Advanced Search
MyIDEAS: Login

Arbitrage in securities markets with short-sales constraints

Contents:

Author Info

  • Jouini, Elyès
  • Kallal, Hedi
Registered author(s):

    Abstract

    In this paper we derive the implications of the absence of arbitrage in securities markets models where traded securities are subject to short-sales constraints and where the borrowing and lending rates differ. We show that a securities price system is arbitrage free if and only if there exists a numeraire and an equivalent probability measure for which the normalized (by the numeraire) price processes of traded securities are supermartingales. Also, the tightest arbitrage bounds that can be inferred on the price of a contingent claim without knowing agents’preferences are equal to its largest and smallest expected normalized payoff with respect to the supermartingale measures. In the case where the underlying security price follows a diffusion process and where short selling is possible but costly, we derive partial differential equations that must be satisfied by the arbitrage bounds on derivative securities prices, and we determine optimal hedging strategies. We compute the arbitrage bounds on common securities numerically for several values of the borrowing and short-selling costs and show that they can be quite sharp.

    Download Info

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below under "Related research" whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Bibliographic Info

    Paper provided by Paris Dauphine University in its series Economics Papers from University Paris Dauphine with number 123456789/5647.

    as in new window
    Length:
    Date of creation: Jul 1995
    Date of revision:
    Publication status: Published in Mathematical Finance, 1995, Vol. 5, no. 3. pp. 197-232.Length: 35 pages
    Handle: RePEc:dau:papers:123456789/5647

    Contact details of provider:
    Web page: http://www.dauphine.fr/en/welcome.html
    More information through EDIRC

    Related research

    Keywords: Short-sales constraints; borrowing costs; martingale approach; equivalent supermatingale and submartingale measures; perturbed heat equation; arbitrage bounds; hedging;

    Find related papers by JEL classification:

    References

    No references listed on IDEAS
    You can help add them by filling out this form.

    Citations

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

    Cited by:
    1. M A H Dempster & I V Evstigneev & M I Taksar, 2005. "Asset pricing and hedging in financial markets with transaction costs: an approach based on the von Neumann-Gale model," Working Papers 062005, University of Cambridge, Judge Business School, Centre for Financial Research.
    2. Borglin, Anders & Flåm, Sjur, 2007. "Rationalizing Constrained Contingent Claims," Working Papers 2007:12, Lund University, Department of Economics.
    3. Jouini, Elyès & Napp, Clotilde & Kallal, Hedi, 2001. "Arbitrage and viability in securities markets with fixed trading costs," Economics Papers from University Paris Dauphine 123456789/5593, Paris Dauphine University.
    4. Kallio, Markku & Ziemba, William T., 2007. "Using Tucker's theorem of the alternative to simplify, review and expand discrete arbitrage theory," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2281-2302, August.
    5. Joao Amaro De Matos & Paula Antao, 2003. "Market illiquidity and bounds on European option prices," The European Journal of Finance, Taylor & Francis Journals, vol. 9(5), pages 475-498.
    6. Jouini, Elyès, 2001. "Arbitrage and control problems in finance: A presentation," Economics Papers from University Paris Dauphine 123456789/5590, Paris Dauphine University.
    7. Peter Bank & Selim G\"okay, 2013. "Superreplication when trading at market indifference prices," Papers 1310.3113, arXiv.org.
    8. Napp, C., 2003. "The Dalang-Morton-Willinger theorem under cone constraints," Journal of Mathematical Economics, Elsevier, vol. 39(1-2), pages 111-126, February.
    9. Touzi, Nizar, 2000. "Direct characterization of the value of super-replication under stochastic volatility and portfolio constraints," Stochastic Processes and their Applications, Elsevier, vol. 88(2), pages 305-328, August.
    10. João Amaro de Matos & Paula Antão, 2001. "Super-replicating Bounds on European Option Prices when the Underlying Asset is Illiquid," Economics Bulletin, AccessEcon, vol. 7(1), pages 1-7.
    11. Arash Fahim & Yu-Jui Huang, 2014. "Model-independent Superhedging under Portfolio Constraints," Papers 1402.2599, arXiv.org.
    12. Gerber, Hans U. & Shiu, Elias S. W., 1996. "Actuarial bridges to dynamic hedging and option pricing," Insurance: Mathematics and Economics, Elsevier, vol. 18(3), pages 183-218, November.
    13. Jochen Wilhelm & Josef Schosser, 2007. "A note on arbitrage-free asset prices with and without personal income taxes," Review of Managerial Science, Springer, vol. 1(2), pages 133-149, August.
    14. Napp, Clotilde, 2001. "Pricing issues with investment flows Applications to market models with frictions," Journal of Mathematical Economics, Elsevier, vol. 35(3), pages 383-408, June.
    15. Pham, Huyen & Touzi, Nizar, 1999. "The fundamental theorem of asset pricing with cone constraints," Journal of Mathematical Economics, Elsevier, vol. 31(2), pages 265-279, March.
    16. Roux, Alet, 2011. "The fundamental theorem of asset pricing in the presence of bid-ask and interest rate spreads," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 159-163, March.
    17. Alexander M. G. Cox & Zhaoxu Hou & Jan Obloj, 2014. "Robust pricing and hedging under trading restrictions and the emergence of local martingale models," Papers 1406.0551, arXiv.org.
    18. Fehle, Frank, 2004. "A note on transaction costs and the existence of derivatives markets," Journal of Economics and Business, Elsevier, vol. 56(1), pages 63-70.
    19. Young, Virginia R. & Zariphopoulou, Thaleia, 2000. "Computation of distorted probabilities for diffusion processes via stochastic control methods," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 1-18, August.

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:dau:papers:123456789/5647. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Alexandre Faure).

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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