Constructing Multinomial Option Pricing Models: Illustrations for Practice and Education

Binomial pricing trees are often used to value options. However, binomial models can easily become very large and cumbersome. Multinomial option pricing trees can be constructed that produce results equivalent to binomial option pricing trees. The advantage of creating multinomial trees is that they are smaller and easier to construct than binomial trees. In this paper, trinomial and quintinomial option pricing trees are developed and compared to simple binomial trees, illustrating the similarities and differences. These multinomial pricing trees are much smaller and more compact because they require fewer calculations to produce results equivalent to binomial trees. Methods for valuing put and call options, European and American options, and accounting for dividends are also illustrated. Multinomial option pricing trees can be helpful to students in understanding how the models work and useful to practitioners in constructing simple option pricing models.