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Risk Aversion, Intertemporal Substitution, and Option Pricing

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  • GARCIA, René
  • RENAULT, Éric

Abstract

This paper develops a general stochastic framework and an equilibrium asset pricing model that make clear how attitudes towards intertemporal substitution and risk matter for option pricing. In particular, we show under which statistical conditions option pricing formulas are not preference-free, in other words, when preferences are not hidden in the stock and bond prices as they are in the standard Black and Scholes (BS) or Hull and White (HW) pricing formulas. The dependence of option prices on preference parameters comes from several instantaneous causality effects such as the so-called leverage effect. We also emphasize that the most standard asset pricing models (CAPM for the stock and BS or HW preference-free option pricing) are valid under the same stochastic setting (typically the absence of leverage effect), regardless of preference parameter values. Even though we propose a general non-preference-free option pricing formula, we always keep in mind that the BS formula is dominant both as a theoretical reference model and as a tool for practitioners. Another contribution of the paper is to characterize why the BS formula is such a benchmark. We show that, as soon as we are ready to accept a basic property of option prices, namely their homogeneity of degree one with respect to the pair formed by the underlying stock price and the strike price, the necessary statistical hypotheses for homogeneity provide BS-shaped option prices in equilibrium. This BS-shaped option-pricing formula allows us to derive interesting characterizations of the volatility smile, that is, the pattern of BS implicit volatilities as a function of the option moneyness. First, the asymmetry of the smile is shown to be equivalent to a particular form of asymmetry of the equivalent martingale measure. Second, this asymmetry appears precisely when there is either a premium on an instantaneous interest rate risk or on a generalized leverage effect or both, in other words, whenever the option pricing formula is not preference-free. Therefore, the main conclusion of our analysis for practitioners should be that an asymmetric smile is indicative of the relevance of preference parameters to price options.

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Bibliographic Info

Paper provided by Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number 9801.

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Length: 45 pages
Date of creation: 1998
Date of revision:
Handle: RePEc:mtl:montde:9801

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Keywords: causality; hidden Markov chains; non-serable utility; equilibrium oion icing; recursive utility; Black-Scholes imicit volatility; smile effect;

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References

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Citations

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Cited by:
  1. Henri Bertholon & Alain Monfort & Fulvio Pegoraro, 2007. "Econometric Asset Pricing Modelling," Working Papers 2007-18, Centre de Recherche en Economie et Statistique.
  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. René Garcia & Richard Luger & Éric Renault, 2001. "Asymmetric Smiles, Leverage Effects and Structural Parameters," CIRANO Working Papers 2001s-01, CIRANO.
  4. René Garcia & Eric Ghysels & Éric Renault, 2004. "The Econometrics of Option Pricing," CIRANO Working Papers 2004s-04, CIRANO.
  5. Bertholon, H. & Monfort, A. & Pegoraro, F., 2007. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working papers 188, Banque de France.
  6. Robert R. Bliss & Nikolaos Panigirtzoglou, 2001. "Recovering risk aversion from options," Working Paper Series WP-01-15, Federal Reserve Bank of Chicago.
  7. Rene Garcia & Richard Luger & Eric Renault, 2004. "Option Prices, Preferences, and State Variables," Emory Economics 0418, Department of Economics, Emory University (Atlanta).
  8. Eric Ghysels & Valentin Patilea & Éric Renault & Olivier Torrès, 1997. "Nonparametric Methods and Option Pricing," CIRANO Working Papers 97s-19, CIRANO.
  9. Stanislav Khrapov, 2012. "Risk Premia: Short and Long-term," Working Papers w0169, Center for Economic and Financial Research (CEFIR).
  10. René Garcia & Ramazan Gençay, 1998. "Pricing and Hedging Derivative Securities with Neural Networks and a Homogeneity Hint," CIRANO Working Papers 98s-35, CIRANO.

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