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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(4), pages 477-495, December.
    • Handle: RePEc:cup:jfinqa:v:26:y:1991:i:04:p:477-495_00
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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. Christoph Woster, 2010. "An efficient algorithm for pricing barrier options in arbitrage-free binomial models with calibrated drift terms," Quantitative Finance, Taylor & Francis Journals, vol. 10(5), pages 555-564.
    3. Yuan Hu & W. Brent Lindquist & Svetlozar T. Rachev & Frank J. Fabozzi, 2024. "Option Pricing Using a Skew Random Walk Binary Tree," JRFM, MDPI, vol. 17(4), pages 1-29, March.
    4. Robert Keller & Lukas Häfner & Thomas Sachs & Gilbert Fridgen, 2020. "Scheduling Flexible Demand in Cloud Computing Spot Markets," Business & Information Systems Engineering: The International Journal of WIRTSCHAFTSINFORMATIK, Springer;Gesellschaft für Informatik e.V. (GI), vol. 62(1), pages 25-39, February.
    5. Yuan Hu & W. Brent Lindquist & Svetlozar T. Rachev & Frank J. Fabozzi, 2023. "Option pricing using a skew random walk pricing tree," Papers 2303.17014, arXiv.org.
    6. 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.
    7. 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.
    8. Ghafarian, Bahareh & Hanafizadeh, Payam & Qahi, Amir Hossein Mortazavi, 2018. "Applying Greek letters to robust option price modeling by binomial-tree," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 632-639.
    9. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    10. T. S. Ho & Richard C. Stapleton & Marti G. Subrahmanyam, 1995. "Correlation risk, cross‐market derivative products and portfolio performance," European Financial Management, European Financial Management Association, vol. 1(2), pages 105-124, July.
    11. Lars Stentoft, 2013. "American option pricing using simulation with an application to the GARCH model," Chapters, in: Adrian R. Bell & Chris Brooks & Marcel Prokopczuk (ed.), Handbook of Research Methods and Applications in Empirical Finance, chapter 5, pages 114-147, Edward Elgar Publishing.
    12. Sandra Peterson & Richard Stapleton, 2002. "The pricing of Bermudan-style options on correlated assets," Review of Derivatives Research, Springer, vol. 5(2), pages 127-151, May.
    13. Nikolai Dokuchaev, 2013. "On strong binomial approximation for stochastic processes and applications for financial modelling," Papers 1311.0675, arXiv.org, revised Feb 2015.
    14. Peterson, Sandra & Stapleton, Richard C. & Subrahmanyam, Marti G., 2003. "A Multifactor Spot Rate Model for the Pricing of Interest Rate Derivatives," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(4), pages 847-880, December.
    15. 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.
    16. Anlong Li, 1992. "Binomial approximation in financial models: computational simplicity and convergence," Working Papers (Old Series) 9201, Federal Reserve Bank of Cleveland.
    17. Gambaro, Anna Maria & Kyriakou, Ioannis & Fusai, Gianluca, 2020. "General lattice methods for arithmetic Asian options," European Journal of Operational Research, Elsevier, vol. 282(3), pages 1185-1199.
    18. Mark Broadie & Jérôme Detemple, 1996. "Recent Advances in Numerical Methods for Pricing Derivative Securities," CIRANO Working Papers 96s-17, CIRANO.
    19. 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.
    20. George Chang, 2018. "Examining the Efficiency of American Put Option Pricing by Monte Carlo Methods with Variance Reduction," International Journal of Economics and Finance, Canadian Center of Science and Education, vol. 10(2), pages 10-13, February.

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