CONDITIONAL EXTREME VALUES THEORY AND TAIL-RELATED RISK MEASURES: EVIDENCE FROM LATIN AMERICAN STOCK MARKETS

Raúl De Jesús Gutiérrez ,Roberto J Santillán‐Salgado

doi:10.32479/ijefi.7596

Raúl De Jesús Gutiérrez , Roberto J Santillán‐Salgado

Open Access

https://doi.org/10.32479/ijefi.7596

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Abstract

The purpose of this work is to extend McNeil and Frey´s (2000) methodology by combining two component GARCH models and extreme value theory to evaluate the performance of the Value at Risk (VaR) and Expected Shortfall (ES) measures in the Latin American stock markets. In-sample analysis, the results of the backtesting indicate that there is no a model that predominates to the others in the estimation of VaR at any confidence level. However, the p-values of the Kupiec test confirm the out-of-sample predictive ability of the CGARCH-EVT models to estimate the VaR for long and short financial positions from Argentina and Mexico, although their performance is insufficient to provide accurate estimates of the ES. The modeling of fat tails, asymmetry and long memory have important implications for risk management, and hedging strategies in volatile stock markets.Keywords: Conditional extreme value theory, Value at Risk, Expected Shortfall.JEL Classifications: G15, G17.DOI: https://doi.org/10.32479/ijefi.7596

Highlights

Value-at-risk (VaR) methodology has been adopted as one of the main paradigms to measure market-risk in the financial industry
The performance of all conditional EVT (CEVT) models is reduced for the 99.5% and 99.9% extreme quantiles; this fact is even more noticeable in the case of the expected shortfall (ES) performance. This implies that the CEVT models underestimate market risk because the number of real failures is significantly small, relative to the expected number of failures, except in the case of the CGARCHEVT model that improves the ES performance at the 99% and 99.5% quantiles
It proposes a family of volatility models with two symmetric and asymmetric components known in the literature as CGARCH models, which allow combining the characteristics of asymmetry and long memory in the volatility in the short and longterm

Summary

Introduction

Value-at-risk (VaR) methodology has been adopted as one of the main paradigms to measure market-risk in the financial industry. Since VaR was adopted as a regulatory risk measurement tool for commercial banks, several approaches were developed to estimate it. Among the most prominent, are the parametric methods based on the assumption of conditional normality and the non-parametric models represented by the method of historical simulation (HS). The literature has shown that conditional volatility models, such as GARCH models, improve the predictions of VaR estimates capturing changing market conditions. The assumption of normality underestimates the true market risk because it ignores the wide tails and leptokurtosis caused by extreme events in financial timeseries (Duffie and Pan, 1997; Vlaar, 2000; Su and Hung, 2011)

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