Anticipating extreme losses using score-driven shape filters

ABSTRACT

We suggest a new value-at-risk (VaR) framework using EGARCH (exponential generalized autoregressive conditional heteroskedasticity) models with score-driven expected return, scale, and shape filters. We use the EGB2 (exponential generalized beta of the second kind), NIG (normal-inverse Gaussian), and Skew-Gen-t (skewed generalized-t) distributions, for which the score-driven shape parameters drive the skewness, tail shape, and peakedness of the distribution. We use daily data on the Standard & Poor's 500 (S&P 500) index for the period of February 1990 to October 2021. For all distributions, likelihood-ratio (LR) tests indicate that several EGARCH models with dynamic shape are superior to the EGARCH models with constant shape. We compare the realized volatility with the conditional volatility estimates, and we find two Skew-Gen-t specifications with dynamic shape, which are superior to the Skew-Gen-t specification with constant shape. The shape parameter dynamics are associated with important events that affected the stock market in the United States (US). VaR backtesting is performed for the dot.com boom (January 1997 to October 2020), the 2008 US Financial Crisis (October 2007 to March 2009), and the coronavirus disease (COVID-19) pandemic (January 2020 to October 2021). We show that the use of the dynamic shape parameters improves the VaR measurements.