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Which Volatility Model for Option Valuation?

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  • Peter Christoffersen

    ()

  • Kris Jacobs

    ()

Abstract

Characterizing asset return dynamics using volatility models is an important part of empirical finance. The existing literature favors some rather complex volatility specifications whose relative performance is usually assessed through their likelihood based on a time-series of asset returns. This paper compares a range of volatility models along a different dimension, using option prices and returns under the risk-neutral as well as the physical probability measure. We judge the relative performance of various models by evaluating an objective function based on option prices. In contrast with returns-based inference, we find that our option-based objective function favors a relatively parsimonious model. Specifically, when evaluated out-of-sample, our analysis favors a model that besides volatility clustering only allows for a standard leverage effect. This empirical analysis is part of a growing literature suggesting that discrete-time option pricing with time-varying volatility is practical and insightful. Caractériser les dynamiques des rendements d'actifs à l'aide de modèles de volatilité est un champ important de la finance empirique. La littérature dans ce domaine privilégie des spécifications de volatilité plutôt complexes dont la performance relative est généralement estimée par leur vraisemblance à partir de séries chronologiques de rendements d'actifs. Cet article compare plusieurs modèles de volatilité selon un critère différent, utilisant les rendements et prix d'options dans une mesure neutre au risque et de probabilité physique. Nous estimons la performance relative des différents modèles en évaluant la fonction objective basée sur les prix d'options. Contrairement à l'inférence basée sur les rendements, nous trouvons que notre fonction objective basée sur les options favorise un modèle relativement parcimonieux. En particulier, lorsqu'elle est évaluée hors-échantillon, notre analyse favorise un modèle qui, outre le groupement de volatilités, ne permet qu'un effet de levier standard. Cette analyse empirique fait partie d'une littérature en plein essor qui suggère que l'évaluation des prix d'options en temps discret, lorsque la volatilité varie dans le temps, est pratique et riche en enseignements.

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Bibliographic Info

Paper provided by CIRANO in its series CIRANO Working Papers with number 2002s-33.

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Date of creation: 01 Apr 2002
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Handle: RePEc:cir:cirwor:2002s-33

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Keywords: option pricing; GARCH; risk-neutral pricing; parsimony; forecasting; out-of-sample; évaluation d'options; GARCH; fixation des prix neutre au risque; prévision; parcimonie; hors-échantillon;

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References

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Citations

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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, vol. 17(2), pages 149-171.
  2. Christoffersen, Peter & Heston, Steve & Jacobs, Kris, 2006. "Option valuation with conditional skewness," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 253-284.
  3. Peter Christoffersen & Kris Dorion & Yintian Wang, 2008. "Volatility Components, Affine Restrictions and Non-Normal Innovations," CREATES Research Papers 2008-10, School of Economics and Management, University of Aarhus.
  4. Duan, Jin-Chuan & Wei, Jason, 2005. "Executive stock options and incentive effects due to systematic risk," Journal of Banking & Finance, Elsevier, vol. 29(5), pages 1185-1211, May.
  5. Peter Christoffersen & Kris Jacobs & Yintian Wang, 2004. "Option Valuation with Long-run and Short-run Volatility Components," CIRANO Working Papers 2004s-56, CIRANO.
  6. Stentoft, Lars, 2005. "Pricing American options when the underlying asset follows GARCH processes," Journal of Empirical Finance, Elsevier, vol. 12(4), pages 576-611, September.

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