Essay on Tail Risk Measure with Application in Volatility Forecast

Abstract

In this paper, we study the tail risk measure in nancial market. Recently, Kelly and Jiang (2014) propose a measure based on Hill (1975)'s method. They arbitrarily estimate the Hill tail risk by xing the threshold at the 0.05 empirical quantile level. We show by various simulation experiments that their measure is very sensitive to the choice of thresholds. To endogenize the threshold choice, we propose a novel composite Pareto-Normal model for tail risk measure. Using the variance decomposition, our tail risk measure natually maps to the overall volatility. We show that the induced total volatility from our estimated tail risk measure matches the market volatility well, whereas that of Kelly and Jiang's Hill estimate deviates substantially from the market volatility. Finally, we investigate the predictive power of tail risk on realized volatility. The results show that our proposed method outperform the Hill estimate in volatility forecast.