FORECASTING VALUE-AT-RISK WITH TIME-VARYING VARIANCE, SKEWNESS AND KURTOSIS IN AN EXPONENTIAL WEIGHTED MOVING AVERAGE FRAMEWORK

Alexandros Gabrielsen, Axel Kirchner, Zhuoshi Liu and Paolo Zagaglia
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Alexandros Gabrielsen: Sumitomo Mitsui Banking Corporation Europe, London, UK
Axel Kirchner: Deutsche Bank, London, UK

Annals of Financial Economics (AFE), 2015, vol. 10, issue 01, 1-29

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 (EWMA) 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, Value-at-Risk (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 generalized autoregressive conditional heteroscedasticity (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.

Keywords: Exponential weighted moving average; time-varying higher moments; Cornish–Fisher expansion; Gram–Charlier density; risk management; value-at-risk; C51; C52; G53; G15 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (4)

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Related works:
Working Paper: Forecasting Value-at-Risk with Time-Varying Variance, Skewness and Kurtosis in an Exponential Weighted Moving Average Framework (2012)
Working Paper: Forecasting Value-at-Risk with Time-Varying Variance, Skewnessn and Kurtosis in an Exponential Weighted Moving Average Framework (2012)
Working Paper: Forecasting Value-at-Risk with time-varying variance, skewness and kurtosis in an exponential weighted moving average framework (2012)
Working Paper: Forecasting Value-at-Risk with Time-Varying Variance, Skewness and Kurtosis in an Exponential Weighted Moving Average Framework (2012)
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DOI: 10.1142/S2010495215500050

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