IDEAS home Printed from
   My bibliography  Save this paper

On the Consistency of the Lucas Pricing Formula


  • Aase, Knut K.

    () (Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration)


In order to find the real market value of an asset in an exchange economy, one would typically apply the formula appearing in Lucas (1978), developed in a discrete time framework. This theory has also been extended to continuous time models, in which case the same pricing formula has been universally applied. While the discrete time theory is rather transparent, there has been some confusion regarding the continuous time analogue. In particular, the continuous time pricing formula must contain a certain type of a square covariance term that does not readily follow from the discrete time formulation. As a result, this term has sometimes been missing in situations where it should have been included. In this paper we reformulate the discrete time theory in such a way that this covariance term does not come as a mystery in the continuous time version. It is shown, e.g., that this term is of importance also in the equivalent martingale measure approach to pricing. In most real life situations dividends are paid out in lump sums, not in rates. This leads to a discontinuous model, and adding a continuous time framework, it appears that our framework is a most natural one in finance.

Suggested Citation

  • Aase, Knut K., 2005. "On the Consistency of the Lucas Pricing Formula," Discussion Papers 2005/9, Norwegian School of Economics, Department of Business and Management Science.
  • Handle: RePEc:hhs:nhhfms:2005_009

    Download full text from publisher

    File URL:
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    1. Duffie, Darrell & Zame, William, 1989. "The Consumption-Based Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 57(6), pages 1279-1297, November.
    2. Kaushik I. Amin & Robert A. Jarrow, 2008. "Pricing Options On Risky Assets In A Stochastic Interest Rate Economy," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 15, pages 327-347 World Scientific Publishing Co. Pte. Ltd..
    3. Jamshidian, Farshid, 1989. " An Exact Bond Option Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 205-209, March.
    4. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters,in: Theory Of Valuation, chapter 8, pages 229-288 World Scientific Publishing Co. Pte. Ltd..
    5. Lars Nielsen, 2007. "Dividends in the theory of derivative securities pricing," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(3), pages 447-471, June.
    6. Ross, Stephen A, 1978. "A Simple Approach to the Valuation of Risky Streams," The Journal of Business, University of Chicago Press, vol. 51(3), pages 453-475, July.
    7. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    8. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    9. Knut K. Aase, 2002. "Equilibrium Pricing in the Presence of Cumulative Dividends Following a Diffusion," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 173-198.
    10. repec:dau:papers:123456789/13604 is not listed on IDEAS
    11. Duffie, Darrell & Shafer, Wayne, 1985. "Equilibrium in incomplete markets: I : A basic model of generic existence," Journal of Mathematical Economics, Elsevier, vol. 14(3), pages 285-300, June.
    Full references (including those not matched with items on IDEAS)

    More about this item


    Exchange economy; state price deflator; discrete time; continuous time; equivalent martingale measure; the Gordon growth model;

    JEL classification:

    • G00 - Financial Economics - - General - - - General

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hhs:nhhfms:2005_009. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Stein Fossen). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.