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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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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 11637.

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Date of creation: 2007
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Handle: RePEc:pra:mprapa:11637

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Keywords: Option; Pricing;

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References

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  2. Constantinides, George M. & Perrakis, Stylianos, 2002. "Stochastic dominance bounds on derivatives prices in a multiperiod economy with proportional transaction costs," Journal of Economic Dynamics and Control, Elsevier, vol. 26(7-8), pages 1323-1352, July.
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Cited by:
  1. 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.
  2. 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.
  3. Wael Bahsoun & Pawel Góra & Silvia Mayoral & Manuel Morales, . "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. Jens Carsten Jackwerth & George M. Constantinides & Michal Czerwonko & Stylianos Perrakis, 2008. "Are Options on Index Futures Profitable for Risk Averse Investors? Empirical Evidence," CoFE Discussion Paper 08-08, Center of Finance and Econometrics, University of Konstanz.
  5. Alexandros Kostakis, 2007. "Mind Coskewness: A Performance Measure for Prudent, Long-Term Investors," Discussion Papers 07/07, Department of Economics, University of York.
  6. Daniel Giamouridis, 2005. "Inferring option-implied investors' risk preferences," Applied Financial Economics, Taylor & Francis Journals, vol. 15(7), pages 479-488.
  7. Jens Carsten Jackwerth & George M. Constantinaides & Stylianos Perrakis, 2005. "Option Pricing: Real and Risk-Neutral Distributions," CoFE Discussion Paper 05-06, Center of Finance and Econometrics, University of Konstanz.
  8. Gustavo Abarca & José Gonzalo Rangel & Guillermo Benavides, 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.

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