Option Pricing: Real and Risk-Neutral Distributions

HANDBOOKS IN OPERATIONS RESEARCH AND MANAGEMENT SCIENCE: FINANCIAL ENGINEERING, J.R. Birge, V. Linetsky, eds., Vol. 15, pp. 565-591, Elsevier, 2007

37 Pages Posted: 18 Nov 2008 Last revised: 5 Dec 2008

See all articles by George M. Constantinides

George M. Constantinides

University of Chicago - Booth School of Business; National Bureau of Economic Research (NBER)

Stylianos Perrakis

Concordia University, Quebec - John Molson School of Business

Jens Carsten Jackwerth

University of Konstanz - Department of Economics

Date Written: January 1, 2007

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.

Suggested Citation

Constantinides, George M. and Perrakis, Stylianos and Jackwerth, Jens Carsten, Option Pricing: Real and Risk-Neutral Distributions (January 1, 2007). HANDBOOKS IN OPERATIONS RESEARCH AND MANAGEMENT SCIENCE: FINANCIAL ENGINEERING, J.R. Birge, V. Linetsky, eds., Vol. 15, pp. 565-591, Elsevier, 2007. Available at SSRN: https://ssrn.com/abstract=1303490

George M. Constantinides

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States
773-702-7258 (Phone)
773-752-0458 (Fax)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Stylianos Perrakis

Concordia University, Quebec - John Molson School of Business ( email )

1455 de Maisonneuve Blvd. W.
Montreal, Quebec H3G 1M8
Canada

Jens Carsten Jackwerth (Contact Author)

University of Konstanz - Department of Economics ( email )

Universitaetsstr. 10
Konstanz, 78457
Germany
+497531882196 (Phone)
+497531883120 (Fax)

HOME PAGE: http://cms.uni-konstanz.de/wiwi/jackwerth/

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