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Generating Volatility Forecasts from Value at Risk Estimates

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  • James W. Taylor

    ()
    (Saïd Business School, University of Oxford, Park End Street, Oxford OX1 1HP, United Kingdom)

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    Abstract

    Statistical volatility models rely on the assumption that the shape of the conditional distribution is fixed over time and that it is only the volatility that varies. The recently proposed conditional autoregressive value at risk (CAViaR) models require no such assumption, and allow quantiles to be modeled directly in an autoregressive framework. Although useful for risk management, CAViaR models do not provide volatility forecasts. Such forecasts are needed for several other important applications, such as option pricing and portfolio management. It has been found that, for a variety of probability distributions, there is a surprising constancy of the ratio of the standard deviation to the interval between symmetric quantiles in the tails of the distribution, such as the 0.025 and 0.975 quantiles. This result has been used in decision and risk analysis to provide an approximation of the standard deviation in terms of quantile estimates provided by experts. Drawing on the same result, we construct financial volatility forecasts as simple functions of the interval between CAViaR forecasts of symmetric quantiles. Forecast comparison, using five stock indices and 20 individual stocks, shows that the method is able to outperform generalized autoregressive conditional heteroskedasticity (GARCH) models and moving average methods.

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    File URL: http://dx.doi.org/10.1287/mnsc.1040.0355
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 51 (2005)
    Issue (Month): 5 (May)
    Pages: 712-725

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    Handle: RePEc:inm:ormnsc:v:51:y:2005:i:5:p:712-725

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    Related research

    Keywords: volatility forecasting; value at risk; CAViaR models;

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    Cited by:
    1. DeRossi, G. & Harvey, A., 2006. "Time-Varying Quantiles," Cambridge Working Papers in Economics 0649, Faculty of Economics, University of Cambridge.
    2. Sylvain Benoit & Christophe Hurlin & Christophe Pérignon, 2013. "Implied Risk Exposures," Working Papers halshs-00836280, HAL.
    3. Colletaz, Gilbert & Hurlin, Christophe & Pérignon, Christophe, 2013. "The Risk Map: A new tool for validating risk models," Journal of Banking & Finance, Elsevier, vol. 37(10), pages 3843-3854.
    4. Pérignon, Christophe & Smith, Daniel R., 2010. "The level and quality of Value-at-Risk disclosure by commercial banks," Journal of Banking & Finance, Elsevier, vol. 34(2), pages 362-377, February.
    5. Thomakos, Dimitrios D. & Wang, Tao, 2010. "'Optimal' probabilistic and directional predictions of financial returns," Journal of Empirical Finance, Elsevier, vol. 17(1), pages 102-119, January.
    6. Lúcio Godeiro, Lucas, 2012. "Estimando o VaR (Value-at-Risk) de carteiras via modelos da família GARCH e via Simulação de Monte Carlo
      [Estimating the VaR (Value-at-Risk) of portfolios via GARCH family models and via Monte C
      ," MPRA Paper 45146, University Library of Munich, Germany.
    7. Huang, Alex YiHou & Peng, Sheng-Pen & Li, Fangjhy & Ke, Ching-Jie, 2011. "Volatility forecasting of exchange rate by quantile regression," International Review of Economics & Finance, Elsevier, vol. 20(4), pages 591-606, October.

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