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Range-based models in estimating value-at-risk (VaR)

Author

Listed:
  • Nikkin L. Beronilla

    (Institute for Popular Democracy)

  • Dennis S. Mapa

    (University of the Philippines School of Statistics)

Abstract

This paper introduces new methods of estimating Value-at-Risk (VaR) using range-based GARCH (general autoregressive conditional heteroskedasticity) models. These models, which could be based on either the Parkinson range or the Garman-Klass range, are applied to ten stock market indices of selected countries in the Asia-Pacific region. The results are compared using the traditional methods such as the econometric method based on the autoregressive moving average (ARMA)-GARCH models and RiskMetricsTM. The performance of the different models is assessed using the out-ofsample VaR forecasts. Series of likelihood ratio (LR) tests—namely, LR of unconditional coverage (LRuc), LR of independence (LRind), and LR of conditional coverage (LRcc)—are performed for comparison. The result of the assessment shows that the model based on the Parkinson range GARCH (1,1) with Student’s t distribution, is the best-performing model on the ten stock market indices. It has a failure rate, defined as the percentage of actual return that is smaller than the one-step-ahead VaR forecast, of zero in nine out of ten stock market indices. This paper finds that range-based GARCH models are good alternatives in modeling volatility and in estimating VaR.

Suggested Citation

  • Nikkin L. Beronilla & Dennis S. Mapa, 2008. "Range-based models in estimating value-at-risk (VaR)," Philippine Review of Economics, University of the Philippines School of Economics and Philippine Economic Society, vol. 45(2), pages 87-99, December.
  • Handle: RePEc:phs:prejrn:v:45:y:2008:i:2:p:87-99
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    File URL: http://pre.econ.upd.edu.ph/index.php/pre/article/view/178/643
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    References listed on IDEAS

    as
    1. Pierre Giot & Sébastien Laurent, 2003. "Value-at-risk for long and short trading positions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(6), pages 641-663.
    2. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-862, November.
    3. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    5. Parkinson, Michael, 1980. "The Extreme Value Method for Estimating the Variance of the Rate of Return," The Journal of Business, University of Chicago Press, vol. 53(1), pages 61-65, January.
    6. Tae-Hwy Lee & Yong Bao & Burak Saltoglu, 2006. "Evaluating predictive performance of value-at-risk models in emerging markets: a reality check," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(2), pages 101-128.
    7. Pierre Giot & Sébastien Laurent, 2003. "Value-at-risk for long and short trading positions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., pages 641-663.
    8. Mapa, Dennis S., 2003. "A Range-Based GARCH Model for Forecasting Volatility," MPRA Paper 21323, University Library of Munich, Germany.
    9. Dennis S. Mapa, 2003. "A range-based GARCH model for forecasting financial volatility," Philippine Review of Economics, University of the Philippines School of Economics and Philippine Economic Society, vol. 40(2), pages 73-90, December.
    10. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    11. Garman, Mark B & Klass, Michael J, 1980. "On the Estimation of Security Price Volatilities from Historical Data," The Journal of Business, University of Chicago Press, vol. 53(1), pages 67-78, January.
    12. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
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    Citations

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    Cited by:

    1. Dilip Kumar, 2016. "Estimating and forecasting value-at-risk using the unbiased extreme value volatility estimator," Proceedings of Economics and Finance Conferences 3205528, International Institute of Social and Economic Sciences.

    More about this item

    Keywords

    value-at-risk; Parkinson range; Garman-Klass range; range-based GARCH;

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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