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Estimating Value-at-Risk (VaR) using TiVEx-POT Models

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  • Mapa, Dennis S.
  • Cayton, Peter Julian
  • Lising, Mary Therese

Abstract

Financial institutions hold risks in their investments that can potentially affect their ability to serve their clients. For banks to weigh their risks, Value-at-Risk (VaR) methodology is used, which involves studying the distribution of losses and formulating a statistic from this distribution. From the myriad of models, this paper proposes a method of formulating VaR using the Generalized Pareto distribution (GPD) with time-varying parameter through explanatory variables (TiVEx) - peaks over thresholds model (POT). The time varying parameters are linked to the linear predictor variables through link functions. To estimate parameters of the linear predictors, maximum likelihood estimation is used with the time-varying parameters being replaced from the likelihood function of the GPD. The test series used for the paper was the Philippine Peso-US Dollar exchange rate with horizon from January 2, 1997 to March 13, 2009. Explanatory variables used were GARCH volatilities, quarter dummies, number of holiday-weekends passed, and annual trend. Three selected permutations of modeling through TiVEx-POT by dropping other covariates were also conducted. Results show that econometric models and static POT models were better-performing in predicting losses from exchange rate risk, but simple TiVEx models have potential as part of the VaR modelling philosophy since it has consistent green status on the number exemptions and lower quadratic loss values.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 25772.

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Date of creation: Dec 2009
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Handle: RePEc:pra:mprapa:25772

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Keywords: Value-at-Risk; Extreme Value Theory; Generalized Pareto Distribution; Time-Varying Parameters; Use of Explanatory Variables; GARCH modeling; Peaks-over-Thresholds Model;

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References

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  1. Bystrom, Hans N. E., 2005. "Extreme value theory and extremely large electricity price changes," International Review of Economics & Finance, Elsevier, vol. 14(1), pages 41-55.
  2. Jose Oliver Q. Suaiso & Dennis S. Mapa, 2009. "Measuring market risk using extreme value theory," Philippine Review of Economics, University of the Philippines School of Economics and Philippine Economic Society, vol. 46(2), pages 91-121, December.
  3. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
  4. Longin, Francois M, 1996. "The Asymptotic Distribution of Extreme Stock Market Returns," The Journal of Business, University of Chicago Press, vol. 69(3), pages 383-408, July.
  5. 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.
  6. Peter Christoffersen, 2004. "Backtesting Value-at-Risk: A Duration-Based Approach," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(1), pages 84-108.
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Cited by:
  1. Cayton, Peter Julian A. & Mapa, Dennis S., 2012. "Time-varying conditional Johnson SU density in value-at-risk (VaR) methodology," MPRA Paper 36206, University Library of Munich, Germany.

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