IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1406.5430.html
   My bibliography  Save this paper

A robust algorithm and convergence analysis for static replications of nonlinear payoffs

Author

Listed:
  • Jingtang Ma
  • Dongya Deng
  • Harry Zheng

Abstract

In this paper we propose a new robust algorithm to find the optimal static replicating portfolios for general nonlinear payoff functions and give the estimate of the rate of convergence that is absent in the literature. We choose the static replication by minimizing the error bound between the nonlinear payoff function and the linear spline approximation and derive the equidistribution equation for selecting the optimal strike prices. The numerical tests for variance swaps and swaptions and also for the static quadratic replication and the model with counterparty risk show that the proposed algorithm is simple, fast and accurate. The paper has generalized and improved the results of the static replication and approximation in the literature.

Suggested Citation

  • Jingtang Ma & Dongya Deng & Harry Zheng, 2014. "A robust algorithm and convergence analysis for static replications of nonlinear payoffs," Papers 1406.5430, arXiv.org.
    • Handle: RePEc:arx:papers:1406.5430
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1406.5430
    File Function: Latest version
    Download Restriction: no
    ---><---

    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. repec:bla:jfinan:v:53:y:1998:i:3:p:1165-1190 is not listed on IDEAS
    3. 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.
    4. Stephen A. Ross, 1976. "Options and Efficiency," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 90(1), pages 75-89.
    5. Ying Jiao & Huyên Pham, 2011. "Optimal investment with counterparty risk: a default-density model approach," Finance and Stochastics, Springer, vol. 15(4), pages 725-753, December.
    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. 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.
    3. Peter Carr & Liuren Wu, 2014. "Static Hedging of Standard Options," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 3-46.
    4. 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.
    5. 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.
    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. Bertrand, Philippe & Prigent, Jean-luc, 2016. "Equilibrium of financial derivative markets under portfolio insurance constraints," Economic Modelling, Elsevier, vol. 52(PA), pages 278-291.
    8. Alexandre M. Baptista, 2005. "Options And Efficiency In Multidate Security Markets," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 569-587, October.
    9. 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.
    10. Peter Van Tassel, 2020. "The Law of One Price in Equity Volatility Markets," Staff Reports 953, Federal Reserve Bank of New York.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Liu, Jun & Pan, Jun, 2003. "Dynamic derivative strategies," Journal of Financial Economics, Elsevier, vol. 69(3), pages 401-430, September.
    16. 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.
    17. 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.
    18. Lokeshwar, Vikranth & Bharadwaj, Vikram & Jain, Shashi, 2022. "Explainable neural network for pricing and universal static hedging of contingent claims," Applied Mathematics and Computation, Elsevier, vol. 417(C).
    19. Ho, Li-Chin Jennifer & Hassell, John M. & Swidler, Steve, 1995. "An empirical examination of the dispersion and accuracy of analyst forecasts surrounding option listing," Review of Financial Economics, Elsevier, vol. 4(2), pages 171-185.
    20. Bondarenko, Oleg, 2014. "Variance trading and market price of variance risk," Journal of Econometrics, Elsevier, vol. 180(1), pages 81-97.

    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:arx:papers:1406.5430. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.