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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)

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.

Suggested Citation

  • James W. Taylor, 2005. "Generating Volatility Forecasts from Value at Risk Estimates," Management Science, INFORMS, vol. 51(5), pages 712-725, May.
  • Handle: RePEc:inm:ormnsc:v:51:y:2005:i:5:p:712-725
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    File URL: http://dx.doi.org/10.1287/mnsc.1040.0355
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Jin-Huei Yeh & Jying-Nan Wang & Chung-Ming Kuan, 2014. "A noise-robust estimator of volatility based on interquantile ranges," Review of Quantitative Finance and Accounting, Springer, vol. 43(4), pages 751-779, November.
    2. Jeremy Berkowitz & Peter Christoffersen & Denis Pelletier, 2011. "Evaluating Value-at-Risk Models with Desk-Level Data," Management Science, INFORMS, vol. 57(12), pages 2213-2227, December.
    3. Yuzhi Cai & Julian Stander, 2018. "The threshold GARCH model: estimation and density forecasting for financial returns," Working Papers 2018-23, Swansea University, School of Management.
    4. Peter F. Christoffersen & Francis X. Diebold, 2006. "Financial Asset Returns, Direction-of-Change Forecasting, and Volatility Dynamics," Management Science, INFORMS, vol. 52(8), pages 1273-1287, August.
    5. Erie Febrian & Aldrin Herwany, 2009. "Volatility Forecasting Models and Market Co-Integration: A Study on South-East Asian Markets," Working Papers in Economics and Development Studies (WoPEDS) 200911, Department of Economics, Padjadjaran University, revised Sep 2009.
    6. DeRossi, G. & Harvey, A., 2006. "Time-Varying Quantiles," Cambridge Working Papers in Economics 0649, Faculty of Economics, University of Cambridge.
    7. Sylvain Benoit & Christophe Hurlin & Christophe Perignon, 2015. "Implied Risk Exposures," Review of Finance, European Finance Association, vol. 19(6), pages 2183-2222.
    8. 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 Carl
      ," MPRA Paper 45146, University Library of Munich, Germany.
    9. Derek Bunn, Arne Andresen, Dipeng Chen, Sjur Westgaard, 2016. "Analysis and Forecasting of Electricty Price Risks with Quantile Factor Models," The Energy Journal, International Association for Energy Economics, vol. 0(Number 1).
    10. 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.
    11. 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.
    12. Alessandra Pasqualina Viola & Marcelo Cabus Klotzle & Antonio Carlos Figueiredo Pinto & Wagner Piazza Gaglianone, 2017. "Predicting Exchange Rate Volatility in Brazil: an approach using quantile autoregression," Working Papers Series 466, Central Bank of Brazil, Research Department.
    13. 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.
    14. Komunjer, Ivana, 2013. "Quantile Prediction," Handbook of Economic Forecasting, Elsevier.
    15. repec:sgm:pzwzuw:v:15:i:66:y:2017:p:107-124 is not listed on IDEAS
    16. 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.

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