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

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  • Kaushik Amin
  • Ajay Khanna

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.

Suggested Citation

  • Kaushik Amin & Ajay Khanna, 1994. "Convergence Of American Option Values From Discrete- To Continuous-Time Financial Models," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 289-304.
  • Handle: RePEc:bla:mathfi:v:4:y:1994:i:4:p:289-304
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    Cited by:

    1. Ralf Korn & Stefanie Müller, 2013. "The optimal-drift model: an accelerated binomial scheme," Finance and Stochastics, Springer, vol. 17(1), pages 135-160, January.
    2. R. Kalantari & S. Shahmorad & D. Ahmadian, 2016. "The Stability Analysis of Predictor–Corrector Method in Solving American Option Pricing Model," Computational Economics, Springer;Society for Computational Economics, vol. 47(2), pages 255-274, February.
    3. 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.
    4. Henry Lam & Zhenming Liu, 2014. "From Black-Scholes to Online Learning: Dynamic Hedging under Adversarial Environments," Papers 1406.6084, arXiv.org.
    5. Tobias Lipp & Grégoire Loeper & Olivier Pironneau, 2013. "Mixing Monte-Carlo and Partial Differential Equations for Pricing Options," Post-Print hal-01558826, HAL.
    6. 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.
    7. repec:bla:stratm:v:38:y:2017:i:2:p:278-299 is not listed on IDEAS
    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. Ross A. Maller & David H. Solomon & Alex Szimayer, 2006. "A Multinomial Approximation For American Option Prices In Lévy Process Models," Mathematical Finance, Wiley Blackwell, vol. 16(4), pages 613-633.
    10. Lo-Bin Chang & Ken Palmer, 2007. "Smooth convergence in the binomial model," Finance and Stochastics, Springer, vol. 11(1), pages 91-105, January.
    11. David Heath & Stefano Herzel, 2002. "Efficient option valuation using trees," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(3), pages 163-178.
    12. 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.
    13. 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.
    14. repec:dau:papers:123456789/5374 is not listed on IDEAS
    15. 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.
    16. Huimin Yao & Frederik Pretorius, 2014. "Demand Uncertainty, Development Timing and Leasehold Land Valuation: Empirical Testing of Real Options in Residential Real Estate Development," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 42(4), pages 829-868, December.
    17. 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.
    18. Mojtaba Hajipour & Alaeddin Malek, 2015. "Efficient High-Order Numerical Methods for Pricing of Options," Computational Economics, Springer;Society for Computational Economics, vol. 45(1), pages 31-47, January.
    19. 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.
    20. Yuri Kifer, 2006. "Error estimates for binomial approximations of game options," Papers math/0607123, arXiv.org.
    21. Mark Broadie & Jérôme B. Detemple, 1996. "Recent Advances in Numerical Methods for Pricing Derivative Securities," CIRANO Working Papers 96s-17, CIRANO.

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