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The Multinomial Option Pricing Model and Its Brownian and Poisson Limits

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

Abstract

The Cox, Ross, and Rubinstein binomial model is generalized to the multinomial case. Limits are investigated and shown to yield the Black-Scholes formula in the case of continuous sample paths fora wide variety of complete market structures. In the discontinuous case a Merton-type formula is shown to result, provided jump probabilities are replacedby their corresponding Arrow-Debreu prices.
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Suggested Citation

  • Milne, Frank & Madan, Dilip & Shefrin, Hersh, 1990. "The Multinomial Option Pricing Model and Its Brownian and Poisson Limits," Queen's Economics Department Working Papers 273638, Queen's University - Department of Economics.
    • Handle: RePEc:ags:quedwp:273638
    DOI: 10.22004/ag.econ.273638
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    References listed on IDEAS

    as
    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. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    4. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    5. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    6. Jones, E. Philip, 1984. "Option arbitrage and strategy with large price changes," Journal of Financial Economics, Elsevier, vol. 13(1), pages 91-113, March.
    7. 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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    Keywords

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    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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