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Option Pricing: Real and Risk-Neutral Distributions

  • Jens Carsten Jackwerth

    ()

    (Department of Economics, University of Konstanz)

  • George M. Constantinaides

    ()

    (University of Chicago and NBER)

  • Stylianos Perrakis

    ()

    (Concordia University)

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 Center of Finance and Econometrics, University of Konstanz in its series CoFE Discussion Paper with number 05-06.

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Length: 36 pages
Date of creation: 16 Sep 2005
Date of revision:
Handle: RePEc:knz:cofedp:0506
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