IDEAS home Printed from https://ideas.repec.org/a/taf/quantf/v16y2016i4p593-603.html
   My bibliography  Save this article

Convergence analysis and optimal strike choice for static hedges of general path-independent pay-offs

Author

Listed:
  • Jingtang Ma
  • Dongya Deng
  • Harry Zheng

Abstract

In this paper, we propose a new algorithm to find the optimal static replicating portfolios for general path-independent nonlinear pay-off functions and give an estimate for the rate of convergence that is absent in the literature. We choose the static replication by designing an adaptation function arising in the error bound between the nonlinear pay-off function and the linear spline approximation and derive the equidistribution equation for selecting the optimal strikes. The numerical tests for variance swaps, swaptions, static quadratic hedges and also for a jump-diffusion process, allowing for the default of the underlying asset, show that the proposed iterative equidistribution equation algorithm is simple, fast and accurate. The paper generalizes and improves the results on static replication and approximation in the literature.

Suggested Citation

  • Jingtang Ma & Dongya Deng & Harry Zheng, 2016. "Convergence analysis and optimal strike choice for static hedges of general path-independent pay-offs," Quantitative Finance, Taylor & Francis Journals, vol. 16(4), pages 593-603, April.
    • Handle: RePEc:taf:quantf:v:16:y:2016:i:4:p:593-603
    DOI: 10.1080/14697688.2015.1046397
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/14697688.2015.1046397
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/14697688.2015.1046397?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
    ---><---

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

    References listed on IDEAS

    as
    1. Peter Carr & Liuren Wu, 2014. "Static Hedging of Standard Options," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 3-46.
    2. Stephen A. Ross, 1976. "Options and Efficiency," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 90(1), pages 75-89.
    3. repec:bla:jfinan:v:53:y:1998:i:3:p:1165-1190 is not listed on IDEAS
    4. Akihiko Takahashi & Akira Yamazaki, 2009. "Efficient static replication of European options under exponential Lévy models," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 29(1), pages 1-15, January.
    5. 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.
    6. Peter Carr & Anita Mayo, 2007. "On the Numerical Evaluation of Option Prices in Jump Diffusion Processes," The European Journal of Finance, Taylor & Francis Journals, vol. 13(4), pages 353-372.
    7. Qiang Liu, 2010. "Optimal approximations of nonlinear payoffs in static replication," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 30(11), pages 1082-1099, November.
    8. Akihiko Takahashi & Akira Yamazaki, 2009. "A new scheme for static hedging of European derivatives under stochastic volatility models," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 29(5), pages 397-413, May.
    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. Tak Kuen Siu & Robert J. Elliott, 2019. "Hedging Options In A Doubly Markov-Modulated Financial Market Via Stochastic Flows," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(08), pages 1-41, December.
    2. Shuxin Guo & Qiang Liu, 2019. "The Black-Scholes-Merton dual equation," Papers 1912.10380, arXiv.org, revised May 2024.
    3. Akira Yamazaki, 2022. "Recovering subjective probability distributions," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(7), pages 1234-1263, July.
    4. Jingtang Ma & Dongya Deng & Harry Zheng, 2014. "A robust algorithm and convergence analysis for static replications of nonlinear payoffs," Papers 1406.5430, arXiv.org.
    5. Vikranth Lokeshwar Dhandapani & Shashi Jain, 2023. "Data-driven Approach for Static Hedging of Exchange Traded Options," Papers 2302.00728, arXiv.org, revised Jan 2024.
    6. Peter Carr & Liuren Wu, 2014. "Static Hedging of Standard Options," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 3-46.
    7. Barone-Adesi, Giovanni & Fusari, Nicola & Mira, Antonietta & Sala, Carlo, 2020. "Option market trading activity and the estimation of the pricing kernel: A Bayesian approach," Journal of Econometrics, Elsevier, vol. 216(2), pages 430-449.
    8. Kitsul, Yuriy & Wright, Jonathan H., 2013. "The economics of options-implied inflation probability density functions," Journal of Financial Economics, Elsevier, vol. 110(3), pages 696-711.
    9. 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.
    10. Bertrand, Philippe & Prigent, Jean-luc, 2016. "Equilibrium of financial derivative markets under portfolio insurance constraints," Economic Modelling, Elsevier, vol. 52(PA), pages 278-291.
    11. Alexandre M. Baptista, 2005. "Options And Efficiency In Multidate Security Markets," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 569-587, October.
    12. 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.
    13. Peter Van Tassel, 2020. "The Law of One Price in Equity Volatility Markets," Staff Reports 953, Federal Reserve Bank of New York.
    14. Nteukam T., Oberlain & Planchet, Frédéric & Thérond, Pierre-E., 2011. "Optimal strategies for hedging portfolios of unit-linked life insurance contracts with minimum death guarantee," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 161-175, March.
    15. Michael Schmutz & Thomas Zürcher, 2014. "Static Hedging with Traffic Light Options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(7), pages 690-702, July.
    16. Vohra, Suprita & Fabozzi, Frank J., 2019. "Effectiveness of developed and emerging market FX options in active currency risk management," Journal of International Money and Finance, Elsevier, vol. 96(C), pages 130-146.
    17. Yoshino, Joe Akira, 2003. "Market Risk and Volatility in the Brazilian Stock Market," Journal of Applied Economics, Universidad del CEMA, vol. 6(2), pages 1-19, November.
    18. Liu, Jun & Pan, Jun, 2003. "Dynamic derivative strategies," Journal of Financial Economics, Elsevier, vol. 69(3), pages 401-430, September.
    19. 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.
    20. Dijkstra, Theo K. & Yao, Yong, 2002. "Moment generating function approach to pricing interest rate and foreign exchange rate claims," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 163-178, October.

    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:taf:quantf:v:16:y:2016:i:4:p:593-603. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RQUF20 .

    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.