Robust Conditional Variance and Value-at-Risk Estimation

Abstract

This article is concerned with robust conditional variance and value-at-risk (VaR) estimation. Losses due to idiosyncratic events can have a disproportionate impact on traditional VaR estimates, upwardly biasing these estimates, increasing capital requirements, and unnecessarily reducing the available capital and profitability of financial institutions. We propose new bias-robust conditional variance estimators based on weighted likelihood at heavy-tailed models, as well as VaR estimators based on the latter and on volatility updated historical simulation. The new VaR estimators also use optimally chosen rolling window length and smoothing parameter value. A simulation study illustrates the strong performance of the proposed methodology and highlights the model's ability to mitigate the potentially costly upward bias generated by idiosyncratic shocks. Real data examples and extensive backtesting results illustrate the impact of idiosyncratic shocks on other VaR estimators.