IDEAS home Printed from https://ideas.repec.org/p/uts/rpaper/118.html
   My bibliography  Save this paper

A Survey of the Integral Representation of American Option Prices

Author

Abstract

This paper surveys some of the literature on American option pricing, in particular the representations of McKean (1965), Kim (1990) and Carr, Jarrow and Myneni (1992). It is proposed that the approach regarding the problem as a free boundary value problem, and solving this via incomplete Fourier transforms, is the most robust for further developments involving more complex payo structures, and higher dimensional problems such as multi-asset American options. Some comparison of di erent numerical solution methods is also provided.

Suggested Citation

  • Carl Chiarella & Adam Kucera & Andrew Ziogas, 2004. "A Survey of the Integral Representation of American Option Prices," Research Paper Series 118, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:118
    as

    Download full text from publisher

    File URL: https://www.uts.edu.au/sites/default/files/qfr-archive-02/QFR-rp118.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    2. Chiarella, Carl & Ziogas, Andrew, 2005. "Evaluation of American strangles," Journal of Economic Dynamics and Control, Elsevier, vol. 29(1-2), pages 31-62, January.
    3. Carl Chiarella, Nadima El-Hassan, & Adam Kucera, "undated". "Option Pricing in a Path Integral Framework Using Fourier-Hermite Series Expansions," Computing in Economics and Finance 1997 132, Society for Computational Economics.
    4. Geske, Robert & Johnson, Herb E, 1984. "The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-1524, December.
    5. Parkinson, Michael, 1977. "Option Pricing: The American Put," The Journal of Business, University of Chicago Press, vol. 50(1), pages 21-36, January.
    6. Brennan, Michael J & Schwartz, Eduardo S, 1977. "The Valuation of American Put Options," Journal of Finance, American Finance Association, vol. 32(2), pages 449-462, May.
    7. Kim, In Joon, 1990. "The Analytic Valuation of American Options," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 547-572.
    8. 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.
    9. 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..
    10. Chiarella, Carl & El-Hassan, Nadima & Kucera, Adam, 1999. "Evaluation of American option prices in a path integral framework using Fourier-Hermite series expansions," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1387-1424, September.
    11. S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14, April.
    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. Louis Bhim & Reiichiro Kawai, 2018. "Smooth Upper Bounds For The Price Function Of American Style Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-38, February.
    2. Carl Chiarella & Christina Nikitopoulos Sklibosios & Erik Schlogl, 2007. "A Control Variate Method for Monte Carlo Simulations of Heath-Jarrow-Morton Models with Jumps," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(5), pages 365-399.
    3. Sha Lin & Song‐Ping Zhu, 2022. "Pricing callable–puttable convertible bonds with an integral equation approach," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(10), pages 1856-1911, October.
    4. Chiarella, Carl & Ziogas, Andrew, 2005. "Evaluation of American strangles," Journal of Economic Dynamics and Control, Elsevier, vol. 29(1-2), pages 31-62, January.
    5. Song-Ping Zhu & Xin-Jiang He & XiaoPing Lu, 2018. "A new integral equation formulation for American put options," Quantitative Finance, Taylor & Francis Journals, vol. 18(3), pages 483-490, March.
    6. Carl Chiarella & Andrew Ziogas, 2009. "American Call Options Under Jump-Diffusion Processes - A Fourier Transform Approach," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(1), pages 37-79.
    7. Pierangelo Ciurlia & Ilir Roko, 2005. "Valuation of American Continuous-Installment Options," Computational Economics, Springer;Society for Computational Economics, vol. 25(1), pages 143-165, February.
    8. Jonathan Ziveyi, 2011. "The Evaluation of Early Exercise Exotic Options," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 12, July-Dece.
    9. Song-Ping Zhu & Nhat-Tan Le & Wen-Ting Chen & Xiaoping Lu, 2015. "Pricing Parisian down-and-in options," Papers 1511.01564, arXiv.org.
    10. Carl Chiarella & Jonathan Ziveyi, 2014. "Pricing American options written on two underlying assets," Quantitative Finance, Taylor & Francis Journals, vol. 14(3), pages 409-426, March.
    11. Le, Nhat-Tan & Dang, Duy-Minh, 2017. "Pricing American-style Parisian down-and-out call options," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 330-347.
    12. Carl Chiarella & Christina Nikitopoulos-Sklibosios & Erik Schlogl, 2005. "A Control Variate Method for Monte Carlo Simulations of Heath-Jarrow-Morton with Jumps," Research Paper Series 167, Quantitative Finance Research Centre, University of Technology, Sydney.
    13. Gorno, Leandro & Iachan, Felipe S., 2020. "Competitive real options under private information," Journal of Economic Theory, Elsevier, vol. 185(C).
    14. Jonathan Ziveyi, 2011. "The Evaluation of Early Exercise Exotic Options," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2011.

