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.
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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:
- 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.
- 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.
- 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.
- 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)
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