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

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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.

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References

  • 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.

    Article  Google Scholar 

  • Barone-Adesi, G., & Whaley, R. (1987). Efficient analytic approximation of American option values. Journal of Finance, 42, 301–320.

    Article  Google Scholar 

  • Barraquant, J., & Martineau, D. (1995). Numerical valuation of high dimensional multivariate American securities. Journal of Financial and Quantitative Analysis, 30, 383–405.

    Article  Google Scholar 

  • Boyle, P., Broadie, M., & Glasserman, P. (1997). Monte Carlo methods for security pricing. Journal of Economic Dynamics and Control, 21, 1267–1321.

    Article  Google Scholar 

  • Broadie, M., & Glasserman, P. (1997). Pricing American-style securities using simulation. Journal of Economic Dynamics and Control, 21, 1323–1352.

    Article  Google Scholar 

  • Broadie, M., Glasserman, P., & Kou, S. (1997). A continuity correction for discrete barrier options. Mathematical Finance, 7, 325–348.

    Article  Google Scholar 

  • Broadie, M., Glasserman, P., & Kou, S. (1999). Connecting discrete and continuous path-dependent options. Finance and Stochastics, 3, 55–82.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Dai, M., & Kwok, Y. K. (2004). Knock-in American options. Journal of Futures Markets, 24, 172–192.

    Article  Google Scholar 

  • Duan, J. C., & Simonato, J. G. (1998). Empirical martingale simulation for asset prices. Management Science, 44, 1218–1233.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Glasserman, P. (2004). Monte Carlo methods in financial engineering. New York: Springer.

    Google Scholar 

  • Haug, E. G. (2001). Closed form valuation of American barrier options. International Journal of Theoretical and Applied Finance, 4, 355–359.

    Article  Google Scholar 

  • Haug, E. G. (2006). The complete guide to option pricing formulas (2nd ed.). New York: McGraw-Hill.

    Google Scholar 

  • Kou, S. G. (2003). On pricing of discrete barrier options. Statistica Sinica, 13, 955–964.

    Google Scholar 

  • Longstaff, F. A., & Schwartz, E. S. (2001). Valuing American options by simulation: A simple least-squares approach. Review of Financial Studies, 14, 113–147.

    Article  Google Scholar 

  • Miao, D. W.-C., & Lee, Y.-H. (2013). A forward Monte Carlo method for American options pricing. Journal of Futures Markets, 33, 369–395.

    Article  Google Scholar 

  • Ritchken,. (1995). On pricing barrier options. Journal of Derivatives, Winter 1995, 19–28.

  • Tilley, J. A. (1993). Regression methods for pricing complex American-style options. Transactions of the Society of Actuaries, 45, 249–266.

    Google Scholar 

Download references

Acknowledgements

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

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Authors and Affiliations

  1. Graduate Institute of Finance, National Taiwan University of Science and Technology, 43, Sec. 4, Keelung Rd., Taipei, 106, Taiwan

    Daniel Wei-Chung Miao

  2. Industrial-Academic Research and Development Center, Lunghwa University of Science and Technology, Taoyuan City, Taiwan

    Yung-Hsin Lee

  3. Department of International Business, National Taiwan University, Taipei, Taiwan

    Jr-Yan Wang

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  1. Daniel Wei-Chung Miao
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  2. Yung-Hsin Lee
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  3. Jr-Yan Wang
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Correspondence to Daniel Wei-Chung Miao.

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Miao, D.WC., Lee, YH. & Wang, JY. Using forward Monte-Carlo simulation for the valuation of American barrier options. Ann Oper Res 264, 339–366 (2018). https://doi.org/10.1007/s10479-017-2639-4

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  • DOI: https://doi.org/10.1007/s10479-017-2639-4

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