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

Quaderni DSE Working Paper No. 831

35 Pages Posted: 8 Jun 2012

See all articles by Alexandros Gabrielsen

Alexandros Gabrielsen

Credit Suisse AG

Paolo Zagaglia

University of Bologna; Rimini Centre for Economic Analysis

Axel Kirchner

University of Edinburgh

Zhuoshi Liu

Bank of England - Monetary Analysis

Date Written: June 7, 2012

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.

Keywords: exponential weighted moving average, time-varying higher moments, Cornish- Fisher expansion, Gram-Charlier density, risk management, Value-at-Risk

JEL Classification: C51, C52, C53, G15

Suggested Citation

Gabrielsen, Alexandros and Zagaglia, Paolo and Kirchner, Axel and Liu, Zhuoshi, Forecasting Value-at-Risk with Time-Varying Variance, Skewness and Kurtosis in an Exponential Weighted Moving Average Framework (June 7, 2012). Quaderni DSE Working Paper No. 831, Available at SSRN: https://ssrn.com/abstract=2079526 or http://dx.doi.org/10.2139/ssrn.2079526

Alexandros Gabrielsen (Contact Author)

Credit Suisse AG ( email )

Giesshübelstrasse 40
Zurich, 8002
Switzerland

Paolo Zagaglia

University of Bologna ( email )

Via degli Ariani 1
Ravenna, 48121
Italy

Rimini Centre for Economic Analysis ( email )

Rimini
Italy

Axel Kirchner

University of Edinburgh ( email )

Old College
South Bridge
Edinburgh, Scotland EH8 9JY
United Kingdom

Zhuoshi Liu

Bank of England - Monetary Analysis ( email )

Threadneedle Street
London EC2R 8AH
United Kingdom

HOME PAGE: http://www.bankofengland.co.uk/research/Pages/economists/Zhuoshi-Liu.aspx

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