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The Multinomial Option Pricing Model and Its Brownian and Poisson Limits

Author

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  • Madan, Dilip B
  • Milne, Frank
  • Shefrin, Hersh

Abstract

The Cox, Ross, and Rubinstein binomial model is generalized to the multinomial case. Limits are investigated and shown to yield the Blacks-Scholes formula in the case of continuous sample paths for formula in the case of complete market structures. In the discontinuous case a Merton-type formula is shown to result, provided jump probabilities are replaced by their corresponding Arrow-Debreu prices. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.

Suggested Citation

  • Madan, Dilip B & Milne, Frank & Shefrin, Hersh, 1989. "The Multinomial Option Pricing Model and Its Brownian and Poisson Limits," The Review of Financial Studies, Society for Financial Studies, vol. 2(2), pages 251-265.
    • Handle: RePEc:oup:rfinst:v:2:y:1989:i:2:p:251-65
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    1. Merton, Robert C., 1977. "On the pricing of contingent claims and the Modigliani-Miller theorem," Journal of Financial Economics, Elsevier, vol. 5(2), pages 241-249, November.
    2. Darrell Duffie & Chi-Fu Huang, 2005. "Implementing Arrow-Debreu Equilibria By Continuous Trading Of Few Long-Lived Securities," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 4, pages 97-127, World Scientific Publishing Co. Pte. Ltd..
    3. David M. Kreps, 1982. "Multiperiod Securities and the Efficient Allocation of Risk: A Comment on the Black-Scholes Option Pricing Model," NBER Chapters, in: The Economics of Information and Uncertainty, pages 203-232, National Bureau of Economic Research, Inc.
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    5. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
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    Cited by:

    1. Vladislav Kargin, 2005. "Lattice Option Pricing By Multidimensional Interpolation," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 635-647, October.
    2. Zdenìk Zmeškal, 2008. "Application of the American Real Flexible Switch Options Methodology A Generalized Approach," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 58(05-06), pages 261-275, August.
    3. Aleš Černý, 2007. "Optimal Continuous‐Time Hedging With Leptokurtic Returns," Mathematical Finance, Wiley Blackwell, vol. 17(2), pages 175-203, April.
    4. Hranaiova, Jana, 2000. "Delivery Options In Futures Contracts And Basis Behavior At Contract Maturity," 2000 Conference, April 17-18 2000, Chicago, Illinois 18936, NCR-134 Conference on Applied Commodity Price Analysis, Forecasting, and Market Risk Management.
    5. Thilini Mahanama & Abootaleb Shirvani & Svetlozar Rachev, 2021. "Global Index on Financial Losses due to Crime in the United States," Papers 2105.03514, arXiv.org.
    6. Luke Miller & Mark Bertus, 2013. "An Exposition On The Mathematics And Economics Of Option Pricing," Business Education and Accreditation, The Institute for Business and Finance Research, vol. 5(1), pages 1-16.
    7. Hranaiova, Jana & Tomek, William G., 2000. "Delivery Option In Futures Contracts And Basis Behavior At Contract Maturity," 2000 Annual meeting, July 30-August 2, Tampa, FL 21732, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    8. Thilini Mahanama & Abootaleb Shirvani & Svetlozar Rachev, 2022. "A Natural Disasters Index," Environmental Economics and Policy Studies, Springer;Society for Environmental Economics and Policy Studies - SEEPS, vol. 24(2), pages 263-284, April.
    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. Kim, Young Shin & Stoyanov, Stoyan & Rachev, Svetlozar & Fabozzi, Frank J., 2019. "Enhancing binomial and trinomial equity option pricing models," Finance Research Letters, Elsevier, vol. 28(C), pages 185-190.
    11. Thilini Mahanama & Abootaleb Shirvani & Svetlozar T. Rachev, 2021. "Global Index on Financial Losses Due to Crime in the United States," JRFM, MDPI, vol. 14(7), pages 1-16, July.
    12. Cho, Junhyun & Kim, Yejin & Lee, Sungchul, 2022. "An accurate and stable numerical method for option hedge parameters," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    13. Luenberger, David G., 1998. "Products of trees for investment analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1403-1417, August.
    14. Thilini V. Mahanama & Abootaleb Shirvani & Svetlozar Rachev, 2023. "The Financial Market of Indices of Socioeconomic Wellbeing," Papers 2303.05654, arXiv.org.
    15. Mark Broadie & Jérôme Detemple, 1996. "Recent Advances in Numerical Methods for Pricing Derivative Securities," CIRANO Working Papers 96s-17, CIRANO.
    16. 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.
    17. Yuan Hu & Abootaleb Shirvani & W. Brent Lindquist & Frank J. Fabozzi & Svetlozar T. Rachev, 2020. "Option Pricing Incorporating Factor Dynamics in Complete Markets," JRFM, MDPI, vol. 13(12), pages 1-33, December.
    18. Yuan Hu & Abootaleb Shirvani & W. Brent Lindquist & Frank J. Fabozzi & Svetlozar T. Rachev, 2020. "Option Pricing Incorporating Factor Dynamics in Complete Markets," Papers 2011.08343, arXiv.org.
    19. Zmeskal, Zdenek, 2010. "Generalised soft binomial American real option pricing model (fuzzy-stochastic approach)," European Journal of Operational Research, Elsevier, vol. 207(2), pages 1096-1103, December.
    20. Thisari K. Mahanama & Abootaleb Shirvani & Svetlozar Rachev & Frank J. Fabozzi, 2023. "The Financial Market of Environmental Indices," Papers 2308.15661, arXiv.org.
    21. Dilip B. Madan & Frank Milne, 1991. "Option Pricing With V. G. Martingale Components," Working Paper 1159, Economics Department, Queen's University.
    22. 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.

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    More about this item

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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