Forecasting Value-at-Risk with Time-Varying Variance, Skewness and Kurtosis in an Exponential Weighted Moving Average Framework
AbstractThis 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by The Rimini Centre for Economic Analysis in its series Working Paper Series with number 34_12.
Date of creation: Jun 2012
Date of revision:
exponential weighted moving average; time-varying higher moments; Cornish-Fisher expansion; Gram-Charlier density; risk management; Value-at-Risk;
Other versions of this item:
- A. Gabrielsen & P. Zagaglia & A. Kirchner & Z. Liu, 2012. "Forecasting Value-at-Risk with Time-Varying Variance, Skewnessn and Kurtosis in an Exponential Weighted Moving Average Framework," Working Papers wp831, Dipartimento Scienze Economiche, Universita' di Bologna.
- A. Gabrielsen & P. Zagaglia & A. Kirchner & Z. Liu, 2012. "Forecasting Value-at-Risk with Time-Varying Variance, Skewness and Kurtosis in an Exponential Weighted Moving Average Framework," Papers 1206.1380, arXiv.org.
- Gabrielsen, A. & Zagaglia, Paolo & Kirchner, A. & Liu, Z., 2012. "Forecasting Value-at-Risk with time-varying variance, skewness and kurtosis in an exponential weighted moving average framework," MPRA Paper 39294, University Library of Munich, Germany.
- C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
- C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
- C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
- G15 - Financial Economics - - General Financial Markets - - - International Financial Markets
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-06-25 (All new papers)
- NEP-BAN-2012-06-25 (Banking)
- NEP-FOR-2012-06-25 (Forecasting)
- NEP-RMG-2012-06-25 (Risk Management)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- Anthony S. Tay & Aamir R. Hashmi, 2004. "Global and Regional Sources of Risk in Equity Markets: Evidence from Factor Models with Time-Varying Conditional Skewness," Econometric Society 2004 Far Eastern Meetings 634, Econometric Society.
- 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.
- Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
- Peter Christoffersen & Steve Heston & Kris Jacobs, 2003.
"Option Valuation with Conditional Skewness,"
CIRANO Working Papers
- 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.
- Esther B. Del Brio & Trino-Manuel Niguez & Javier Perote, 2009. "Gram-Charlier densities: a multivariate approach," Quantitative Finance, Taylor and Francis Journals, vol. 9(7), pages 855-868.
- 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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Roberto Patuelli).
If references are entirely missing, you can add them using this form.