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Risk Aversion, Intertemporal Substitution, and Option Pricing

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  • René Garcia
  • Eric Renault

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
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  • René Garcia & Eric Renault, 1998. "Risk Aversion, Intertemporal Substitution, and Option Pricing," CIRANO Working Papers 98s-02, CIRANO.
    • Handle: RePEc:cir:cirwor:98s-02
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    Cited by:

    1. 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.
    2. H. Bertholon & A. Monfort & F. Pegoraro, 2008. "Econometric Asset Pricing Modelling," Journal of Financial Econometrics, Oxford University Press, vol. 6(4), pages 407-458, Fall.
    3. 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.
    4. René Garcia & Richard Luger & Eric Renault, 2000. "Asymmetric Smiles, Leverage Effects and Structural Parameters," Working Papers 2000-57, Center for Research in Economics and Statistics.
    5. Robert R. Bliss & Nikolaos Panigirtzoglou, 2001. "Recovering risk aversion from options," Working Paper Series WP-01-15, Federal Reserve Bank of Chicago.
    6. Garcia, Rene & Gencay, Ramazan, 2000. "Pricing and hedging derivative securities with neural networks and a homogeneity hint," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 93-115.
    7. GHYSELS, Eric & PATILEA, Valentin & RENAULT, Eric & TORRES, Olivier, 1997. "Nonparametric methods and option pricing," LIDAM Discussion Papers CORE 1997075, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Stanislav Khrapov, 2012. "Risk Premia: Short and Long-term," Working Papers w0169, New Economic School (NES).
    9. Jacquier, Eric & Jarrow, Robert, 2000. "Bayesian analysis of contingent claim model error," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 145-180.
    10. René Garcia & Eric Ghysels & Eric Renault, 2004. "The Econometrics of Option Pricing," CIRANO Working Papers 2004s-04, CIRANO.
    11. Fengler, Matthias R. & Hin, Lin-Yee, 2015. "Semi-nonparametric estimation of the call-option price surface under strike and time-to-expiry no-arbitrage constraints," Journal of Econometrics, Elsevier, vol. 184(2), pages 242-261.
    12. 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

    Causality; hidden Markov chains; non-separable utility; equilibrium option pricing; recursive utility; Black-Scholes implicit volatility; smile effect; Causalité; chaînes de Markov cachées; utilité non séparable; évaluation d.options par modèle d'équilibre; utilité récursive; volatilité implicite de Black-Scholes; sourire de volatilité;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • G1 - Financial Economics - - General Financial Markets

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