IDEAS home Printed from https://ideas.repec.org/a/bla/mathfi/v14y2004i4p487-513.html
   My bibliography  Save this article

The Squared Ornstein‐Uhlenbeck Market

Author

Listed:
  • J. Aquilina
  • L. C. G. Rogers

Abstract

We study a complete market containing J assets, each asset contributing to the production of a single commodity at a rate that is a solution to the squared Ornstein‐Uhlenbeck (Cox‐Ingersoll‐Ross) SDE. The assets are owned by K agents with CRRA utility functions, who follow feasible consumption/investment regimes so as to maximize their expected time‐additive utility from consumption. We compute the equilibrium for this economy and determine the state‐price density process from market clearing. Reducing to a single (representative) agent, and exploiting the relation between the squared‐OU and squared‐Bessel SDEs, we obtain closed‐form expressions for the values of bonds, assets, and options on the total asset value. Typical model parameters are estimated by fitting bond price data, and we use these parameters to price the assets and options numerically. Implications for the total asset price itself as a diffusion are discussed. We also estimate implied volatility surfaces for options and bond yields.

Suggested Citation

  • J. Aquilina & L. C. G. Rogers, 2004. "The Squared Ornstein‐Uhlenbeck Market," Mathematical Finance, Wiley Blackwell, vol. 14(4), pages 487-513, October.
  • Handle: RePEc:bla:mathfi:v:14:y:2004:i:4:p:487-513
    DOI: 10.1111/j.0960-1627.2004.00202.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.0960-1627.2004.00202.x
    Download Restriction: no

    File URL: https://libkey.io/10.1111/j.0960-1627.2004.00202.x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Hara, Chiaki & Huang, James & Kuzmics, Christoph, 2007. "Representative consumer's risk aversion and efficient risk-sharing rules," Journal of Economic Theory, Elsevier, vol. 137(1), pages 652-672, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Huantian Xie & Nenghui Kuang, 2021. "Sequential Maximum Likelihood Estimation for the Squared Radial Ornstein-Uhlenbeck Process," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1409-1417, December.

    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. Laurent E. Calvet & Paolo Sodini, 2014. "Twin Picks: Disentangling the Determinants of Risk-Taking in Household Portfolios," Journal of Finance, American Finance Association, vol. 69(2), pages 867-906, April.
    2. Nicole Branger & An Chen & Antje Mahayni & Thai Nguyen, 2023. "Optimal collective investment: an analysis of individual welfare," Mathematics and Financial Economics, Springer, volume 17, number 5, October.
    3. Carlier, G. & Lachapelle, A., 2011. "A numerical approach for a class of risk-sharing problems," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 1-13, January.
    4. Alexis Akira Toda & Kieran James Walsh & Stijn Van Nieuwerburgh, 2020. "The Equity Premium and the One Percent [Stock return predictability: Is it there?]," Review of Financial Studies, Society for Financial Studies, vol. 33(8), pages 3583-3623.
    5. Chiaki Hara, 2018. "Equilibrium Prices of the Market Portfolio in the CAPM with Incomplete Financial Markets," KIER Working Papers 1005, Kyoto University, Institute of Economic Research.
    6. Felix Kubler & Karl Schmedders, 2010. "Non-parametric counterfactual analysis in dynamic general equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 181-200, October.
    7. Hennessy, David A. & Lapan, Harvey E., 2006. "On the nature of certainty equivalent functionals," Journal of Mathematical Economics, Elsevier, vol. 43(1), pages 1-10, December.
    8. Sara Jonsson & Inga-Lill Söderberg, 2018. "Investigating explanatory theories on laypeople’s risk perception of personal economic collapse in a bank crisis – the Cyprus case," Journal of Risk Research, Taylor & Francis Journals, vol. 21(6), pages 763-779, June.
    9. Calvet, Laurent-Emmanuel & Grandmont, Jean-Michel & Lemaire, Isabelle, 2018. "Aggregation of heterogenous beliefs, asset pricing, and risk sharing in complete financial markets," Research in Economics, Elsevier, vol. 72(1), pages 117-146.
    10. Elyès Jouini & Clotilde Napp & Diego Nocetti, 2013. "Collective risk aversion," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 411-437, February.
    11. Hara, Chiaki & Huang, James & Kuzmics, Christoph, 2011. "Effects of background risks on cautiousness with an application to a portfolio choice problem," Journal of Economic Theory, Elsevier, vol. 146(1), pages 346-358, January.
    12. Marc Fleurbaey & Stéphane Zuber, 2021. "Fair Utilitarianism," American Economic Journal: Microeconomics, American Economic Association, vol. 13(2), pages 370-401, May.
    13. Flåm, Sjur Didrik, 2016. "Borch’s theorem, equal margins, and efficient allocation," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 162-168.
    14. Evren Ceritoğlu, 2018. "Self-insurance and consumption risk-sharing between birth-year cohorts in Turkey," Review of Economics of the Household, Springer, vol. 16(4), pages 1085-1118, December.
    15. Ghiglino, Christian & Venditti, Alain, 2011. "Wealth distribution and output fluctuations," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2478-2509.
    16. Suen, Richard M.H., 2018. "Standard risk aversion and efficient risk sharing," Economics Letters, Elsevier, vol. 173(C), pages 23-26.
    17. Christian Ghiglino & Alain Venditti, 2008. "The role of the wealth distribution on output volatility," Working Papers halshs-00281379, HAL.
    18. Gollier, Christian, 2003. "Who Should we Believe? Collective Risk-Taking Decisions with Heterogeneous Beliefs," IDEI Working Papers 201, Institut d'Économie Industrielle (IDEI), Toulouse.
    19. Christian Gollier, 2003. "Collective Risk-Taking Decisions with Heterogeneous Beliefs," CESifo Working Paper Series 909, CESifo.
    20. Chiaki Hara & James Huang & Christoph Kuzmics, 2006. "Efficient Risk-Sharing Rules with Heterogeneous Risk Attitudes and Background Risks," KIER Working Papers 621, Kyoto University, Institute of Economic Research.

    More about this item

    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:bla:mathfi:v:14:y:2004:i:4:p:487-513. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0960-1627 .

    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.