IDEAS home Printed from https://ideas.repec.org/p/cdl/anderf/qt6gk6b0xw.html
   My bibliography  Save this paper

On the Consistency of the Lucas Pricing Formula

Author

Listed:
  • Aase, Knut K

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 that this term is also of importance 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," University of California at Los Angeles, Anderson Graduate School of Management qt6gk6b0xw, Anderson Graduate School of Management, UCLA.
    • Handle: RePEc:cdl:anderf:qt6gk6b0xw
    as

    Download full text from publisher

    File URL: https://www.escholarship.org/uc/item/6gk6b0xw.pdf;origin=repeccitec
    Download Restriction: no
    ---><---

    Other versions of this item:

    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.
    2. repec:bla:jfinan:v:44:y:1989:i:1:p:205-09 is not listed on IDEAS
    3. 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.
    4. 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.
    5. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    6. 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, July.
    7. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    8. Kaushik I. Amin & Robert A. Jarrow, 1992. "Pricing Options On Risky Assets In A Stochastic Interest Rate Economy1," Mathematical Finance, Wiley Blackwell, vol. 2(4), pages 217-237, October.
    9. 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.
    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)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Anderson, Robert M. & Raimondo, Roberto C., 2007. "Equilibrium in Continuous-Time Financial Markets: Endogenously Dynamically Complete Markets," Department of Economics, Working Paper Series qt0zq6v5gd, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    2. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    3. repec:dau:papers:123456789/5374 is not listed on IDEAS
    4. René Garcia & Richard Luger & Eric Renault, 2000. "Asymmetric Smiles, Leverage Effects and Structural Parameters," Working Papers 2000-57, Center for Research in Economics and Statistics.
    5. GARCIA, René & RENAULT, Éric, 1998. "Risk Aversion, Intertemporal Substitution, and Option Pricing," Cahiers de recherche 9801, Universite de Montreal, Departement de sciences economiques.
    6. René Garcia & Eric Renault, 1999. "Latent Variable Models for Stochastic Discount Factors," CIRANO Working Papers 99s-47, CIRANO.
    7. Ibáñez, Alfredo, 2008. "Factorization of European and American option prices under complete and incomplete markets," Journal of Banking & Finance, Elsevier, vol. 32(2), pages 311-325, February.
    8. Sebastián A. Rey, 2016. "The Valuation of Equities and the GDP Growth Effect: A Global Empirical Study," IJFS, MDPI, vol. 4(4), pages 1-18, October.
    9. René Garcia & Richard Luger & Éric Renault, 2005. "Viewpoint: Option prices, preferences, and state variables," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 38(1), pages 1-27, February.
    10. Brisset, Nicolas, 2017. "On Performativity: Option Theory And The Resistance Of Financial Phenomena," Journal of the History of Economic Thought, Cambridge University Press, vol. 39(4), pages 549-569, December.
    11. Ait-Sahalia, Yacine & Lo, Andrew W., 2000. "Nonparametric risk management and implied risk aversion," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 9-51.
    12. Rojo Suárez, Javier & Alonso Conde, Ana Belén & Ferrero Pozo, Ricardo, 2020. "European equity markets: Who is the truly representative investor?," The Quarterly Review of Economics and Finance, Elsevier, vol. 75(C), pages 325-346.
    13. Yong-Jin Kim & Naoto Kunitomo, 1999. "Pricing Options under Stochastic Interest Rates: A New Approach," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 6(1), pages 49-70, January.
    14. Maria Arduca & Cosimo Munari, 2020. "Fundamental theorem of asset pricing with acceptable risk in markets with frictions," Papers 2012.08351, arXiv.org, revised Apr 2022.
    15. Bizid, Abdelhamid & Jouini, Elyès, 2005. "Equilibrium Pricing in Incomplete Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 40(4), pages 833-848, December.
    16. Jean-Paul Décamps, 1993. "Valorisation de produits obligataires dans un modéle d'équilibre général en temps discret," Annals of Economics and Statistics, GENES, issue 31, pages 73-100.
    17. John Y. Campbell, 2000. "Asset Pricing at the Millennium," Journal of Finance, American Finance Association, vol. 55(4), pages 1515-1567, August.
    18. Rosenberg, Joshua V. & Engle, Robert F., 2002. "Empirical pricing kernels," Journal of Financial Economics, Elsevier, vol. 64(3), pages 341-372, June.
    19. Jin-Chuan Duan & Jean-Guy Simonato, 1995. "Empirical Martingale Simulation for Asset Prices," CIRANO Working Papers 95s-43, CIRANO.
    20. René Garcia & Richard Luger & Eric Renault, 2001. "Empirical Assessment of an Intertemporal Option Pricing Model with Latent Variables (Note : Nouvelle version Février 2002)," CIRANO Working Papers 2001s-02, CIRANO.
    21. Aase, Knut K., 2004. "The perpetual American put option for jump-diffusions: Implications for equity premiums," Discussion Papers 2004/19, Norwegian School of Economics, Department of Business and Management Science.

    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

    Statistics

    Access and download statistics

    Corrections

    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:cdl:anderf:qt6gk6b0xw. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Lisa Schiff (email available below). General contact details of provider: https://edirc.repec.org/data/aguclus.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.