Using extreme value theory to estimate value‐at‐risk

Abstract

This study examines problems that may occur when conventional Value‐at‐Risk (VaR) estimators are used to quantify market risks in an agricultural context. For example, standard VaR methods, such as the variance‐covariance method or historical simulation, can fail when the return distribution is fat tailed. This problem is aggravated when long‐term VaR forecasts are desired. Extreme Value Theory (EVT) is proposed to overcome these problems. The application of EVT is illustrated by an example from the German hog market. Multi‐period VaR forecasts derived by EVT are found to deviate considerably from standard forecasts. We conclude that EVT is a useful complement to traditional VaR methods.