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Asymmetric Smiles, Leverage Effects and Structural Parameters

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  • René Garcia

    (Crest)

  • Richard Luger

    (Crest)

  • Eric Renault

    (Crest)

Abstract

In this paper, we characterize the asymmetries of the smile through multiple leverage effects in a stochastic dynamic asset pricing framework. The dependence between price movements and future volatility is introduced through a set of latent state variables. These latent variables can capture not only the volatility risk and the interest rate risk which potentially affect option prices, but also any kind of correlation risk and jump risk. The standard financial leverage effect is produced by a cross-correlation effect between the state variables which enter into the stochastic volatility process of the stock price and the stock price process itself. However, we provide a more general framework where asymmetric implied volatility curves result from any source of instantaneous correlation between the state variables and, either the return on the stock or the stochastic discount factor. In order to draw the shapes of the implied volatility curves generated by a model with latent variables, we specify an equilibrium-based stochastic discount factor with time non-separable preferences. When we calibrate this model to empirically reasonable values of the parameters, we are able to reproduce the various types of implied volatility curves inferred from option market data. Dans cet article, nous caractérisons les asymétries observées dans les courbes de volatilités implicites par la présence d'effets de levier multiples dans un modèle dynamique stochastique d'évaluation des actifs financiers. La dépendance entre les mouvements de prix et la volatilité future est introduite par l'intermédiaire d'un ensemble de variables d'état latentes. Ces variables d'état sont susceptibles de capter non seulement le risque de volatilité et le risque de taux d'intérêt qui peuvent influer sur les prix d'options,0501s encore les risques de corrélation et de saut. L'effet de levier financier traditionnel est produit quant à lui par une corrélation instantanée entre les variab

(This abstract was borrowed from another version of this item.)

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Paper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 2000-57.

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Date of creation: 2000
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Handle: RePEc:crs:wpaper:2000-57

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Citations

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Cited by:
  1. Garcia, R. & Renault, E., 2000. "Letent Variable Models for Stochastic Discount Factors," Cahiers de recherche 2000-01, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  2. repec:ebl:ecbull:v:30:y:2010:i:1:p:182-191 is not listed on IDEAS
  3. René Garcia & Richard Luger & Eric Renault, 2000. "Empirical Assessment of an Intertemporal Option Pricing Model with Latent Variables," Working Papers 2000-56, Centre de Recherche en Economie et Statistique.
  4. Ali Alami & Éric Renault, 2001. "Risque de modèle de volatilité," CIRANO Working Papers 2001s-06, CIRANO.
  5. MEDDAHI, Nour, 2001. "An Eigenfunction Approach for Volatility Modeling," Cahiers de recherche 2001-29, Universite de Montreal, Departement de sciences economiques.
  6. Alexander David & Pietro Veronesi, 1998. "Option Prices with Uncertain Fundamentals: Theory and Evidence on the Dynamics of Implied Volatilities," CRSP working papers 485, Center for Research in Security Prices, Graduate School of Business, University of Chicago.
  7. Bertholon, H. & Monfort, A. & Pegoraro, F., 2007. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working papers 188, Banque de France.
  8. Fousseni Chabi-Yo & René Garcia & Eric Renault, 2005. "State Dependence in Fundamentals and Preferences Explains Risk-Aversion Puzzle," Working Papers 05-9, Bank of Canada.
  9. Rene Garcia & Richard Luger & Eric Renault, 2004. "Option Prices, Preferences, and State Variables," Emory Economics 0418, Department of Economics, Emory University (Atlanta).
  10. René Garcia & Richard Luger & Éric Renault, 2001. "Empirical Assessment of an Intertemporal Option Pricing Model with Latent Variables (Note : New version February 2002) / Empirical Assessment of an Intertemporal Option Pricing Model with Latent Varia," CIRANO Working Papers 2001s-02, CIRANO.
  11. Frederik Lundtofte, 2010. "Implied volatility and risk aversion in a simple model with uncertain growth," Economics Bulletin, AccessEcon, vol. 30(1), pages 182-191.
  12. Almut E. D. Veraart, 2008. "Impact of time–inhomogeneous jumps and leverage type effects on returns and realised variances," CREATES Research Papers 2008-57, School of Economics and Management, University of Aarhus.

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