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Asymmetric Smiles, Leverage Effects and Structural Parameters

Author

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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.

Suggested Citation

  • GARCIA,René & LUGER, Richard & RENAULT, Éric, 2001. "Asymmetric Smiles, Leverage Effects and Structural Parameters," Cahiers de recherche 2001-09, Universite de Montreal, Departement de sciences economiques.
    • Handle: RePEc:mtl:montde:2001-09
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    Cited by:

    1. René Garcia & Richard Luger & Éric Renault, 2005. "Viewpoint: Option prices, preferences, and state variables," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 38(1), pages 1-27, February.
    2. Garcia, Rene & Luger, Richard & Renault, Eric, 2003. "Empirical assessment of an intertemporal option pricing model with latent variables," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 49-83.
    3. repec:ebl:ecbull:v:30:y:2010:i:1:p:182-191 is not listed on IDEAS
    4. Daglish, Toby & Maheu, John & McCurdy, Tom, 2008. "A Financial Metric for Comparing Volatility Models: Do Better Models Make Money?," Working Paper Series 4009, Victoria University of Wellington, The New Zealand Institute for the Study of Competition and Regulation.
    5. Almut E. D. Veraart, 2008. "Impact of time–inhomogeneous jumps and leverage type effects on returns and realised variances," CREATES Research Papers 2008-57, Department of Economics and Business Economics, Aarhus University.
    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. Anindya Biswas & Biswajit Mandal, 2016. "Estimating Preference Parameters From Stock Returns Using Simulated Method Of Moments," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 1-13, March.
    8. Ali Alami & Eric Renault, 2001. "Risque de modèle de volatilité," CIRANO Working Papers 2001s-06, CIRANO.
    9. Henri Bertholon & Alain Monfort & Fulvio Pegoraro, 2006. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working Papers 2006-28, Center for Research in Economics and Statistics.
    10. MEDDAHI, Nour, 2001. "An Eigenfunction Approach for Volatility Modeling," Cahiers de recherche 2001-29, Universite de Montreal, Departement de sciences economiques.
    11. Benzoni, Luca & Collin-Dufresne, Pierre & Goldstein, Robert S., 2011. "Explaining asset pricing puzzles associated with the 1987 market crash," Journal of Financial Economics, Elsevier, vol. 101(3), pages 552-573, September.
    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.
    13. Fousseni Chabi-Yo & René Garcia & Eric Renault, 2005. "State Dependence in Fundamentals and Preferences Explains Risk-Aversion Puzzle," Staff Working Papers 05-9, Bank of Canada.
    14. repec:vuw:vuwscr:19110 is not listed on IDEAS
    15. Daglish, Toby & Maheu, John & McCurdy, Tom, 2008. "A Financial Metric for Comparing Volatility Models: Do Better Models Make Money?," Working Paper Series 19110, Victoria University of Wellington, The New Zealand Institute for the Study of Competition and Regulation.
    16. René Garcia & Eric Renault, 1999. "Latent Variable Models for Stochastic Discount Factors," CIRANO Working Papers 99s-47, CIRANO.
    17. René Garcia & Richard Luger & Eric Renault, 2001. "Empirical Assessment of an Intertemporal Option Pricing Model with Latent Variables (Note : Nouvelle version Février 2002)," CIRANO Working Papers 2001s-02, CIRANO.

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    More about this item

    Keywords

    oion icing; stochastic discount factor; stochastic volatility; Black-Scholes imied volatility; smile effect; equilibrium oion icing;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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