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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
Date of revision:
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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  18. Christensen, B. J. & Prabhala, N. R., 1998. "The relation between implied and realized volatility," Journal of Financial Economics, Elsevier, vol. 50(2), pages 125-150, November.
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Citations

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Cited by:
  1. Sascha Mergner & Jan Bulla, 2005. "Time-varying Beta Risk of Pan-European Industry Portfolios: A Comparison of Alternative Modeling Techniques," Finance 0510029, EconWPA.
  2. Peter Carr & Liuren Wu, 2004. "Variance Risk Premia," Finance 0409015, EconWPA.
  3. 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, vol. 26(6), pages 1201-1207, November.
  4. 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, vol. 27(4), pages 1089-1107, October.
  5. Assaf, Ata, 2006. "The stochastic volatility in mean model and automation: Evidence from TSE," The Quarterly Review of Economics and Finance, Elsevier, vol. 46(2), pages 241-253, May.
  6. 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, vol. 17(2), pages 149-171.
  7. 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 294, Econometric Society.
  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 79, Money Macro and Finance Research Group.

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