IDEAS home Printed from https://ideas.repec.org/a/rpo/ripoec/v98y2008i6p43-78.html
   My bibliography  Save this article

Arbitrages and Arrow-Debreu Prices

Author

Listed:
  • Gaia Barone

    (Università LUISS “Guido Carli”)

Abstract

The goal of this work is to check that there are no arbitrage opportunities in the CBOE market for S&P500 options and to extract from these options’ quotes the state-price density consistent with the Merton model. The structure of the article is as follows: in Section 2 we examine the relations between arbitrages and Arrow-Debreu prices; in Section 3 we consider two models which seem to be consistent with the market prices of index options: the CEV model and the Merton model; finally, in Section 4 we estimate the state-price density consistent with the Merton-Geske model. Some conclusions follow.

Suggested Citation

  • Gaia Barone, 2008. "Arbitrages and Arrow-Debreu Prices," Rivista di Politica Economica, SIPI Spa, vol. 98(6), pages 43-78, November-.
  • Handle: RePEc:rpo:ripoec:v:98:y:2008:i:6:p:43-78
    as

    Download full text from publisher

    File URL: http://www.rivistapoliticaeconomica.it/2008/nov-dic/pdf/Barone_en.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hansen, Lars Peter & Jagannathan, Ravi, 1991. "Implications of Security Market Data for Models of Dynamic Economies," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 225-262, April.
    2. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    3. Stephen A. Ross, 1976. "Options and Efficiency," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 90(1), pages 75-89.
    4. Scholes, Myron S. & Wolfson, Mark A., 1989. "Decentralized investment banking : The case of discount dividend-reinvestment and stock-purchase plans," Journal of Financial Economics, Elsevier, vol. 24(1), pages 7-35, September.
    5. Geske, Robert, 1977. "The Valuation of Corporate Liabilities as Compound Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 541-552, November.
    6. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    7. Vernon L. Smith, 2003. "Constructivist and Ecological Rationality in Economics," American Economic Review, American Economic Association, vol. 93(3), pages 465-508, June.
    8. K. J. Arrow, 1964. "The Role of Securities in the Optimal Allocation of Risk-bearing," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 31(2), pages 91-96.
    9. Rubinstein, Mark, 1994. "Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    10. Garman, Mark B., 1976. "An algebra for evaluating hedge portfolios," Journal of Financial Economics, Elsevier, vol. 3(4), pages 403-427, October.
    11. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    12. Banz, Rolf W & Miller, Merton H, 1978. "Prices for State-contingent Claims: Some Estimates and Applications," The Journal of Business, University of Chicago Press, vol. 51(4), pages 653-672, October.
    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. 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.
    2. Bhupinder Bahra, 1997. "Implied risk-neutral probability density functions from option prices: theory and application," Bank of England working papers 66, Bank of England.
    3. Ait-Sahalia, Yacine & Wang, Yubo & Yared, Francis, 2001. "Do option markets correctly price the probabilities of movement of the underlying asset?," Journal of Econometrics, Elsevier, vol. 102(1), pages 67-110, May.
    4. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    5. Zhangxin (Frank) Liu & Michael J. O'Neill & Tom Smith, 2017. "State-preference pricing and volatility indices," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 57(3), pages 815-836, September.
    6. Carole Bernard & Oleg Bondarenko & Steven Vanduffel, 2021. "A model-free approach to multivariate option pricing," Review of Derivatives Research, Springer, vol. 24(2), pages 135-155, July.
    7. Joe Akira Yoshino, 2003. "Market Risk and Volatility in the Brazilian Stock Market," Journal of Applied Economics, Universidad del CEMA, vol. 6, pages 385-403, November.
    8. Bakshi, Gurdip & Madan, Dilip & Panayotov, George, 2010. "Returns of claims on the upside and the viability of U-shaped pricing kernels," Journal of Financial Economics, Elsevier, vol. 97(1), pages 130-154, July.
    9. Carole Bernard & Oleg Bondarenko & Steven Vanduffel, 2018. "Rearrangement algorithm and maximum entropy," Annals of Operations Research, Springer, vol. 261(1), pages 107-134, February.
    10. Liu, Zhangxin (Frank) & Faff, Robert, 2017. "Hitting SKEW for SIX," Economic Modelling, Elsevier, vol. 64(C), pages 449-464.
    11. Joshua Rosenberg, 2000. "Asset Pricing Puzzles: Evidence from Options Markets," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-025, New York University, Leonard N. Stern School of Business-.
    12. Christoffersen, Peter & Heston, Steven & Jacobs, Kris, 2010. "Option Anomalies and the Pricing Kernel," Working Papers 11-17, University of Pennsylvania, Wharton School, Weiss Center.
    13. Jarno Talponen, 2013. "Matching distributions: Asset pricing with density shape correction," Papers 1312.4227, arXiv.org, revised Mar 2018.
    14. Merton, Robert, 1990. "Capital market theory and the pricing of financial securities," Handbook of Monetary Economics, in: B. M. Friedman & F. H. Hahn (ed.), Handbook of Monetary Economics, edition 1, volume 1, chapter 11, pages 497-581, Elsevier.
    15. Scholes, Myron S, 1998. "Derivatives in a Dynamic Environment," American Economic Review, American Economic Association, vol. 88(3), pages 350-370, June.
    16. Li, Yifan & Nolte, Ingmar & Pham, Manh Cuong, 2024. "Parametric risk-neutral density estimation via finite lognormal-Weibull mixtures," Journal of Econometrics, Elsevier, vol. 241(2).
    17. Vladislav Kargin, 2003. "Consistent Estimation of Pricing Kernels from Noisy Price Data," Papers math/0310223, arXiv.org.
    18. Almeida, Caio & Freire, Gustavo, 2022. "Pricing of index options in incomplete markets," Journal of Financial Economics, Elsevier, vol. 144(1), pages 174-205.
    19. José Renato Haas Ornelas & José Santiago Fajardo Barbachan & Aquiles Rocha de Farias, 2012. "Estimating Relative Risk Aversion, Risk-Neutral and Real-World Densities using Brazilian Real Currency Options," Working Papers Series 269, Central Bank of Brazil, Research Department.
    20. Marco Avellaneda & Craig Friedman & Richard Holmes & Dominick Samperi, 1997. "Calibrating volatility surfaces via relative-entropy minimization," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(1), pages 37-64.

    More about this item

    Keywords

    state-price density; index options; Merton-Geske model;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

    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:rpo:ripoec:v:98:y:2008:i:6:p:43-78. 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: Sabrina Marino (email available below). General contact details of provider: .

    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.