Completing Market with One Step Trinomial Model: A European Call Approach

Abstract

The fundamental defect of the market constructed under a trinomial tree model lies in its incompleteness with initial risk-free and risky assets only. This paper analyzes the first-step probability behaviors of the trinomial tree model and summarizes how could introduce derivatives being a general solution to such a market. The European call option is used for demonstration. This paper further discusses the first-step pricing method for this call option under arbitrary market parameters. Results show that any derivatives being linearly independent of initial primary assets could complete such a market. When pricing such derivatives, their portfolio should be bounded by three sub-binomial tree structures that recombined from three possible branches of the initial model.