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Asymmetric Smiles, Leverage Effects and Structural Parameters

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  • GARCIA,René
  • LUGER, Richard
  • RENAULT, Éric

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.

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Bibliographic Info

Paper provided by Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number 2001-09.

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Length: 50 pages
Date of creation: 2001
Date of revision:
Handle: RePEc:mtl:montde:2001-09

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Keywords: oion icing; stochastic discount factor; stochastic volatility; Black-Scholes imied volatility; smile effect; equilibrium oion icing;

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References

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Citations

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Cited by:
  1. Nour Meddahi, 2001. "An Eigenfunction Approach for Volatility Modeling," CIRANO Working Papers 2001s-70, CIRANO.
  2. 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.
  3. Henri Bertholon & Alain Monfort & Fulvio Pegoraro, 2006. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working Papers 2006-28, Centre de Recherche en Economie et Statistique.
  4. repec:ebl:ecbull:v:30:y:2010:i:1:p:182-191 is not listed on IDEAS
  5. Garcia, R. & Luger, R. & Renault, E., 2001. "Empirical Assessment of an Intertemporal option Pricing Model with Latent variables," Cahiers de recherche 2001-10, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  6. Ali Alami & Éric Renault, 2001. "Risque de modèle de volatilité," CIRANO Working Papers 2001s-06, CIRANO.
  7. 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.
  8. Rene Garcia & Richard Luger & Eric Renault, 2004. "Option Prices, Preferences, and State Variables," Emory Economics 0418, Department of Economics, Emory University (Atlanta).
  9. René Garcia & Éric Renault, 1999. "Latent Variable Models for Stochastic Discount Factors," CIRANO Working Papers 99s-47, CIRANO.
  10. 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.
  11. 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.
  12. Frederik Lundtofte, 2010. "Implied volatility and risk aversion in a simple model with uncertain growth," Economics Bulletin, AccessEcon, vol. 30(1), pages 182-191.

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