Conditional Tail Expectation for Integrated Processes with Stochastic Volatility

Abstract

The present paper investigates the conditional tail expectation (CTE) for I(1) processes of returns following a general class of multivariate stochastic volatility model. We propose a non-parametric consistent estimate of CTE. The estimate is easy to implement, and the long-run variance of the estimate's limiting normal distributions is derived explicitly. Monte Carlo experiments are conducted to demonstrate the superiority of our approach in terms of coverage ratios for confidence intervals. Results on the estimation of CTE for the long-horizon returns of the S&P 500 index and other indices are also presented.