    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. Barone-Adesi, Giovanni, 2005. "The saga of the American put," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2909-2918, November.
    2. Manuel Moreno & Javier Navas, 2003. "On the Robustness of Least-Squares Monte Carlo (LSM) for Pricing American Derivatives," Review of Derivatives Research, Springer, vol. 6(2), pages 107-128, May.
    3. Mark Broadie & Jérôme Detemple, 1996. "Recent Advances in Numerical Methods for Pricing Derivative Securities," CIRANO Working Papers 96s-17, CIRANO.
    4. Minqiang Li, 2010. "A quasi-analytical interpolation method for pricing American options under general multi-dimensional diffusion processes," Review of Derivatives Research, Springer, vol. 13(2), pages 177-217, July.
    5. Chiarella, Carl & Ziogas, Andrew, 2005. "Evaluation of American strangles," Journal of Economic Dynamics and Control, Elsevier, vol. 29(1-2), pages 31-62, January.
    6. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    7. In oon Kim & Bong-Gyu Jang & Kyeong Tae Kim, 2013. "A simple iterative method for the valuation of American options," Quantitative Finance, Taylor & Francis Journals, vol. 13(6), pages 885-895, May.
    8. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    9. Antonio Cosma & Stefano Galluccio & Paola Pederzoli & O. Scaillet, 2012. "Valuing American Options Using Fast Recursive Projections," Swiss Finance Institute Research Paper Series 12-26, Swiss Finance Institute.
    10. Andrew Ziogas & Carl Chiarella, 2003. "McKean’s Method applied to American Call Options on Jump-Diffusion Processes," Computing in Economics and Finance 2003 39, Society for Computational Economics.
    11. Jun Cheng & Jin Zhang, 2012. "Analytical pricing of American options," Review of Derivatives Research, Springer, vol. 15(2), pages 157-192, July.
    12. Muthuraman, Kumar, 2008. "A moving boundary approach to American option pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 32(11), pages 3520-3537, November.
    13. Ruas, João Pedro & Dias, José Carlos & Vidal Nunes, João Pedro, 2013. "Pricing and static hedging of American-style options under the jump to default extended CEV model," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4059-4072.
    14. Laminou Abdou, Souleymane & Moraux, Franck, 2016. "Pricing and hedging American and hybrid strangles with finite maturity," Journal of Banking & Finance, Elsevier, vol. 62(C), pages 112-125.
    15. Andrew Ziogas & Carl Chiarella, 2004. "Pricing American Options on Jump-Diffusion Processes using Fourier-Hermite Series Expansions," Computing in Economics and Finance 2004 177, Society for Computational Economics.
    16. B. Gao J. Huang, "undated". "The Valuation of American Barrier Options Using the Decomposition Technique," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-002, New York University, Leonard N. Stern School of Business-.
    17. Mark Broadie & Jérôme Detemple, 1996. "American Options on Dividend-Paying Assets," CIRANO Working Papers 96s-16, CIRANO.
    18. Jonathan Ziveyi, 2011. "The Evaluation of Early Exercise Exotic Options," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 12, July-Dece.
    19. Chuang-Chang Chang & Jun-Biao Lin & Wei-Che Tsai & Yaw-Huei Wang, 2012. "Using Richardson extrapolation techniques to price American options with alternative stochastic processes," Review of Quantitative Finance and Accounting, Springer, vol. 39(3), pages 383-406, October.
    20. Zhongkai Liu & Tao Pang, 2016. "An efficient grid lattice algorithm for pricing American-style options," International Journal of Financial Markets and Derivatives, Inderscience Enterprises Ltd, vol. 5(1), pages 36-55.

    More about this item

    Keywords

    American options; Volterra integral equation; incomplete Fourier transform; free-boundary problem;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:uts:rpaper:118. 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: Duncan Ford (email available below). General contact details of provider: https://edirc.repec.org/data/qfutsau.html .

    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.