IDEAS home Printed from https://ideas.repec.org/p/fth/nystfi/98-067.html
   My bibliography  Save this paper

The Valuation of American Barrier Options Using the Decomposition Technique

Author

Listed:
  • Marti G. Subrahmanyam
  • Bin Gao
  • Jing-zhi Huang

Abstract

In this paper, we propose an alternative approach for pricing and hedging non-standard American options. In principle, the proposed approach applies to any kind of American-style contract for which the payoff function has a Markovian representation in the state space. Specifically, we obtain an analytic solution for the value and hedge parameters of barrier options, an important example of path-dependent options. The solution includes standard American options as a special case. The analytic formula also allows us to identify and exploit two key properties of the optimal exercise boundary - homogeneity in price parameters and time-invariance - for American options. In addition, some new put-call ``symmetry" relations are also derived. These properties suggest a new, efficient and integrated approach to pricing and hedging a variety of standard and non-standard American options. From an implementation perspective, this approach avoids the current practice of repetitive computation of option prices and hedge ratios. Our implementation of the analytic formula for barrier options indicates that the proposed approach is both efficient and accurate in computing option values and option hedge parameters. In some cases, our method is substantially faster than existing numerical methods with equal accuracy. In particular, the method overcomes the difficulty that existing numerical methods have in dealing with prices close to the barrier, the case where the barrier matters most.

