| Summary: | <p>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 <em>p</em>-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.</p><p><strong>Keywords</strong>: Conditional extreme value theory, Value at Risk, Expected Shortfall.</p><p><strong>JEL Classifications</strong>: G15, G17.</p><p>DOI: <a href="https://doi.org/10.32479/ijefi.7596">https://doi.org/10.32479/ijefi.7596</a></p>
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