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Market Viability and Completeness for Multinomial Models

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  • Nahuel I. Arca

Abstract

We study a generalization of the classical binomial model that consists in allowing any finite number of branches in each node of the tree representation. In this model, we show that the two fundamental theorems of asset pricing have a geometric interpretation and, using this, we give necessary and sufficient conditions for a market to be arbitrage-free and complete. We also present an algorithm for completing arbitrage-free markets in every possible way. We apply these results to the study of a discrete-time version of the Korn-Kreer-Lenssen model.

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  • Nahuel I. Arca, 2025. "Market Viability and Completeness for Multinomial Models," Papers 2508.13966, arXiv.org.
    • Handle: RePEc:arx:papers:2508.13966
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    References listed on IDEAS

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    1. Mark Rubinstein., 2000. "On the Relation Between Binomial and Trinomial Option Pricing Models," Research Program in Finance Working Papers RPF-292, University of California at Berkeley.
    2. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    3. Rendleman, Richard J, Jr & Bartter, Brit J, 1979. "Two-State Option Pricing," Journal of Finance, American Finance Association, vol. 34(5), pages 1093-1110, December.
    4. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    5. Rubinstein, Mark, 2000. "On the Relation Between Binomial and Trinomial Option Pricing Models," Research Program in Finance, Working Paper Series qt3bw450n0, Research Program in Finance, Institute for Business and Economic Research, UC Berkeley.
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