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

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  • 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.

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File URL: http://pre.econ.upd.edu.ph/index.php/pre/article/view/178/643
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Bibliographic Info

Article provided by University of the Philippines School of Economics and Philippine Economic Society in its journal Philippine Review of Economics.

Volume (Year): 45 (2008)
Issue (Month): 2 (December)
Pages: 87-99

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Handle: RePEc:phs:prejrn:v:45:y:2008:i:2:p:87-99

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

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  1. Pierre Giot and S»bastien Laurent, 2001. "Value-At-Risk For Long And Short Trading Positions," Computing in Economics and Finance 2001 94, Society for Computational Economics.
  2. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  3. Lawrence R. Glosten & Ravi Jagannathan & David E. Runkle, 1993. "On the relation between the expected value and the volatility of the nominal excess return on stocks," Staff Report 157, Federal Reserve Bank of Minneapolis.
  4. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  5. Mapa, Dennis S., 2003. "A Range-Based GARCH Model for Forecasting Volatility," MPRA Paper 21323, University Library of Munich, Germany.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. 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 841-62, November.
  11. GIOT, Pierre & LAURENT, Sébastien, . "Value-at-Risk for long and short trading positions," CORE Discussion Papers RP -1707, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  12. 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.
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