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Estimating Value-At-Risk (Var) Using TIVEX-POT Models

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  • Peter Julian A. Cayton

    ()
    (School of Statistics, University of the Philippines, Diliman, Quzeon City, Philippines)

  • Dennis S. Mapa, Ph. D.

    ()
    (School of Statistics, University of the Philippines, Diliman, Quzeon City, Philippines)

  • Mary Therese A. Lising

    ()
    (ACS Manufacturing Corporation, Philippines)

Abstract

Financial institutions hold risks in their investments that can potentially affect their ability to serve 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 time-varying parameter through explanatory variables (TiVEx) - peaks over thresholds model (POT). The time varying parameters are linked to linear predictor variables through link functions. To estimate parameters, maximum likelihood estimation is used with the time-varying parameters being replaced from the likelihood function of the generalized Pareto distribution. The test series used for the paper was the Philippine Peso-US Dollar exchange rate 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 TiVEx-POT models by dropping covariates were 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 VaR modeling since it has consistent green status on the number of exemptions and lower risk capital.

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Bibliographic Info

Article provided by ASERS Publishing in its journal Journal of Advanced Studies in Finance.

Volume (Year): I (2010)
Issue (Month): 2 (December)
Pages: 152 - 170

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Handle: RePEc:srs:jasf12:6:v:1:y:2010:i:2:p:152-170

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Related research

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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  1. 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.
  2. 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.
  3. Mapa, Dennis S. & Suaiso, Oliver Q., 2009. "Measuring market risk using extreme value theory," MPRA Paper 21246, University Library of Munich, Germany.
  4. 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.
  5. 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.
  6. 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.
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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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