A New Simple Proof of the No-arbitrage Theorem for Multi-period Binomial Model
Liang Hong, Ahmed Elshahat

Abstract
Binomial option pricing model is one of the widely used models to price option contracts, which are commonly employed to hedge against risks in the insurance field. One of the main underlying assumptions of the binomial model is the no-arbitrage condition. This condition simply provides a necessary and sufficient condition for the model to be free of arbitrage opportunities. Previous attempts were made to assess the viability of this assumption. But they were quite complicated and lengthy which tend to obscure the underlying meaning, and may appear to be daunting and inaccessible to the general audience. In this paper, we supply a clear, clean and simple proof using only pre-trigonometric algebra.

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