IDEAS home Printed from https://ideas.repec.org/a/taf/apmtfi/v4y1997i1p1-20.html
   My bibliography  Save this article

Fast numerical valuation of American, exotic and complex options

Author

Listed:
  • M. A. H. Dempster
  • J. P. Hutton

Abstract

The purpose of this paper is to present evidence in support of the hypothesis that fast, accurate and parametrically robust numerical valuation of a wide range of derivative securities can be achieved by use of direct numerical methods in the solution of the associated PDE problems. Specifically, linear programming methods for American vanilla and exotic options, and explicit methods for a three stochastic state variable problem (a multi-period terminable differential swap) are explored and promising numerical results are discussed. The resulting value surface gives, simultaneously, valuation for many maturities and underlying prices, and the parameters required for risk analysis.

Suggested Citation

  • M. A. H. Dempster & J. P. Hutton, 1997. "Fast numerical valuation of American, exotic and complex options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(1), pages 1-20.
  • Handle: RePEc:taf:apmtfi:v:4:y:1997:i:1:p:1-20
    DOI: 10.1080/135048697334809
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/135048697334809
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/135048697334809?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. Patrick Jaillet & Damien Lamberton & Bernard Lapeyre, 1990. "Variational inequalities and the pricing of American options," Post-Print hal-01667008, HAL.
    2. J. M. Borwein & M. A. H. Dempster, 1989. "The Linear Order Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 14(3), pages 534-558, August.
    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. 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.
    2. Vladimir V. Piterbarg, 2004. "Risk Sensitivities Of Bermuda Swaptions," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(04), pages 465-509.
    3. Jérôme Detemple, 2014. "Optimal Exercise for Derivative Securities," Annual Review of Financial Economics, Annual Reviews, vol. 6(1), pages 459-487, December.
    4. 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.
    5. Nigel Clarke & Kevin Parrott, 1999. "Multigrid for American option pricing with stochastic volatility," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(3), pages 177-195.

    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. Sándor Zoltán Németh & Lianghai Xiao, 2018. "Linear Complementarity Problems on Extended Second Order Cones," Journal of Optimization Theory and Applications, Springer, vol. 176(2), pages 269-288, February.
    2. Min Dai & Yue Kuen Kwok, 2006. "Characterization Of Optimal Stopping Regions Of American Asian And Lookback Options," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 63-82, January.
    3. Ciarcià, Carla & Daniele, Patrizia, 2016. "New existence theorems for quasi-variational inequalities and applications to financial models," European Journal of Operational Research, Elsevier, vol. 251(1), pages 288-299.
    4. Rafael Company & Vera Egorova & Lucas J'odar & Fazlollah Soleymani, 2017. "Computing stable numerical solutions for multidimensional American option pricing problems: a semi-discretization approach," Papers 1701.08545, arXiv.org.
    5. Zakaria Marah, 2023. "American Exchange option driven by a L\'evy process," Papers 2307.10900, arXiv.org.
    6. Ken-ichi Mitsui & Yoshio Tabata, 2005. "Wavelet based Multi-grid analysis, Wavelet Galerkin method and their Applications to American option: A Survey," Discussion Papers in Economics and Business 05-26, Osaka University, Graduate School of Economics.
    7. Pressacco, Flavio & Gaudenzi, Marcellino & Zanette, Antonino & Ziani, Laura, 2008. "New insights on testing the efficiency of methods of pricing and hedging American options," European Journal of Operational Research, Elsevier, vol. 185(1), pages 235-254, February.
    8. Jean-Paul Décamps & Thomas Mariotti & Stéphane Villeneuve, 2006. "Irreversible investment in alternative projects," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(2), pages 425-448, June.
    9. Cheng Cai & Tiziano De Angelis & Jan Palczewski, 2021. "The American put with finite-time maturity and stochastic interest rate," Papers 2104.08502, arXiv.org, revised Feb 2024.
    10. Battauz, A. & Pratelli, M., 2004. "Optimal stopping and American options with discrete dividends and exogenous risk," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 255-265, October.
    11. Massimo Marinacci & Luigi Montrucchio, 2017. "Unique Tarski Fixed Points," Working Papers 604, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    12. Zhongdi Cen & Anbo Le & Aimin Xu, 2012. "A Second-Order Difference Scheme for the Penalized Black–Scholes Equation Governing American Put Option Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 40(1), pages 49-62, June.
    13. Erhan Bayraktar & Hao Xing, 2009. "Pricing American options for jump diffusions by iterating optimal stopping problems for diffusions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(3), pages 505-525, December.
    14. Darae Jeong & Minhyun Yoo & Changwoo Yoo & Junseok Kim, 2019. "A Hybrid Monte Carlo and Finite Difference Method for Option Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 53(1), pages 111-124, January.
    15. Damien Lamberton & Giulia Terenzi, 2019. "Properties of the American price function in the Heston-type models," Working Papers hal-02088487, HAL.
    16. Abel Azze & Bernardo D'Auria & Eduardo Garc'ia-Portugu'es, 2022. "Optimal exercise of American options under time-dependent Ornstein-Uhlenbeck processes," Papers 2211.04095, arXiv.org, revised Jun 2024.
    17. repec:dau:papers:123456789/7818 is not listed on IDEAS
    18. Ivan Guo & Nicolas Langren'e & Jiahao Wu, 2023. "Simultaneous upper and lower bounds of American option prices with hedging via neural networks," Papers 2302.12439, arXiv.org, revised Apr 2024.
    19. Barbagallo, Annamaria & Daniele, Patrizia & Giuffrè, Sofia & Maugeri, Antonino, 2014. "Variational approach for a general financial equilibrium problem: The Deficit Formula, the Balance Law and the Liability Formula. A path to the economy recovery," European Journal of Operational Research, Elsevier, vol. 237(1), pages 231-244.
    20. Massimo Marinacci & Luigi Montrucchio, 2019. "Unique Tarski Fixed Points," Management Science, INFORMS, vol. 44(4), pages 1174-1191, November.
    21. Anna Battauz & Francesco Rotondi, 2022. "American options and stochastic interest rates," Computational Management Science, Springer, vol. 19(4), pages 567-604, October.

    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:apmtfi:v:4:y:1997:i:1:p:1-20. 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/RAMF20 .

    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.