Statistica Sinica 26 (2016), 1631-1648
Abstract: The present paper investigates the distribution quantile for integrated portfolio returns that follow a general class of multivariate stochastic volatility model. We propose a non-parametric quantile estimate that incorporates the rate with which the true quantile diverges as the integration horizon expands. The asymptotic normality established for the estimate enables us to construct the confidence interval for the true quantile. Monte Carlo experiments are conducted to demonstrate both the consistency and the advantages of our approach. Results on quantile estimates for the return distribution of the S&P 500 index are also presented.
Key words and phrases: Quantile, integrated returns, stochastic volatility model, value at risk.