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Annals of Operations Research

, Volume 264, Issue 1–2, pp 339–366 | Cite as

Using forward Monte-Carlo simulation for the valuation of American barrier options

  • Daniel Wei-Chung Miao
  • Yung-Hsin Lee
  • Jr-Yan Wang
Original Paper

Abstract

This paper extends the forward Monte-Carlo methods, which have been developed for the basic types of American options, to the valuation of American barrier options. The main advantage of these methods is that they do not require backward induction, the most time-consuming and memory-intensive step in the simulation approach to American options pricing. For these methods to work, we need to define the so-called pseudo critical prices which are used to determine whether early exercise should happen. In this study, we define a new and more flexible version of the pseudo critical prices which can be conveniently extended to all fourteen types of American barrier options. These pseudo critical prices are shown to satisfy the criteria of a sufficient indicator which guarantees the effectiveness of the proposed methods. A series of numerical experiments are provided to compare the performance between the forward and backward Monte-Carlo methods and demonstrate the computational advantages of the forward methods.

Keywords

American barrier option Forward Monte-Carlo method Pseudo critical price Sufficient indicator 

Notes

Acknowledgements

The authors acknowledge the support from the National Science Council of Taiwan under the grant number NSC 100-2410-H-011-006.

References

  1. Areal, N., Rodrigues, A., & Armada, M. R. (2008). On improving the least squares Monte Carlo option valuation method. Review of Derivatives Research, 11, 119–151.CrossRefGoogle Scholar
  2. Barone-Adesi, G., & Whaley, R. (1987). Efficient analytic approximation of American option values. Journal of Finance, 42, 301–320.CrossRefGoogle Scholar
  3. Barraquant, J., & Martineau, D. (1995). Numerical valuation of high dimensional multivariate American securities. Journal of Financial and Quantitative Analysis, 30, 383–405.CrossRefGoogle Scholar
  4. Boyle, P., Broadie, M., & Glasserman, P. (1997). Monte Carlo methods for security pricing. Journal of Economic Dynamics and Control, 21, 1267–1321.CrossRefGoogle Scholar
  5. Broadie, M., & Glasserman, P. (1997). Pricing American-style securities using simulation. Journal of Economic Dynamics and Control, 21, 1323–1352.CrossRefGoogle Scholar
  6. Broadie, M., Glasserman, P., & Kou, S. (1997). A continuity correction for discrete barrier options. Mathematical Finance, 7, 325–348.CrossRefGoogle Scholar
  7. Broadie, M., Glasserman, P., & Kou, S. (1999). Connecting discrete and continuous path-dependent options. Finance and Stochastics, 3, 55–82.CrossRefGoogle Scholar
  8. Chang, G., Kang, J., Kim, H.-S., & Kim, I. J. (2007). An efficient approximation method for American exotic options. Journal of Futures Markets, 27, 29–59.CrossRefGoogle Scholar
  9. Dai, M., & Kwok, Y. K. (2004). Knock-in American options. Journal of Futures Markets, 24, 172–192.CrossRefGoogle Scholar
  10. Duan, J. C., & Simonato, J. G. (1998). Empirical martingale simulation for asset prices. Management Science, 44, 1218–1233.CrossRefGoogle Scholar
  11. Gao, B., Huang, J., & Subrahmanyam, M. (2000). The valuation of American barrier options using the decomposition techniques. Journal of Economic Dynamics & Control, 24, 1783–1827.CrossRefGoogle Scholar
  12. Glasserman, P. (2004). Monte Carlo methods in financial engineering. New York: Springer.Google Scholar
  13. Haug, E. G. (2001). Closed form valuation of American barrier options. International Journal of Theoretical and Applied Finance, 4, 355–359.CrossRefGoogle Scholar
  14. Haug, E. G. (2006). The complete guide to option pricing formulas (2nd ed.). New York: McGraw-Hill.Google Scholar
  15. Kou, S. G. (2003). On pricing of discrete barrier options. Statistica Sinica, 13, 955–964.Google Scholar
  16. Longstaff, F. A., & Schwartz, E. S. (2001). Valuing American options by simulation: A simple least-squares approach. Review of Financial Studies, 14, 113–147.CrossRefGoogle Scholar
  17. Miao, D. W.-C., & Lee, Y.-H. (2013). A forward Monte Carlo method for American options pricing. Journal of Futures Markets, 33, 369–395.CrossRefGoogle Scholar
  18. Ritchken,. (1995). On pricing barrier options. Journal of Derivatives, Winter 1995, 19–28.Google Scholar
  19. Tilley, J. A. (1993). Regression methods for pricing complex American-style options. Transactions of the Society of Actuaries, 45, 249–266.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • Daniel Wei-Chung Miao
    • 1
  • Yung-Hsin Lee
    • 2
  • Jr-Yan Wang
    • 3
  1. 1.Graduate Institute of FinanceNational Taiwan University of Science and TechnologyTaipeiTaiwan
  2. 2.Industrial-Academic Research and Development CenterLunghwa University of Science and TechnologyTaoyuan CityTaiwan
  3. 3.Department of International BusinessNational Taiwan UniversityTaipeiTaiwan

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