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Forecasting the Variability of Stock Index Returns with Stochastic Volatility Models and Implied Volatility

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Author Info

  • Eugenie Hol

    (University of Birmingham)

  • Siem Jan Koopman

    ()
    (Vrije Universiteit Amsterdam)

Abstract

In this paper we compare the predictive abilility of Stochastic Volatility (SV)models to that of volatility forecasts implied by option prices. We develop anSV model with implied volatility as an exogeneous var able in the varianceequation which facilitates the use of statistical tests for nested models; werefer to this model as the SVX model. The SVX model is then extended to avolatility model with persistence adjustment term and this we call the SVX+model.This class of SV models can be estimated by quasi maximum likelihood methods butthe main emphasis will be on methods for exact maximum likelihood using MonteCarlo importance sampling methods. The performance of the models is evaluated,both within sample and out-of-sample, for daily returns on the Standard & Poor's100 index. Similar studies have been undertaken with GARCH models where findingswere initially mixed but recent research has indicated that impliedvolatilityprovides superior forecasts. We find that implied volatilityoutperforms historical returns in-sample but that the latter containsincremental information in the form of stochastic shocks incorporated in the SVXmodels. The out-of-sample volatility forecasts are evaluated against dailysquared returns and intradaily squared returns for forecasting horizons rangingfrom 1 to 10 days. For the daily squared returns we obtain mixed results, butwhen we use intradaily squared returns as a measure of realised volatility wefind that the SVX+ model produces the most accurate out-of-sample volatilityforecasts and that the model that only utilises implied volatility performes theworst as its volatility forecasts are upwardly biased.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 00-104/4.

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Date of creation: 21 Nov 2000
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Handle: RePEc:dgr:uvatin:20000104

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Web page: http://www.tinbergen.nl

Related research

Keywords: Forecasting; Implied Volatility; Monte Carlo likelihood method; Stochastic volatility; Stock indice;

References

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  1. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, Econometric Society, vol. 50(4), pages 987-1007, July.
  2. Kim, Sangjoon & Shephard, Neil & Chib, Siddhartha, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 65(3), pages 361-93, July.
  3. David Walsh & Glenn Yu-Gen Tsou, 1998. "Forecasting index volatility: sampling interval and non-trading effects," Applied Financial Economics, Taylor & Francis Journals, Taylor & Francis Journals, vol. 8(5), pages 477-485.
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  7. Stephen J. Taylor, 1994. "Modeling Stochastic Volatility: A Review And Comparative Study," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 4(2), pages 183-204.
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  11. Neil Shephard & Jurgen Doornik & Siem Jan Koopman, 1998. "Statistical algorithms for models in state space using SsfPack 2.2," Economics Series Working Papers, University of Oxford, Department of Economics 1998-W06, University of Oxford, Department of Economics.
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  15. Sandmann, Gleb & Koopman, Siem Jan, 1998. "Estimation of stochastic volatility models via Monte Carlo maximum likelihood," Journal of Econometrics, Elsevier, Elsevier, vol. 87(2), pages 271-301, September.
  16. Akgiray, Vedat, 1989. "Conditional Heteroscedasticity in Time Series of Stock Returns: Evidence and Forecasts," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 62(1), pages 55-80, January.
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Cited by:
  1. Stavros Degiannakis & Evdokia Xekalaki, 2007. "Assessing the performance of a prediction error criterion model selection algorithm in the context of ARCH models," Applied Financial Economics, Taylor & Francis Journals, Taylor & Francis Journals, vol. 17(2), pages 149-171.
  2. Chortareas, Georgios & Jiang, Ying & Nankervis, John. C., 2011. "Forecasting exchange rate volatility using high-frequency data: Is the euro different?," International Journal of Forecasting, Elsevier, Elsevier, vol. 27(4), pages 1089-1107, October.
  3. Sascha Mergner & Jan Bulla, 2008. "Time-varying beta risk of Pan-European industry portfolios: A comparison of alternative modeling techniques," The European Journal of Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 14(8), pages 771-802.
  4. Garland Durham, 2004. "Likelihood-based estimation and specification analysis of one- and two-factor SV models with leverage effects," Econometric Society 2004 North American Summer Meetings, Econometric Society 294, Econometric Society.
  5. Peter Carr & Liuren Wu, 2004. "Variance Risk Premia," Finance, EconWPA 0409015, EconWPA.
  6. Assaf, Ata, 2006. "The stochastic volatility in mean model and automation: Evidence from TSE," The Quarterly Review of Economics and Finance, Elsevier, Elsevier, vol. 46(2), pages 241-253, May.
  7. Berument, Hakan & Yalcin, Yeliz & Yildirim, Julide, 2009. "The effect of inflation uncertainty on inflation: Stochastic volatility in mean model within a dynamic framework," Economic Modelling, Elsevier, Elsevier, vol. 26(6), pages 1201-1207, November.
  8. Georgios Chortareas & John Nankervis & Ying Jiang, 2007. "Forecasting Exchange Rate Volatility with High Frequency Data: Is the Euro Different?," Money Macro and Finance (MMF) Research Group Conference 2006, Money Macro and Finance Research Group 79, Money Macro and Finance Research Group.

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