Existence Conditions of Super-Replication Cost in a Multinomial Model

Mei Xing

Journal of Mathematics Research, 2017, vol. 9, issue 4, 185-195

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.

Keywords: multinomial model; super-replication cost; L\'{e}vy process (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:ibn:jmrjnl:v:9:y:2017:i:4:p:185-195

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