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Equilibrium Pricing in the Presence of Cumulative Dividends Following a Diffusion

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  • Knut K. Aase

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 It� 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. Copyright 2002 Blackwell Publishing, Inc..

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Bibliographic Info

Article provided by Wiley Blackwell in its journal Mathematical Finance.

Volume (Year): 12 (2002)
Issue (Month): 3 ()
Pages: 173-198

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Handle: RePEc:bla:mathfi:v:12:y:2002:i:3:p:173-198

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Cited by:
  1. Aase, Knut K, 2005. "On the Consistency of the Lucas Pricing Formula," University of California at Los Angeles, Anderson Graduate School of Management qt6gk6b0xw, Anderson Graduate School of Management, UCLA.
  2. Aase, Knut K., 2004. "The perpetual American put option for jump-diffusions: Implications for equity premiums," Discussion Papers 2004/19, Department of Business and Management Science, Norwegian School of Economics.
  3. Aase, Knut K., 2005. "The perpetual American put option for jump-diffusions with applications," Discussion Papers 2005/12, Department of Business and Management Science, Norwegian School of Economics.
  4. Aase, Knut K, 2005. "Using Option Pricing Theory to Infer About Historical Equity Premiums," University of California at Los Angeles, Anderson Graduate School of Management qt3dd602j5, Anderson Graduate School of Management, UCLA.
  5. Masaaki Kijima & Akihisa Tamura, 2014. "Buhlmann’s Economic Premium Principle in The Presence of Transaction Costs," KIER Working Papers 893, Kyoto University, Institute of Economic Research.
  6. Lars Nielsen, 2007. "Dividends in the theory of derivative securities pricing," Economic Theory, Springer, vol. 31(3), pages 447-471, June.
  7. Aase, Knut K., 2005. "Using Option Pricing Theory to Infer About Equity Premiums," Discussion Papers 2005/11, Department of Business and Management Science, Norwegian School of Economics.
  8. Aase, Knut K., 2004. "Negative volatility and the Survival of Western Financial Markets," Discussion Papers 2004/5, Department of Business and Management Science, Norwegian School of Economics.
  9. Aase, Knut K., 2004. "Jump Dynamics: The Equity Premium and the Risk-Free Rate Puzzles," Discussion Papers 2004/12, Department of Business and Management Science, Norwegian School of Economics.

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