TRIMOMIAL TREE METHOD FOR OPTION PRICING WITH TRANSACTION COST

Abstract

This paper describes the progression of research initiated in MATH 424: Mathematical Finance course, with an emphasis on the creation and development of the Trinomial Tree Method for option pricing, particularly in the presence of transaction costs. We begin by reviewing the Cox-Ross-Rubenstein binomial scheme and then go on to trinomial approaches in financial literature, demonstrating their enhanced effectiveness over the binomial method. Our study includes complex models such as the Boyle and Vorst model, widening the scope beyond the standard Black-Scholes model covered in the course. However, the Boyle and Vorst’s method only covers transaction cost for binomial models. Our objective is to review the literature on the Trinomial Tree Method considering transaction cost which requires solving the absolute value matrix equation Ax − |X| = b along the tree. We have extended the results of the Boyle and Vorst from a binomial to trinomial method for a European call option. We implemented numerically our method and these results were inconsistent with the results of the Boyle and Vorst’s method comparable to the binomial results. The research extends the practical application of option pricing models by providing a complete framework for solving absolute value equations in the setting of trinomial trees, yielding useful insights for the Trinomial Tree Method with transaction cost.