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Range-Based Models in Estimating Value-at-Risk (VaR)

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  • Mapa, Dennis
  • Beronilla, Nikkin

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 either based on the Parkinson Range or Garman-Klasss Range, are applied to 10 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 ARMA-GARCH models and RiskMetricsTM. The performance of the different models is assessed using the out-of-sample 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 10 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 9 out 10 stock market indices. The finding of this paper is that Range-Based GARCH Models are good alternatives in modeling volatility and in estimating VaR.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 21223.

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Date of creation: 2008
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Publication status: Published in The Philippine Review of Economics 2.XLV(2008): pp. 87-100
Handle: RePEc:pra:mprapa:21223

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Keywords: Value-at-Risk (VaR); Parkinson Range; Garman-Klasss Range; Range-Based GARCH (General Autoregressive Conditional Heteroskedasticity);

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  1. 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., John Wiley & Sons, Ltd., vol. 25(2), pages 101-128.
  2. 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.
  3. GIOT, Pierre & LAURENT, Sébastien, . "Value-at-Risk for long and short trading positions," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -1707, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Mapa, Dennis S., 2003. "A Range-Based GARCH Model for Forecasting Volatility," MPRA Paper 21323, University Library of Munich, Germany.
  5. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  6. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, Econometric Society, vol. 59(2), pages 347-70, March.
  7. Pierre Giot and S»bastien Laurent, 2001. "Value-At-Risk For Long And Short Trading Positions," Computing in Economics and Finance 2001, Society for Computational Economics 94, Society for Computational Economics.
  8. 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, American Finance Association, vol. 48(5), pages 1779-1801, December.
  9. 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, University of Chicago Press, vol. 53(1), pages 67-78, January.
  10. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, Econometric Society, vol. 50(4), pages 987-1007, July.
  11. Parkinson, Michael, 1980. "The Extreme Value Method for Estimating the Variance of the Rate of Return," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 53(1), pages 61-65, January.
  12. 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, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-62, November.
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