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

Author

Listed:
  • 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.)

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.

Suggested Citation

  • Alejandro Iván Aguirre Salado & Humberto Vaquera Huerta & Martha Elva Ramírez Guzmán & José René Valdez Lazalde & Carlos Arturo Aguirre Salado, 2013. "Value-at-Risk-Estimation in the Mexican Stock Exchange Using Conditional Heteroscedasticity Models and Theory of Extreme Values," Economía Mexicana NUEVA ÉPOCA, , vol. 0(1), pages 177-205., January-J.
  • Handle: RePEc:emc:ecomex:v:22:y:2013:i:1:p:177-205
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    More about this item

    Keywords

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

    JEL classification:

    • A23 - General Economics and Teaching - - Economic Education and Teaching of Economics - - - Graduate
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications
    • F37 - International Economics - - International Finance - - - International Finance Forecasting and Simulation: Models and Applications
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • Y - Miscellaneous Categories
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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