Suggested Citation

  • Marti G. Subrahmanyam & Bin Gao & Jing-zhi Huang, 1998. "The Valuation of American Barrier Options Using the Decomposition Technique," New York University, Leonard N. Stern School Finance Department Working Paper Seires 98-067, New York University, Leonard N. Stern School of Business-.
  • Handle: RePEc:fth:nystfi:98-067
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below 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.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Huang, Jing-zhi & Subrahmanyam, Marti G & Yu, G George, 1996. "Pricing and Hedging American Options: A Recursive Integration Method," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 277-300.
    2. Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, vol. 31(2), pages 351-367, May.
    3. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters,in: Theory Of Valuation, chapter 8, pages 229-288 World Scientific Publishing Co. Pte. Ltd..
    4. Breen, Richard, 1991. "The Accelerated Binomial Option Pricing Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(02), pages 153-164, June.
    5. Carr, Peter, 1998. "Randomization and the American Put," Review of Financial Studies, Society for Financial Studies, vol. 11(3), pages 597-626.
    6. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    7. Asbjørn T. Hansen & Peter Løchte Jørgensen, 2000. "Analytical Valuation of American-Style Asian Options," Management Science, INFORMS, vol. 46(8), pages 1116-1136, August.
    8. L.C.G. Rogers & E.J. Stapleton, 1997. "Fast accurate binomial pricing," Finance and Stochastics, Springer, vol. 2(1), pages 3-17.
    9. Mark Broadie & Jérôme Detemple, 1997. "The Valuation of American Options on Multiple Assets," Mathematical Finance, Wiley Blackwell, vol. 7(3), pages 241-286.
    10. 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.
    11. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    12. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    13. Barone-Adesi, Giovanni & Whaley, Robert E, 1987. " Efficient Analytic Approximation of American Option Values," Journal of Finance, American Finance Association, vol. 42(2), pages 301-320, June.
    14. Michael J. P. Selby & Stewart D. Hodges, 1987. "On the Evaluation of Compound Options," Management Science, INFORMS, vol. 33(3), pages 347-355, March.
    15. Mark Schroder, 1989. "A Reduction Method Applicable to Compound Option Formulas," Management Science, INFORMS, vol. 35(7), pages 823-827, July.
    16. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    17. Peter Carr & Robert Jarrow & Ravi Myneni, 2008. "Alternative Characterizations Of American Put Options," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 5, pages 85-103 World Scientific Publishing Co. Pte. Ltd..
    18. Broadie, Mark & Detemple, Jerome, 1996. "American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods," Review of Financial Studies, Society for Financial Studies, vol. 9(4), pages 1211-1250.
    19. Broadie, Mark & Detemple, Jerome, 1995. "American Capped Call Options on Dividend-Paying Assets," Review of Financial Studies, Society for Financial Studies, vol. 8(1), pages 161-191.
    20. Ju, Nengjiu, 1998. "Pricing an American Option by Approximating Its Early Exercise Boundary as a Multipiece Exponential Function," Review of Financial Studies, Society for Financial Studies, vol. 11(3), pages 627-646.
    21. S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Vidal Nunes, João Pedro & Ruas, João Pedro & Dias, José Carlos, 2015. "Pricing and static hedging of American-style knock-in options on defaultable stocks," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 343-360.
    2. Marc Chesney & Laurent Gauthier, 2006. "American Parisian options," Finance and Stochastics, Springer, vol. 10(4), pages 475-506, December.
    3. Detemple, Jérôme & Emmerling, Thomas, 2009. "American chooser options," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 128-153, January.
    4. repec:spr:annopr:v:264:y:2018:i:1:d:10.1007_s10479-017-2639-4 is not listed on IDEAS
    5. Alfredo Ibáñez, 2003. "Robust Pricing of the American Put Option: A Note on Richardson Extrapolation and the Early Exercise Premium," Management Science, INFORMS, vol. 49(9), pages 1210-1228, September.
    6. Wei Xiong & Ronnie Sircar, 2004. "Evaluating Incentive Options," Econometric Society 2004 North American Winter Meetings 253, Econometric Society.
    7. Jérôme B. Detemple, 1999. "American Options: Symmetry Properties," CIRANO Working Papers 99s-45, CIRANO.
    8. Chung, Y. Peter & Johnson, Herb & Polimenis, Vassilis, 2011. "The critical stock price for the American put option," Finance Research Letters, Elsevier, vol. 8(1), pages 8-14, March.
    9. Tebaldi, Claudio, 2005. "Hedging using simulation: a least squares approach," Journal of Economic Dynamics and Control, Elsevier, vol. 29(8), pages 1287-1312, August.
    10. Antonella Basso & Martina Nardon & Paolo Pianca, 2004. "A two-step simulation procedure to analyze the exercise features of American options," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 27(1), pages 35-56, August.
    11. Dai, Min & Li, Peifan & Zhang, Jin E., 2010. "A lattice algorithm for pricing moving average barrier options," Journal of Economic Dynamics and Control, Elsevier, vol. 34(3), pages 542-554, March.
    12. J. C. Ndogmo & D. B. Ntwiga, 2007. "High-order accurate implicit methods for the pricing of barrier options," Papers 0710.0069, arXiv.org.
    13. Minh Ha-Duong & Benoit Morel, 2003. "The real option with an absorbing barrier," Post-Print halshs-00003976, HAL.
    14. Zvan, R. & Vetzal, K. R. & Forsyth, P. A., 2000. "PDE methods for pricing barrier options," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1563-1590, October.
    15. Garcia, Diego, 2003. "Convergence and Biases of Monte Carlo estimates of American option prices using a parametric exercise rule," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1855-1879, August.
    16. Jérôme Detemple & Weidong Tian, 2002. "The Valuation of American Options for a Class of Diffusion Processes," Management Science, INFORMS, vol. 48(7), pages 917-937, July.
    17. Liu, Yanchu & Cui, Zhenyu & Zhang, Ning, 2016. "Integral representation of vega for American put options," Finance Research Letters, Elsevier, vol. 19(C), pages 204-208.
    18. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    19. Sircar, Ronnie & Xiong, Wei, 2007. "A general framework for evaluating executive stock options," Journal of Economic Dynamics and Control, Elsevier, vol. 31(7), pages 2317-2349, July.
    20. Chung, San-Lin & Shih, Pai-Ta & Tsai, Wei-Che, 2013. "Static hedging and pricing American knock-in put options," Journal of Banking & Finance, Elsevier, vol. 37(1), pages 191-205.
    21. Roland Mallier & Ghada Alobaidi, 2000. "Laplace transforms and American options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 7(4), pages 241-256.
    22. Carl Chiarella & Boda Kang & Gunter H. Meyer, 2010. "The Evaluation Of Barrier Option Prices Under Stochastic Volatility," Research Paper Series 266, Quantitative Finance Research Centre, University of Technology, Sydney.
    23. Das, Sanjiv R. & Kim, Seoyoung, 2015. "Credit spreads with dynamic debt," Journal of Banking & Finance, Elsevier, vol. 50(C), pages 121-140.

    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:fth:nystfi:98-067. 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: (Thomas Krichel). General contact details of provider: http://edirc.repec.org/data/fdnyuus.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.