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Value at Risk (VaR) Using Volatility Forecasting Models: EWMA, GARCH and Stochastic Volatility

Author

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  • Fernando Caio Galdi

    (University of São Paulo)

  • Leonel Molero Pereira

    (University of São Paulo)

Abstract

This paper explores three models to estimate volatility: exponential weighted moving average (EWMA), generalized autoregressive conditional heteroskedasticity (GARCH) and stochastic volatility (SV). The volatility estimated by these models can be used to measure the market risk of a portfolio of assets, called Value at Risk (VaR). VaR depends on the volatility, time horizon and confidence interval for the continuous returns under analysis. For empirical assessment of these models, we used a sample based on Petrobras stock prices to specify the GARCH and SV models. Additionally, we adjusted these models by violation backtesting for one-day VaR, to compare the efficiency of the SV, GARCH and EWMA volatility models (suggested by RiskMetrics). The results suggest that VaR calculated considering EWMA was less violated than when considering SV and GARCH for a 1500-observation window. Hence, for our sample, the model suggested by RiskMetrics (1999), which uses exponential smoothing and is easier to implement, did not produce inferior violation test results when compared to more sophisticated tests such as SV and GARCH.

Suggested Citation

  • Fernando Caio Galdi & Leonel Molero Pereira, 2007. "Value at Risk (VaR) Using Volatility Forecasting Models: EWMA, GARCH and Stochastic Volatility," Brazilian Business Review, Fucape Business School, vol. 4(1), pages 74-94, January.
    • Handle: RePEc:bbz:fcpbbr:v:4:y:2007:i:1:p:74-94
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    Citations

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    Cited by:

    1. Bogdan ZUGRAVU & Dumitru Cristian OANEA & Victoria Gabriela ANGHELACHE, 2013. "Analysis Based on the Risk Metrics Model," Romanian Statistical Review Supplement, Romanian Statistical Review, vol. 61(2), pages 145-154, May.
    2. Gabriela Anghelache & Dumitru-Cristian Oanea, 2014. "Main Romanian Commercial Banks’ Systemic Risk during Financial Crisis: a CoVar Approach," The Review of Finance and Banking, Academia de Studii Economice din Bucuresti, Romania / Facultatea de Finante, Asigurari, Banci si Burse de Valori / Catedra de Finante, vol. 6(2), pages 069-080, December.
    3. Pengfei Zhao & Haoren Zhu & Wilfred Siu Hung NG & Dik Lun Lee, 2024. "From GARCH to Neural Network for Volatility Forecast," Papers 2402.06642, arXiv.org.
    4. Max van der Lecq & Gary van Vuuren, 2024. "Estimating Value at Risk and Expected Shortfall: A Kalman Filter Approach," International Journal of Economics and Financial Issues, Econjournals, vol. 14(1), pages 1-14, January.
    5. Victoria Gabriela ANGHELACHE & Dumitru Cristian OANEA & Bogdan ZUGRAVU, 2013. "General Aspects Regarding the Methodology for Prediction Risk," Romanian Statistical Review Supplement, Romanian Statistical Review, vol. 61(2), pages 66-72, May.

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