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Value-at-Risk-Estimation in the Mexican Stock Exchange Using Conditional Heteroscedasticity Models and Theory of Extreme Values

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  • Alejandro Iván Aguirre Salado

    ()
    (Posgrado en Estadística, Colegio de Posgraduados, Campus Montecillo. Texcoco, E.M. Mexico.)

  • Humberto Vaquera Huerta

    ()
    (Profesor investigador titular, Posgrado Forestal, Colegio de Posgraduados, Campus Montecillo. Texcoco, E.M. Mexico.)

  • Martha Elva Ramírez Guzmán

    ()
    (Profesora investigadora titular, Posgrado en Estadística, Colegio de Posgraduados, Campus Montecillo. Texcoco, E.M. Mexico.)

  • José René Valdez Lazalde

    ()
    (Profesor investigador titular, Posgrado forestal, Colegio de Posgraduados, Campus Montecillo. Texcoco, E.M. Mexico.)

  • Carlos Arturo Aguirre Salado

    ()
    (Profesor investigador, Facultad de Ingeniería, Universidad Autónoma de San Luis Potosí. San Luis Potosí, S.L.P. Mexico.)

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    Abstract

    This work proposes an approach for estimating value at risk (VaR) of the Mexican stock exchange index (IPC) by using a combination of the autoregressive moving average models (ARMA); three different models of the arch family, one symmetric (GARCH) and two asymmetric (GJR-GARCH and EGARCH); and the extreme value theory (EVT). The ARMA models were initially used to obtain uncorrelated residuals, which were later used for the analysis of extreme values. The GARCH, EGARCH and GJR-GARCH models, by including past volatility, are particularly useful both in instability and calm periods. Moreover, the asymmetric models GJR-GARCH and EGARCH handle differently the impact of positive and negative shocks in the market. The importance of the IPC in the Mexican economy raises the need to study its variations, particularly its downward movement; so, we propose to use VaR to calculate the maximum loss that IPC may have, at a certain level of reliability, in a given period of time, using more efficient models to dynamically quantify volatility. The RiskMetrics approach was parallelly used as a way to compare the methodology proposed. The results indicate that the ARMA-GARCH-EVT methodology showed a better performance than RiskMetrics, because of the simultaneous adjustment of ARMA-GARCH models for returns and variances respectively. Although estimates of the EGARCH models had fewer violations of VaR, the estimates of the three models used for volatility were more accurate than the others, evaluated at the same error and reliability levels through the Kupiec Likelihood Ratio test.

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    Bibliographic Info

    Article provided by in its journal Economia Mexicana NUEVA EPOCA.

    Volume (Year): XXII (2013)
    Issue (Month): 1 (January-June)
    Pages: 177-205.

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    Handle: RePEc:emc:ecomex:v:22:y:2013:i:1:p:177-205

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    Related research

    Keywords: ARMA; VaR; GARCH; EVT; financial risk.;

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