A Quantile Regression Approach to Estimating the Distribution of Multiperiod Returns

Abstract

Time-varying and stochastic volatility, non-lognormaility, mean reversion, price jumps, and non-zero correlation between volatility changes and asset returns all characterize asset returns, at least in some markets and some time periods. This can make accurately estimating the location of the tail of a returns distribution, as in a Value at Risk calculation, exceedingly difficult, especially when multiperiod returns distribution, as in a value at risk calculation, exceedingly difficult, especially when multiperiod returns are involved. The conceptual problem of determining which returns model to use brings out the inherent dependence of the answer on this assumption, and suggests that a non-parametric approach may be superior. In this article, Taylor offers a technique that focuses specifically on fitting the particular quantile of the distribution one is interested in, the 1% tail, for instance, using the non-parametric technique of quantile regression. In empirical comparisons against exponential smoothing or GARCH for three exchange rates, the quantile regression technique is shown to perform well.