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Existence Conditions of Super-Replication Cost in a Multinomial Model

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  • Mei Xing

Abstract

This paper gives a theorem for the continuous time super-replication cost of European options in an unbounded multinomial market. An approximation multinomial scheme is put forward on a finite time interval [0,1] corresponding to a pure jump L\'{e}vy model with unbounded jumps. Under the assumption that the expected underlying stock price at time 1 is bounded, the limit of the sequence of the super-replication cost in a multinomial model is proved to be greater than or equal to an optimal control problem. Furthermore, it is discussed that the existence conditions of a super-replication cost and a liquidity premium for the multinomial model. This paper concentrates on a multinomial tree with unbounded jumps, which can be seen as an extension of the work of(Xing, 2015). The super-replication cost and the liquidity premium under the variance gamma model and the normal inverse Gaussian model are calculated and illustrated.

Suggested Citation

  • Mei Xing, 2017. "Existence Conditions of Super-Replication Cost in a Multinomial Model," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 9(4), pages 185-195, August.
    • Handle: RePEc:ibn:jmrjnl:v:9:y:2017:i:4:p:185-195
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    References listed on IDEAS

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    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Szimayer, Alex & Maller, Ross A., 2007. "Finite approximation schemes for Lévy processes, and their application to optimal stopping problems," Stochastic Processes and their Applications, Elsevier, vol. 117(10), pages 1422-1447, October.
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    More about this item

    Keywords

    multinomial model; super-replication cost; L'{e}vy process;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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