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Convergence Of American Option Values From Discrete- To Continuous-Time Financial Models

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  • Kaushik Amin
  • Ajay Khanna
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    Abstract

    Given a sequence of discrete-time option valuation models in which the sequence of processes defining the state variables converges weakly to a diffusion, we prove that the sequence of American option values obtained from these discrete-time models also converges to the corresponding value obtained from the continuous-time model for the standard models in the finance/economics literature. the convergence proof carries over to the case when the limiting risky asset price process follows a diffusion, except it pays discrete dividends on some fixed dates. Copyright 1994 Blackwell Publishers.

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    File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9965.1994.tb00059.x
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    Bibliographic Info

    Article provided by Wiley Blackwell in its journal Mathematical Finance.

    Volume (Year): 4 (1994)
    Issue (Month): 4 ()
    Pages: 289-304

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    Handle: RePEc:bla:mathfi:v:4:y:1994:i:4:p:289-304

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    Cited by:
    1. Lo-Bin Chang & Ken Palmer, 2007. "Smooth convergence in the binomial model," Finance and Stochastics, Springer, vol. 11(1), pages 91-105, January.
    2. Das, Sanjiv Ranjan, 1998. "A direct discrete-time approach to Poisson-Gaussian bond option pricing in the Heath-Jarrow-Morton model," Journal of Economic Dynamics and Control, Elsevier, vol. 23(3), pages 333-369, November.
    3. Garcia, Diego, 2003. "Convergence and Biases of Monte Carlo estimates of American option prices using a parametric exercise rule," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1855-1879, August.
    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. Yuri Kifer, 2006. "Error estimates for binomial approximations of game options," Papers math/0607123, arXiv.org.
    6. David Heath & Stefano Herzel, 2002. "Efficient option valuation using trees," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(3), pages 163-178.
    7. Ralf Korn & Stefanie Müller, 2013. "The optimal-drift model: an accelerated binomial scheme," Finance and Stochastics, Springer, vol. 17(1), pages 135-160, January.
    8. Duan, Jin-Chuan & Simonato, Jean-Guy, 2001. "American option pricing under GARCH by a Markov chain approximation," Journal of Economic Dynamics and Control, Elsevier, vol. 25(11), pages 1689-1718, November.
    9. N. Hilber & N. Reich & C. Schwab & C. Winter, 2009. "Numerical methods for Lévy processes," Finance and Stochastics, Springer, vol. 13(4), pages 471-500, September.
    10. Mark Broadie & Jérôme B. Detemple, 1996. "Recent Advances in Numerical Methods for Pricing Derivative Securities," CIRANO Working Papers 96s-17, CIRANO.
    11. 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.
    12. Elisa Appolloni & Lucia Caramellino & Antonino Zanette, 2013. "A robust tree method for pricing American options with CIR stochastic interest rate," Papers 1305.0479, arXiv.org.
    13. Nagae, Takeshi & Akamatsu, Takashi, 2008. "A generalized complementarity approach to solving real option problems," Journal of Economic Dynamics and Control, Elsevier, vol. 32(6), pages 1754-1779, June.

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