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On the Consistency of the Lucas Pricing Formula

Author

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  • Aase, Knut K.

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

Abstract

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
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    File URL: http://hdl.handle.net/11250/163764
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    References listed on IDEAS

    as
    1. Duffie, Darrell & Zame, William, 1989. "The Consumption-Based Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 57(6), pages 1279-1297, November.
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    More about this item

    Keywords

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

    JEL classification:

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

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