IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v50y2004i9p1193-1203.html
   My bibliography  Save this article

Convergence of the Least Squares Monte Carlo Approach to American Option Valuation

Author

Listed:
  • Lars Stentoft

    (School of Economics and Management, University of Aarhus, 322 University Park, DK-8000 Aarhus C, Denmark)

Abstract

In a recent paper, Longstaff and Schwartz (2001) suggest a method to American option valuation based on simulation. The method is termed the Least Squares Monte Carlo (LSM) method, and although it has become widely used, not much is known about the properties of the estimator. This paper corrects this shortcoming using theory from the literature on seminonparametric series estimators. A central part of the LSM method is the approximation of a set of conditional expectation functions. We show that the approximations converge to the true expectation functions under general assumptions in a multiperiod, multidimensional setting. We obtain convergence rates in the two-period, multidimensional case, and we discuss the relation between the optimal rate of convergence and the properties of the conditional expectation. Furthermore, we show that the actual price estimates converge to the true price. This provides the mathematical foundation for the use of the LSM method in derivatives research.

Suggested Citation

  • Lars Stentoft, 2004. "Convergence of the Least Squares Monte Carlo Approach to American Option Valuation," Management Science, INFORMS, vol. 50(9), pages 1193-1203, September.
    • Handle: RePEc:inm:ormnsc:v:50:y:2004:i:9:p:1193-1203
    DOI: 10.1287/mnsc.1030.0155
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.1030.0155
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.1030.0155?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
    ---><---

    References listed on IDEAS

    as
    1. Carriere, Jacques F., 1996. "Valuation of the early-exercise price for options using simulations and nonparametric regression," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 19-30, December.
    2. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    3. Barnett,William A. & Powell,James & Tauchen,George E. (ed.), 1991. "Nonparametric and Semiparametric Methods in Econometrics and Statistics," Cambridge Books, Cambridge University Press, number 9780521424318, September.
    4. Boyle, Phelim P., 1977. "Options: A Monte Carlo approach," Journal of Financial Economics, Elsevier, vol. 4(3), pages 323-338, May.
    5. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    6. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    7. Barnett,William A. & Powell,James & Tauchen,George E. (ed.), 1991. "Nonparametric and Semiparametric Methods in Econometrics and Statistics," Cambridge Books, Cambridge University Press, number 9780521370905, September.
    8. 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.
    9. Barraquand, Jérôme & Martineau, Didier, 1995. "Numerical Valuation of High Dimensional Multivariate American Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 30(3), pages 383-405, September.
    10. Jèôme Barraquand, 1995. "Numerical Valuation of High Dimensional Multivariate European Securities," Management Science, INFORMS, vol. 41(12), pages 1882-1891, December.
    11. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    12. Broadie, Mark & Glasserman, Paul, 1997. "Pricing American-style securities using simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1323-1352, June.
    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. Lars Stentoft, 2013. "American option pricing using simulation with an application to the GARCH model," Chapters, in: Adrian R. Bell & Chris Brooks & Marcel Prokopczuk (ed.), Handbook of Research Methods and Applications in Empirical Finance, chapter 5, pages 114-147, Edward Elgar Publishing.
    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. Dimitrakopoulos, Roussos G. & Abdel Sabour, Sabry A., 2007. "Evaluating mine plans under uncertainty: Can the real options make a difference?," Resources Policy, Elsevier, vol. 32(3), pages 116-125, September.
    4. R. Mark Reesor & T. James Marshall, 2020. "Forest of Stochastic Trees: A Method for Valuing Multiple Exercise Options," JRFM, MDPI, vol. 13(5), pages 1-31, May.
    5. Chung-Gee Lin & Yu-Shan Wang, 2012. "Evaluating natural resource projects with embedded options and limited reserves," Applied Economics, Taylor & Francis Journals, vol. 44(12), pages 1471-1482, April.
    6. Zbigniew Palmowski & Tomasz Serafin, 2020. "A Note on Simulation Pricing of π -Options," Risks, MDPI, vol. 8(3), pages 1-19, August.
    7. Chen Liu & Henry Schellhorn & Qidi Peng, 2019. "American Option Pricing With Regression: Convergence Analysis," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(08), pages 1-31, December.
    8. Leif Andersen & Mark Broadie, 2004. "Primal-Dual Simulation Algorithm for Pricing Multidimensional American Options," Management Science, INFORMS, vol. 50(9), pages 1222-1234, September.
    9. Jin, Xing & Yang, Cheng-Yu, 2016. "Efficient estimation of lower and upper bounds for pricing higher-dimensional American arithmetic average options by approximating their payoff functions," International Review of Financial Analysis, Elsevier, vol. 44(C), pages 65-77.
    10. Sebastian Maier, 2021. "Re-evaluating natural resource investments under uncertainty: An alternative to limited traditional approaches," Annals of Operations Research, Springer, vol. 299(1), pages 907-937, April.
    11. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    12. Pringles, Rolando & Olsina, Fernando & Garcés, Francisco, 2015. "Real option valuation of power transmission investments by stochastic simulation," Energy Economics, Elsevier, vol. 47(C), pages 215-226.
    13. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    14. Nelson Areal & Artur Rodrigues & Manuel Armada, 2008. "On improving the least squares Monte Carlo option valuation method," Review of Derivatives Research, Springer, vol. 11(1), pages 119-151, March.
    15. Berridge, S.J. & Schumacher, J.M., 2002. "An Irregular Grid Approach for Pricing High Dimensional American Options," Other publications TiSEM 416a6d43-3466-47e0-b656-d, Tilburg University, School of Economics and Management.
    16. Zhu, Lei & Zhang, ZhongXiang & Fan, Ying, 2015. "Overseas oil investment projects under uncertainty: How to make informed decisions?," Journal of Policy Modeling, Elsevier, vol. 37(5), pages 742-762.
    17. Zbigniew Palmowski & Tomasz Serafin, 2020. "Note on simulation pricing of $\pi$-options," Papers 2007.02076, arXiv.org, revised Aug 2020.
    18. 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.
    19. 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.
    20. Sebastian Becker & Patrick Cheridito & Arnulf Jentzen & Timo Welti, 2019. "Solving high-dimensional optimal stopping problems using deep learning," Papers 1908.01602, arXiv.org, revised Aug 2021.

    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:inm:ormnsc:v:50:y:2004:i:9:p:1193-1203. 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 Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.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.