Dividends in the Theory of Derivative Securities Pricing

Economic Theory, Vol. 31, pp. 447-471, 2007

Posted: 17 Sep 2003 Last revised: 30 Jan 2010

Date Written: January 27, 2010

Abstract

This paper develops the fundamental aspects of the theory of martingale pricing of derivative securities in a setting where the cumulative gains processes are Ito processes while the cumulative dividend processes of both the underliers and the derivative securities are general enough to cover all cases encountered in practical applications. A key ingredient is a general formula for how to change the unit of account of a cumulative dividend process. The formula is inconsistent with parts of the earlier literature. It obeys a unit-invariance rule for trading strategies, satisfies a consistency property when the unit is changed twice in a row, gives the correct results in well-known and uncontroversial special cases, and fits perfectly into a generalization of the martingale valuation theory. Using that generalized theory, we show that the value of a dividend process equals the value of a claim to the nominal amount of dividends yet to be accumulated plus the value of a flow of interest on the cumulative dividends at each point in time.

Keywords: Dividends, cumulative dividend process, derivatives pricing, martingale valuation

JEL Classification: G100, G120, G130

Suggested Citation

Nielsen, Lars Tyge, Dividends in the Theory of Derivative Securities Pricing (January 27, 2010). Economic Theory, Vol. 31, pp. 447-471, 2007, Available at SSRN: https://ssrn.com/abstract=442561 or http://dx.doi.org/10.2139/ssrn.442561

Lars Tyge Nielsen (Contact Author)

Columbia University

3022 Broadway
New York, NY 10027
United States

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