empirical investigation on four stock index futures return series: FTSE-100, Nikkei 225, S&P 500 and HSI. The empirical results show that the proposed method provides improved forecasts of the VaR when the confidence level exceeds 99%.

Keywords and phrases:

• Value-at-Risk
• power EWMA estimator
• extreme value theory
• backtesting
• hill estimator