Estimating tail-risk using semiparametric conditional variance with an application to meme stocks

In this paper, we propose using Mishra, Su, Ullah’s (2010) semiparametric variance to estimate Value at Risk (VaR) and Expected Shortfall (ES). Although the variance estimate is established in the literature, it has not been applied to VaR and ES estimation. Here the returns’ variance is estimated using Mishra, Su, Ullah’s (2010) conditional semiparametric estimator, and the standardized residuals’ distribution is fitted nonparametrically. In order to reduce possible misspecification bias, the proposed estimators decouple the assumption of the returns’ distribution and the variance estimation. Empirical and simulated data are used to compare the performance of the new estimators against existing parametric and nonparametric VaR and ES models, both conditional and unconditional. The estimators are further applied to daily returns of certain meme stocks to estimate tail risk and test the performance of the estimators during periods of extreme volatility. Compared to the models studied, the proposed conditional, semiparametric VaR model produces fewer violations, and violations without a recognizable pattern - upholding the regulatory requirements. The expected shortfall estimated by the conditional, semiparametric model is also closest to the observed mean of the violations.