Value at Risk and Expected Shortfall Estimation for Mexico’s Isthmus Crude Oil Using Long-Memory GARCH-EVT Combined Approaches

Abstract

This paper estimates a variety of CGARCH and FIGARCH models with normal distribution to capture salient features of Mexico’s Isthmus crude oil return series such as fat tails and volatility clustering as well as asymmetry and long memory; this to obtain independent and identically distributed standardized residuals series. Furthermore, extreme value theory is applied to model the tail behavior of the innovation distribution of the volatility models in estimating one-day-ahead VaR and Expected Shortfall (ES). In- and out-of-sample forecasting performance is evaluated by the unconditional coverage test of Kupiec and the Dynamic Quantile test of Engle and Manganelli. Backtesting results show strong and consistent evidence confirming that FIGARCH-EVT, ACGARCH1-EVT and CGARCH-EVT approaches yield the most accurate out-of-sample VaR and ES forecasts, for both short and long trading positions at quantiles ranging 95% to 99.9%. Findings provide useful tools for producers, consumers and portfolio investors who need sophisticated models for sound risk management and optimal hedging strategies to mitigate price risk exposure for the Isthmus crude oil.

Keywords

• Crude Oil, Conditional Extreme Value Theory, Value at Risk and Expected Shortfall, Mexico’s Isthmus Oil