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A Matched Asymptotic Expansions Approach to Continuity Corrections for Discretely Sampled Options. Part 2: Bermudan Options

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  • Sam Howison

Abstract

The paper discusses the 'continuity correction' that should be applied to connect the prices of discretely sampled American put options (i.e. Bermudan options) and their continuously-sampled equivalents. Using a matched asymptotic expansions approach the correction is computed and related to that discussed by Broadie, Glasserman & Kou (1997) (Mathematical Finance, 7, p.325 for barrier options. In the Bermudan case, the continuity correction is an order of magnitude smaller than in the corresponding barrier problem. It is also shown that the optimal exercise boundary in the discrete case is slightly higher than in the continuously sampled case.

Suggested Citation

  • Sam Howison, 2007. "A Matched Asymptotic Expansions Approach to Continuity Corrections for Discretely Sampled Options. Part 2: Bermudan Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(1), pages 91-104.
    • Handle: RePEc:taf:apmtfi:v:14:y:2007:i:1:p:91-104
    DOI: 10.1080/13504860600858410
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    1. Sam Howison & Mario Steinberg, 2007. "A Matched Asymptotic Expansions Approach to Continuity Corrections for Discretely Sampled Options. Part 1: Barrier Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(1), pages 63-89.
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    Cited by:

    1. Takashi Kato & Akihiko Takahashi & Toshihiro Yamada, 2014. "A Semi-group Expansion for Pricing Barrier Options," CARF F-Series CARF-F-349, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    2. Xiao, Shuang & Ma, Shihua, 2016. "Pricing discrete double barrier options under Lévy processes: An extension of the method by Milev and Tagliani," Finance Research Letters, Elsevier, vol. 19(C), pages 67-74.
    3. Liming Feng & Vadim Linetsky, 2008. "Pricing Discretely Monitored Barrier Options And Defaultable Bonds In Lévy Process Models: A Fast Hilbert Transform Approach," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 337-384, July.
    4. Tian, Miao & Yang, Xiangfeng & Zhang, Yi, 2019. "Barrier option pricing of mean-reverting stock model in uncertain environment," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 126-143.
    5. Lingfei Li & Vadim Linetsky, 2015. "Discretely monitored first passage problems and barrier options: an eigenfunction expansion approach," Finance and Stochastics, Springer, vol. 19(4), pages 941-977, October.
    6. Sam Howison & Mario Steinberg, 2007. "A Matched Asymptotic Expansions Approach to Continuity Corrections for Discretely Sampled Options. Part 1: Barrier Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(1), pages 63-89.
    7. Takashi Kato & Akihiko Takahashi & Toshihiro Yamada, 2012. "Semi-group Expansion for Pricing Barrier Options," CARF F-Series CARF-F-271, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Jun 2013.
    8. Takashi Kato & Akihiko Takahashi & Toshihiro Yamada, 2012. "A Semi-group Expansion for Pricing Barrier Options," CIRJE F-Series CIRJE-F-841, CIRJE, Faculty of Economics, University of Tokyo.
    9. Yang, Nian & Chen, Nan & Liu, Yanchu & Wan, Xiangwei, 2017. "Approximate arbitrage-free option pricing under the SABR model," Journal of Economic Dynamics and Control, Elsevier, vol. 83(C), pages 198-214.
    10. Ballestra, Luca Vincenzo & Cecere, Liliana, 2016. "A numerical method to estimate the parameters of the CEV model implied by American option prices: Evidence from NYSE," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 100-106.
    11. Jiefei Yang & Guanglian Li, 2023. "On Sparse Grid Interpolation for American Option Pricing with Multiple Underlying Assets," Papers 2309.08287, arXiv.org, revised Sep 2023.
    12. Cai, Ning & Li, Chenxu & Shi, Chao, 2021. "Pricing discretely monitored barrier options: When Malliavin calculus expansions meet Hilbert transforms," Journal of Economic Dynamics and Control, Elsevier, vol. 127(C).
    13. Li, Chenxu & Ye, Yongxin, 2019. "Pricing and Exercising American Options: an Asymptotic Expansion Approach," Journal of Economic Dynamics and Control, Elsevier, vol. 107(C), pages 1-1.
    14. Lian, Guanghua & Zhu, Song-Ping & Elliott, Robert J. & Cui, Zhenyu, 2017. "Semi-analytical valuation for discrete barrier options under time-dependent Lévy processes," Journal of Banking & Finance, Elsevier, vol. 75(C), pages 167-183.
    15. Michael B. Giles & Francisco Bernal, 2017. "Multilevel estimation of expected exit times and other functionals of stopped diffusions," Papers 1710.07492, arXiv.org, revised Sep 2018.
    16. Simona Svoboda-Greenwood, 2009. "Displaced Diffusion as an Approximation of the Constant Elasticity of Variance," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(3), pages 269-286.
    17. Bernard, Carole & Le Courtois, Olivier & Quittard-Pinon, François, 2008. "Pricing derivatives with barriers in a stochastic interest rate environment," Journal of Economic Dynamics and Control, Elsevier, vol. 32(9), pages 2903-2938, September.
    18. Ballestra, Luca Vincenzo & Pacelli, Graziella, 2013. "Pricing European and American options with two stochastic factors: A highly efficient radial basis function approach," Journal of Economic Dynamics and Control, Elsevier, vol. 37(6), pages 1142-1167.
    19. Rad, Jamal Amani & Parand, Kourosh & Ballestra, Luca Vincenzo, 2015. "Pricing European and American options by radial basis point interpolation," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 363-377.

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    13. Liming Feng & Vadim Linetsky, 2008. "Pricing Discretely Monitored Barrier Options And Defaultable Bonds In Lévy Process Models: A Fast Hilbert Transform Approach," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 337-384, July.
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