IDEAS home Printed from https://ideas.repec.org/a/oup/rfinst/v19y2006i2p493-529.html
   My bibliography  Save this article

Pricing Options in an Extended Black Scholes Economy with Illiquidity: Theory and Empirical Evidence

Author

Listed:
  • U. Çetin
  • R. Jarrow
  • P. Protter
  • M. Warachka

Abstract

This article studies the pricing of options in an extended Black Scholes economy in which the underlying asset is not perfectly liquid. The resulting liquidity risk is modeled as a stochastic supply curve, with the transaction price being a function of the trade size. Consistent with the market microstructure literature, the supply curve is upward sloping with purchases executed at higher prices and sales at lower prices. Optimal discrete time hedging strategies are then derived. Empirical evidence reveals a significant liquidity cost intrinsic to every option. Copyright 2006, Oxford University Press.

Suggested Citation

  • U. Çetin & R. Jarrow & P. Protter & M. Warachka, 2006. "Pricing Options in an Extended Black Scholes Economy with Illiquidity: Theory and Empirical Evidence," The Review of Financial Studies, Society for Financial Studies, vol. 19(2), pages 493-529.
    • Handle: RePEc:oup:rfinst:v:19:y:2006:i:2:p:493-529
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/rfs/hhj014
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Hausman, Jerry A. & Lo, Andrew W. & MacKinlay, A. Craig, 1992. "An ordered probit analysis of transaction stock prices," Journal of Financial Economics, Elsevier, vol. 31(3), pages 319-379, June.
    2. Eckhard Platen & Martin Schweizer, 1998. "On Feedback Effects from Hedging Derivatives," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 67-84, January.
    3. Leland, Hayne E, 1985. "Option Pricing and Replication with Transactions Costs," Journal of Finance, American Finance Association, vol. 40(5), pages 1283-1301, December.
    4. Zhiwu Chen & Werner Stanzl & Masahiro Watanabe, 2002. "Price Impact Costs and the Limit of Arbitrage," Yale School of Management Working Papers ysm251, Yale School of Management, revised 08 Jun 2006.
    5. Edirisinghe, Chanaka & Naik, Vasanttilak & Uppal, Raman, 1993. "Optimal Replication of Options with Transactions Costs and Trading Restrictions," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(1), pages 117-138, March.
    6. Rubinstein, Mark, 1985. "Nonparametric Tests of Alternative Option Pricing Models Using All Reported Trades and Quotes on the 30 Most Active CBOE Option Classes from August 23, 1976 through August 31, 1978," Journal of Finance, American Finance Association, vol. 40(2), pages 455-480, June.
    7. Lee, Charles M C & Ready, Mark J, 1991. "Inferring Trade Direction from Intraday Data," Journal of Finance, American Finance Association, vol. 46(2), pages 733-746, June.
    8. Boyle, Phelim P & Vorst, Ton, 1992. "Option Replication in Discrete Time with Transaction Costs," Journal of Finance, American Finance Association, vol. 47(1), pages 271-293, March.
    9. RØdiger Frey, 1998. "Perfect option hedging for a large trader," Finance and Stochastics, Springer, vol. 2(2), pages 115-141.
    10. Fabrizio Lillo & J. Doyne Farmer & Rosario N. Mantegna, 2002. "Single Curve Collapse of the Price Impact Function for the New York Stock Exchange," Papers cond-mat/0207428, arXiv.org.
    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. Pascal Franc{c}ois & Genevi`eve Gauthier & Fr'ed'eric Godin & Carlos Octavio P'erez Mendoza, 2024. "Enhancing Deep Hedging of Options with Implied Volatility Surface Feedback Information," Papers 2407.21138, arXiv.org.
    2. Olivier Guéant, 2016. "The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making," Post-Print hal-01393136, HAL.
    3. Huh, Sahn-Wook & Lin, Hao & Mello, Antonio S., 2015. "Options market makers׳ hedging and informed trading: Theory and evidence," Journal of Financial Markets, Elsevier, vol. 23(C), pages 26-58.
    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. Siu, Tak Kuen, 2023. "European option pricing with market frictions, regime switches and model uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 233-250.
    6. Reiß, Ariane, 1997. "Option replication with large transactions costs," Tübinger Diskussionsbeiträge 106, University of Tübingen, School of Business and Economics.
    7. Gondzio, Jacek & Kouwenberg, Roy & Vorst, Ton, 2003. "Hedging options under transaction costs and stochastic volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 27(6), pages 1045-1068, April.
    8. Jose Cruz & Maria Grossinho & Daniel Sevcovic & Cyril Izuchukwu Udeani, 2022. "Linear and Nonlinear Partial Integro-Differential Equations arising from Finance," Papers 2207.11568, arXiv.org.
    9. Perrakis, Stylianos & Lefoll, Jean, 2000. "Option pricing and replication with transaction costs and dividends," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1527-1561, October.
    10. Clewlow, Les & Hodges, Stewart, 1997. "Optimal delta-hedging under transactions costs," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1353-1376, June.
    11. Joao Amaro de Matos & Paula Antao, 2000. "Market illiquidity and the Bid-Ask spread of derivatives," Nova SBE Working Paper Series wp386, Universidade Nova de Lisboa, Nova School of Business and Economics.
    12. Lionel Martellini, 2000. "Efficient Option Replication in the Presence of Transactions Costs," Review of Derivatives Research, Springer, vol. 4(2), pages 107-131, May.
    13. Joel Vanden, 2006. "Exact Superreplication Strategies for a Class of Derivative Assets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(1), pages 61-87.
    14. Tokarz, Krzysztof & Zastawniak, Tomasz, 2006. "American contingent claims under small proportional transaction costs," Journal of Mathematical Economics, Elsevier, vol. 43(1), pages 65-85, December.
    15. Alet Roux, 2007. "The fundamental theorem of asset pricing under proportional transaction costs," Papers 0710.2758, arXiv.org.
    16. Monoyios, Michael, 2004. "Option pricing with transaction costs using a Markov chain approximation," Journal of Economic Dynamics and Control, Elsevier, vol. 28(5), pages 889-913, February.
    17. Dimitris Bertsimas & Leonid Kogan & Andrew W. Lo, 2001. "Hedging Derivative Securities and Incomplete Markets: An (epsilon)-Arbitrage Approach," Operations Research, INFORMS, vol. 49(3), pages 372-397, June.
    18. Jinqiang Yang & Zhaojun Yang, 2012. "Arbitrage-free interval and dynamic hedging in an illiquid market," Quantitative Finance, Taylor & Francis Journals, vol. 13(7), pages 1029-1039, May.
    19. Dimitris Bertsimas & Leonid Kogan & Andrew W. Lo, 2001. "When Is Time Continuous?," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar(Volume II), chapter 3, pages 71-102, World Scientific Publishing Co. Pte. Ltd..
    20. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.

    More about this item

    JEL classification:

    • B26 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Financial Economics
    • O16 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Financial Markets; Saving and Capital Investment; Corporate Finance and Governance
    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy

    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:oup:rfinst:v:19:y:2006:i:2:p:493-529. 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: Oxford University Press (email available below). General contact details of provider: https://edirc.repec.org/data/sfsssea.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.