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Option pricing: Real and risk-neutral distributions

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  • Constantinides, George M.
  • Jackwerth, Jens Carsten
  • Perrakis, Stylianos

Abstract

The central premise of the Black and Scholes [Black, F., Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy 81, 637–659] and Merton [Merton, R. (1973). Theory of rational option pricing. Bell Journal of Economics and Management Science 4, 141–184] option pricing theory is that there exists a self-financing dynamic trading policy of the stock and risk free accounts that renders the market dynamically complete. This requires that the market be complete and perfect. In this essay, we are concerned with cases in which dynamic trading breaks down either because the market is incomplete or because it is imperfect due to the presence of trading costs, or both. Market incompleteness renders the risk-neutral probability measure non unique and allows us to determine the option price only within a range. Recognition of trading costs requires a refinement in the definition and usage of the concept of a risk-neutral probability measure. Under these market conditions, a replicating dynamic trading policy does not exist. Nevertheless, we are able to impose restrictions on the pricing kernel and derive testable restrictions on the prices of options.We illustrate the theory in a series of market setups, beginning with the single period model, the two-period model and, finally, the general multiperiod model, with or without transaction costs.We also review related empirical results that document widespread violations of these restrictions.
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  • Constantinides, George M. & Jackwerth, Jens Carsten & Perrakis, Stylianos, 2005. "Option pricing: Real and risk-neutral distributions," CoFE Discussion Papers 05/06, University of Konstanz, Center of Finance and Econometrics (CoFE).
    • Handle: RePEc:zbw:cofedp:0506
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    3. Wael Bahsoun & Pawel Góra & Silvia Mayoral & Manuel Morales, 2006. "Random Dynamics and Finance: Constructing Implied Binomial Trees from a Predetermined Stationary Den," Faculty Working Papers 13/06, School of Economics and Business Administration, University of Navarra.
    4. Bozic, Marin & Newton, John & Thraen, Cameron S. & Gould, Brian W., 2014. "Parametric Bootstrap Tests for Futures Price and Implied Volatility Biases With Application to Rating Dairy Margin Insurance," 2014 Annual Meeting, July 27-29, 2014, Minneapolis, Minnesota 170416, Agricultural and Applied Economics Association.
    5. Guenter Franke & James Huang & Richard Stapleton, 2006. "Two-dimensional risk-neutral valuation relationships for the pricing of options," Review of Derivatives Research, Springer, vol. 9(3), pages 213-237, November.
    6. Abarca Gustavo & Rangel José Gonzalo & Benavides Guillermo, 2010. "Exchange Rate Market Expectations and Central Bank Policy: The case of the Mexican Peso-US Dollar from 2005-2009," Working Papers 2010-17, Banco de México.
    7. Alexandros Kostakis, 2007. "Mind Coskewness: A Performance Measure for Prudent, Long-Term Investors," Discussion Papers 07/07, Department of Economics, University of York.
    8. Nicola Secomandi & Sunder Kekre, 2014. "Optimal Energy Procurement in Spot and Forward Markets," Manufacturing & Service Operations Management, INFORMS, vol. 16(2), pages 270-282, May.
    9. M. Benko & M. Fengler & W. Härdle & M. Kopa, 2007. "On extracting information implied in options," Computational Statistics, Springer, vol. 22(4), pages 543-553, December.

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    More about this item

    Keywords

    Derivative pricing; risk-neutral distribution; incomplete markets; stochastic dominance bounds; transaction costs; index options; volatility smile;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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