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The Multinomial Option Pricing Model and Its Brownian and Poisson Limits

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Author Info
Frank Milne () (Queen's University)
Dilip Madan (University of Maryland)
Hersh Shefrin (Santa Clara University)

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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 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://www.econ.queensu.ca/working_papers/papers/qed_wp_1162.pdf
File Format: application/pdf
File Function: First version 1990
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Publisher Info
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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Postal: Kingston, Ontario, K7L 3N6
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Web page: http://www.econ.queensu.ca/
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Related research
Keywords: Multinomial; option; pricing; Brownian; Poisson;

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Find related papers by JEL classification:
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  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. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  3. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144. [Downloadable!] (restricted)
    Other versions:
  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. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Frank Milne & Dilip Madan, 1991. "Option Pricing With V. G. Martingale Components," Working Papers 1159, Queen's University, Department of Economics. [Downloadable!]
  2. 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). [Downloadable!]
  3. Vladislav Kargin, 2003. "Lattice Option Pricing By Multidimensional Interpolation," Finance 0309003, EconWPA, revised 29 Oct 2004. [Downloadable!]
    Other versions:
  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. [Downloadable!]
  5. Mark Broadie & Jérôme B. Detemple, 1996. "Recent Advances in Numerical Methods for Pricing Derivative Securities," CIRANO Working Papers 96s-17, CIRANO. [Downloadable!]
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