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Option Pricing: Real and Risk-Neutral Distributions

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Author Info
Constantinides, George M.
Jackwerth, Jens Carsten
Perrakis, Stylianos

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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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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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Related research
Keywords: Option; Pricing;

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Find related papers by JEL classification:
D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

References listed on IDEAS
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    Other versions:
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    Other versions:
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  8. 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. [Downloadable!] (restricted)
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  32. Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. " Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1611-32, December. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. 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. [Downloadable!]
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