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Forecasting Value-at-Risk with Time-Varying Variance, Skewness and Kurtosis in an Exponential Weighted Moving Average Framework

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  • A. Gabrielsen
  • P. Zagaglia
  • A. Kirchner
  • Z. Liu

Abstract

This paper provides an insight to the time-varying dynamics of the shape of the distribution of financial return series by proposing an exponential weighted moving average model that jointly estimates volatility, skewness and kurtosis over time using a modified form of the Gram-Charlier density in which skewness and kurtosis appear directly in the functional form of this density. In this setting VaR can be described as a function of the time-varying higher moments by applying the Cornish-Fisher expansion series of the first four moments. An evaluation of the predictive performance of the proposed model in the estimation of 1-day and 10-day VaR forecasts is performed in comparison with the historical simulation, filtered historical simulation and GARCH model. The adequacy of the VaR forecasts is evaluated under the unconditional, independence and conditional likelihood ratio tests as well as Basel II regulatory tests. The results presented have significant implications for risk management, trading and hedging activities as well as in the pricing of equity derivatives.

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File URL: http://arxiv.org/pdf/1206.1380
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Paper provided by arXiv.org in its series Papers with number 1206.1380.

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Date of creation: Jun 2012
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Handle: RePEc:arx:papers:1206.1380

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  1. Timotheos Angelidis & Alexandros Benos & Stavros Degiannakis, 2007. "A robust VaR model under different time periods and weighting schemes," Review of Quantitative Finance and Accounting, Springer, vol. 28(2), pages 187-201, February.
  2. Marcucci Juri, 2005. "Forecasting Stock Market Volatility with Regime-Switching GARCH Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 9(4), pages 1-55, December.
  3. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  4. Aamir R. Hashmi & Anthony S. Tay, 2001. "Global and Regional Sources of Risk in Equity Markets: Evidence from Factor Models with Time-Varying Conditional Skewness," Departmental Working Papers wp0116, National University of Singapore, Department of Economics.
  5. Esther B. Del Brio & Trino-Manuel Niguez & Javier Perote, 2009. "Gram-Charlier densities: a multivariate approach," Quantitative Finance, Taylor & Francis Journals, vol. 9(7), pages 855-868.
  6. Christoffersen, Peter & Heston, Steve & Jacobs, Kris, 2006. "Option valuation with conditional skewness," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 253-284.
  7. Alizadeh, Amir H. & Gabrielsen, Alexandros, 2013. "Dynamics of credit spread moments of European corporate bond indexes," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 3125-3144.
  8. Anders Wilhelmsson, 2009. "Value at Risk with time varying variance, skewness and kurtosis--the NIG-ACD model," Econometrics Journal, Royal Economic Society, vol. 12(1), pages 82-104, 03.
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