Statistical Methods in Finance 2017

Abstract

Quantile Estimation based on asset return data

by Santanu Dutta

Value at risk (VaR), median shortfall (MS) and expected shortfall (ES) are well known measures of market risk. While VaR and MS are extreme quantiles of the marginal asset return distribution, ES is a functional of the quantile function. Time series on asset returns are known to exhibit certain stylized facts, such as heavy tails, skewness, volatility clustering, etc. Therefore estimation of quantiles in the presence of such features in the data are of interest in the context of market risk assessment based on asset returns. It is difficult to capture most of these stylized facts using one specific time series model. This motivates nonparametric and extreme value theory-based estimation of extreme quantiles that do not require exact specification of the asset return model. We review some well known quantile estimators and their properties. Their finite sample performance are compared using Monte Carlo simulation. A new quantile estimator exhibiting encouraging finite sample performance is proposed, and its asymptotic properties are obtained. The new estimator enables reliable estimation of VaR, MS and ES based on asset return data.

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