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On the Computation of Continuous Time Option Prices Using Discrete Approximations

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  • Amin, Kaushik I.

Abstract

We develop a class of discrete, path-independent models to compute prices of American options within the Black-Scholes (1973) framework, including models in which state variables have time-varying volatility functions and models with multiple state variables. Time-varying volatility functions are illustrated with applications to term structure models developed by Vasicek (1977) and Heath, Jarrow, and Morton (1988), (1990). Distinct from previous work in the literature, the multivariate models suggested in this paper are consistent with arbitrarily large, though constant, covariance functions. Finally, we compare and contrast the numerical accuracy of a large number of models with simulation results.

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  • Amin, Kaushik I., 1991. "On the Computation of Continuous Time Option Prices Using Discrete Approximations," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(04), pages 477-495, December.
  • Handle: RePEc:cup:jfinqa:v:26:y:1991:i:04:p:477-495_00
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    1. Shleifer, Andrei & Vishny, Robert W, 1986. "Large Shareholders and Corporate Control," Journal of Political Economy, University of Chicago Press, vol. 94(3), pages 461-488, June.
    2. Harris, Milton & Raviv, Artur, 1988. "Corporate control contests and capital structure," Journal of Financial Economics, Elsevier, vol. 20(1-2), pages 55-86, January.
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    Cited by:

    1. Ekvall, Niklas, 1996. "A lattice approach for pricing of multivariate contingent claims," European Journal of Operational Research, Elsevier, vol. 91(2), pages 214-228, June.
    2. Andrea Gamba & Lenos Trigeorgis, 2007. "An Improved Binomial Lattice Method for Multi-Dimensional Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(5), pages 453-475.
    3. Ariste, Ruolz & Lasserre, Pierre, 2001. "La gestion optimale d’une forêt exploitée pour son potentiel de diminution des gaz à effet de serre et son bois," L'Actualité Economique, Société Canadienne de Science Economique, vol. 77(1), pages 27-51, mars.
    4. Sandra Peterson & Richard Stapleton, 2002. "The pricing of Bermudan-style options on correlated assets," Review of Derivatives Research, Springer, pages 127-151.
    5. Anlong Li, 1992. "Binomial approximation in financial models: computational simplicity and convergence," Working Paper 9201, Federal Reserve Bank of Cleveland.
    6. 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.
    7. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, pages 1145-1177.
    8. Lars Stentoft, 2013. "American option pricing using simulation with an application to the GARCH model," Chapters,in: Handbook of Research Methods and Applications in Empirical Finance, chapter 5, pages 114-147 Edward Elgar Publishing.
    9. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    10. 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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