Estimating value-at-risk using quantile regression and implied volatilities

Petter E. de Lange, Morten Risstad and Sjur Westgaard

Abstract

In this paper we propose a semi-parametric, parsimonious value-at-risk forecasting model based on quantile regression and readily available market prices of option contracts from the over-the-counter foreign exchange interbank market. Explanatory variables are implied volatilities with plausible economic interpretation. The forward-looking nature of the model, induced by the application of implied moments as risk factors, ensures that new information is rapidly reflected in value-at-risk estimates. The proposed model outperforms traditional benchmark models when evaluated in-sample and out-of-sample on EUR/USD data. The model is relatively easy to estimate, which facilitates practical application. Our quantile regression implied moments model is subjected to extensive risk model validation by means of backtesting, using both coverage tests and loss functions. Thus, his paper is relevant for both risk modeling and risk model validation in the context of foreign exchange risk.