IDEAS home Printed from https://ideas.repec.org/p/cfi/fseres/cf325.html
   My bibliography  Save this paper

Pricing Bounds on Barrier Options (forthcoming in "Journal of Futures Markets")

Author

Listed:
  • Yukihiro Tsuzuki

    (The University of Tokyo)

Abstract

This paper proposes the optimal pricing bounds on barrier options in an environment where plain-vanilla options and no-touch options can be used as hedging instruments. Super-hedging and sub-hedging portfolios are derived without specifying any underlying processes, which are static ones consisting of not only plain-vanilla options but also cash-paying no-touch options and/or asset paying no-touch options that pay one cash or one underlying asset respectively if the barrier has not been hit. Moreover, the prices of these portfolios turn out to be the optimal pricing bounds through finding risk-neutral measures under which the barrier option price is equal to the hedging portfolio's value. The model-independent pricing bounds are useful because a price of a barrier option is significantly dependent on a model. It is demonstrated through numerical examples that prices outside the pricing bounds can be produced by models which are calibrated to market prices of plain-vanilla options, but not to that of a no-touch option.

Suggested Citation

  • Yukihiro Tsuzuki, 2013. "Pricing Bounds on Barrier Options (forthcoming in "Journal of Futures Markets")," CARF F-Series CARF-F-325, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  • Handle: RePEc:cfi:fseres:cf325
    as

    Download full text from publisher

    File URL: https://www.carf.e.u-tokyo.ac.jp/old/pdf/workingpaper/fseries/F325.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. "Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
    2. Peter Carr & John Crosby, 2010. "A class of Levy process models with almost exact calibration to both barrier and vanilla FX options," Quantitative Finance, Taylor & Francis Journals, vol. 10(10), pages 1115-1136.
    3. Peter Carr & Katrina Ellis & Vishal Gupta, 1998. "Static Hedging of Exotic Options," Journal of Finance, American Finance Association, vol. 53(3), pages 1165-1190, June.
    4. 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.
    5. Haydyn Brown & David Hobson & L. C. G. Rogers, 2001. "Robust Hedging of Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 11(3), pages 285-314, July.
    6. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    7. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
    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. 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.
    2. Baule, Rainer & Shkel, David, 2021. "Model risk and model choice in the case of barrier options and bonus certificates," Journal of Banking & Finance, Elsevier, vol. 133(C).
    3. René Garcia & Eric Ghysels & Eric Renault, 2004. "The Econometrics of Option Pricing," CIRANO Working Papers 2004s-04, CIRANO.
    4. Carol Alexandra & Leonardo M. Nogueira, 2005. "Optimal Hedging and Scale Inavriance: A Taxonomy of Option Pricing Models," ICMA Centre Discussion Papers in Finance icma-dp2005-10, Henley Business School, University of Reading, revised Nov 2005.
    5. Peter Carr & Liuren Wu, 2014. "Static Hedging of Standard Options," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 12(1), pages 3-46.
    6. 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.
    7. Carvalho, Augusto & Guimaraes, Bernardo, 2018. "State-controlled companies and political risk: Evidence from the 2014 Brazilian election," Journal of Public Economics, Elsevier, vol. 159(C), pages 66-78.
    8. Christoffersen, Peter & Heston, Steven & Jacobs, Kris, 2010. "Option Anomalies and the Pricing Kernel," Working Papers 11-17, University of Pennsylvania, Wharton School, Weiss Center.
    9. Jobst, Andreas A., 2014. "Measuring systemic risk-adjusted liquidity (SRL)—A model approach," Journal of Banking & Finance, Elsevier, vol. 45(C), pages 270-287.
    10. Christoffersen, Peter & Jacobs, Kris & Chang, Bo Young, 2013. "Forecasting with Option-Implied Information," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 581-656, Elsevier.
    11. Sergey Badikov & Mark H. A. Davis & Antoine Jacquier, 2018. "Perturbation analysis of sub/super hedging problems," Papers 1806.03543, arXiv.org, revised May 2021.
    12. Park, Yang-Ho, 2016. "The effects of asymmetric volatility and jumps on the pricing of VIX derivatives," Journal of Econometrics, Elsevier, vol. 192(1), pages 313-328.
    13. David Hobson & Anthony Neuberger, 2016. "On the value of being American," Papers 1604.02269, arXiv.org.
    14. Simona Sanfelici, 2007. "Calibration of a nonlinear feedback option pricing model," Quantitative Finance, Taylor & Francis Journals, vol. 7(1), pages 95-110.
    15. Liu, Jun & Pan, Jun, 2003. "Dynamic derivative strategies," Journal of Financial Economics, Elsevier, vol. 69(3), pages 401-430, September.
    16. Christoffersen, Peter & Heston, Steve & Jacobs, Kris, 2006. "Option valuation with conditional skewness," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 253-284.
    17. Marcos Escobar & Christoph Gschnaidtner, 2018. "A multivariate stochastic volatility model with applications in the foreign exchange market," Review of Derivatives Research, Springer, vol. 21(1), pages 1-43, April.
    18. Jin Zhang & Yi Xiang, 2008. "The implied volatility smirk," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 263-284.
    19. Detering, Nils & Packham, Natalie, 2018. "Model risk of contingent claims," IRTG 1792 Discussion Papers 2018-036, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    20. 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.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:cfi:fseres:cf325. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/catokjp.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.