On the Consistency of the Lucas Pricing Formula
AbstractIn 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Department of Business and Management Science, Norwegian School of Economics in its series Discussion Papers with number 2005/9.
Length: 19 pages
Date of creation: 30 Nov 2005
Date of revision:
Contact details of provider:
Postal: NHH, Department of Business and Management Science, Helleveien 30, N-5045 Bergen, Norway
Phone: +47 55 95 92 93
Fax: +47 55 95 96 50
Web page: http://www.nhh.no/en/research-faculty/department-of-business-and-management-science.aspx
More information through EDIRC
Exchange economy; state price deflator; discrete time; continuous time; equivalent martingale measure; the Gordon growth model;
Find related papers by JEL classification:
- G00 - Financial Economics - - General - - - General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-10-21 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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 453-75, July.
- Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
- Darrell Duffie & William Zame, 1988.
"The Consumption-Based Capital Asset Pricing Model,"
88-10, University of Copenhagen. Department of Economics.
- Kaushik I. Amin & Robert A. Jarrow, 1992. "Pricing Options On Risky Assets In A Stochastic Interest Rate Economy," Mathematical Finance, Wiley Blackwell, vol. 2(4), pages 217-237.
- 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.
- Lars Nielsen, 2007. "Dividends in the theory of derivative securities pricing," Economic Theory, Springer, vol. 31(3), pages 447-471, June.
- 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.
- Jamshidian, Farshid, 1989. " An Exact Bond Option Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 205-09, March.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Stein Fossen).
If references are entirely missing, you can add them using this form.