IDEAS home Printed from https://ideas.repec.org/a/bla/mathfi/v6y1996i1p17-51.html
   My bibliography  Save this article

Pricing Of American Path‐Dependent Contingent Claims

Author

Listed:
  • Jérôme Barraquand
  • Thierry Pudet

Abstract

We consider the problem of pricing path‐dependent contingent claims. Classically, this problem can be cast into the Black‐Scholes valuation framework through inclusion of the path‐dependent variables into the state space. This leads to solving a degenerate advection‐diffusion partial differential equation (PDE). We first estabilish necessary and sufficient conditions under which degenerate diffusions can be reduced to lower‐dimensional nondegenerate diffusions. We apply these results to path‐dependent options. Then, we describe a new numerical technique, called forward shooting grid (FSG) method, that efficiently copes with degenerate diffusion PDEs. Finally, we show that the FSG method is unconditionally stable and convergent. the FSG method is the first capable of dealing with the early exercise condition of American options. Several numerical examples are presented and discussed.2

Suggested Citation

  • Jérôme Barraquand & Thierry Pudet, 1996. "Pricing Of American Path‐Dependent Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 6(1), pages 17-51, January.
    • Handle: RePEc:bla:mathfi:v:6:y:1996:i:1:p:17-51
    DOI: 10.1111/j.1467-9965.1996.tb00111.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9965.1996.tb00111.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9965.1996.tb00111.x?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
    ---><---

    Citations

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


    Cited by:

    1. Min Dai & Zuo Quan Xu, 2009. "Optimal Redeeming Strategy of Stock Loans," Papers 0906.0702, arXiv.org.
    2. Emilio Russo & Alessandro Staino, 2018. "A Lattice-Based Model For Evaluating Bonds And Interest-Sensitive Claims Under Stochastic Volatility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 1-18, June.
    3. S. Dyrting, 2004. "Pricing equity options everywhere," Quantitative Finance, Taylor & Francis Journals, vol. 4(6), pages 663-676.
    4. Benhamou, Eric & Duguet, Alexandre, 2003. "Small dimension PDE for discrete Asian options," Journal of Economic Dynamics and Control, Elsevier, vol. 27(11), pages 2095-2114.
    5. Wong, Hoi Ying & Guan, Peiqiu, 2011. "An FFT-network for Lévy option pricing," Journal of Banking & Finance, Elsevier, vol. 35(4), pages 988-999, April.
    6. Bergenthum Jan & Rüschendorf Ludger, 2008. "Comparison results for path-dependent options," Statistics & Risk Modeling, De Gruyter, vol. 26(1), pages 53-72, March.
    7. Gambaro, Anna Maria & Kyriakou, Ioannis & Fusai, Gianluca, 2020. "General lattice methods for arithmetic Asian options," European Journal of Operational Research, Elsevier, vol. 282(3), pages 1185-1199.
    8. Hatem Ben-Ameur & Michèle Breton & Pierre L'Ecuyer, 2002. "A Dynamic Programming Procedure for Pricing American-Style Asian Options," Management Science, INFORMS, vol. 48(5), pages 625-643, May.
    9. Vicky Henderson & Kamil Klad'ivko & Michael Monoyios & Christoph Reisinger, 2017. "Executive stock option exercise with full and partial information on a drift change point," Papers 1709.10141, arXiv.org, revised Jul 2020.
    10. Cen, Zhongdi & Xu, Aimin & Le, Anbo, 2015. "A hybrid finite difference scheme for pricing Asian options," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 229-239.
    11. Lee, Huai-I & Hsieh, Tsung-Yu & Kuo, Wen-Hsiu & Hsu, Hsinan, 2015. "Can a path-dependent strategy outperform a path-independent strategy?," The Quarterly Review of Economics and Finance, Elsevier, vol. 58(C), pages 119-127.
    12. Yulian Fan & Huadong Zhang, 2017. "The pricing of average options with jump diffusion processes in the uncertain volatility model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 1-31, March.
    13. Noorani, Idin & Mehrdoust, Farshid & Nasroallah, Abdelaziz, 2021. "A generalized antithetic variates Monte-Carlo simulation method for pricing of Asian option in a Markov regime-switching model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 1-15.
    14. Ömür Ugur, 2008. "An Introduction to Computational Finance," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number p556, February.
    15. Rongwen Wu & Michael C. Fu, 2003. "Optimal Exercise Policies and Simulation-Based Valuation for American-Asian Options," Operations Research, INFORMS, vol. 51(1), pages 52-66, February.
    16. Jérôme Lelong & Antonino Zanette, 2010. "Tree methods," Post-Print hal-00776713, HAL.
    17. P. A. Forsyth & K. R. Vetzal & R. Zvan, 1999. "A finite element approach to the pricing of discrete lookbacks with stochastic volatility," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(2), pages 87-106.
    18. Andrea Pascucci, 2008. "Free boundary and optimal stopping problems for American Asian options," Finance and Stochastics, Springer, vol. 12(1), pages 21-41, January.
    19. RØdiger Frey, 2000. "Superreplication in stochastic volatility models and optimal stopping," Finance and Stochastics, Springer, vol. 4(2), pages 161-187.
    20. Erhan Bayraktar & Qi Feng & Zhaoyu Zhang, 2022. "Deep Signature Algorithm for Multi-dimensional Path-Dependent Options," Papers 2211.11691, arXiv.org, revised Jan 2024.
    21. Massimo Costabile & Ivar Massabó & Emilio Russo, 2006. "An adjusted binomial model for pricing Asian options," Review of Quantitative Finance and Accounting, Springer, vol. 27(3), pages 285-296, November.
    22. Frank Wusterhausen, 2015. "An Analysis of Path-Dependent Options," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 874-887, December.
    23. George Chacko & Sanjiv Ranjan Das, 1997. "Average Interest," NBER Working Papers 6045, National Bureau of Economic Research, Inc.
    24. Naoki Kishimoto, 2004. "Pricing Path-Dependent Securities by the Extended Tree Method," Management Science, INFORMS, vol. 50(9), pages 1235-1248, September.

    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:bla:mathfi:v:6:y:1996:i:1:p:17-51. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0960-1627 .

    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.