Equilibrium Pricing in the Presence of Cumulative Dividends Following a Diffusion

26 Pages Posted: 15 Nov 2002

See all articles by Knut K. Aase

Knut K. Aase

Norwegian School of Economics (NHH) - Department of Business and Management Science

Abstract

The paper presents some security market pricing results in the setting of a security market equilibrium in continuous time. The theme of the paper is financial valuation theory when the primitive assets pay out real dividends represented by processes of unbounded variation. In continuous time, when the models are also continuous, this is the most general representation of real dividends, and it can be of practical interest to analyze such models.

Taking as the starting point an extension to continuous time of the Lucas consumption-based model, we derive the equilibrium short-term interest rate, present a new derivation of the consumption-based capital asset pricing model, demonstrate how equilibrium forward and futures prices can be derived, including several examples, and finally we derive the equilibrium price of a European call option in a situation where the underlying asset pays dividends according to an Ito process of unbounded variation. In the latter case we demonstrate how this pricing formula simplifies to known results in special cases, among them the famous Black-Scholes formula and the Merton formula for a special dividend rate process.

Suggested Citation

Aase, Knut K., Equilibrium Pricing in the Presence of Cumulative Dividends Following a Diffusion. Mathematical Finance, Vol. 12, pp. 173-198, 2002. Available at SSRN: https://ssrn.com/abstract=316204

Knut K. Aase (Contact Author)

Norwegian School of Economics (NHH) - Department of Business and Management Science ( email )

Helleveien 30
Bergen, NO-5045
Norway

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