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The Multinomial Option Pricing Model and Its Brownian and Poisson Limits

  • Frank Milne

    ()

    (Queen's University)

  • Dilip Madan

    (University of Maryland)

  • Hersh Shefrin

    (Santa Clara University)

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 for a wide variety 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.

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File URL: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_1162.pdf
File Function: First version 1990
Download Restriction: no

Paper provided by Queen's University, Department of Economics in its series Working Papers with number 1162.

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Length: 15 pages
Date of creation: Jan 1990
Date of revision:
Publication status: Published in The Review of Financial Studies, 1989 Volume 2, Number 2, pp. 251-265
Handle: RePEc:qed:wpaper:1162
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  1. Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  2. Duffie, J Darrell & Huang, Chi-fu, 1985. "Implementing Arrow-Debreu Equilibria by Continuous Trading of Few Long-lived Securities," Econometrica, Econometric Society, vol. 53(6), pages 1337-56, November.
  3. 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.
  4. 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 637-54, May-June.
  5. 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.
  6. 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.
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