The Bino-trinomial Tree: A Simple Model for Efficient and Accurate Option Pricing

Most derivatives do not have simple valuation formulas and must be priced by numerical methods such as tree models. Although the option prices computed by a tree model converges to the theoretical value as the number of time steps increases, the distribution error and the nonlinearity error may make the prices converge slowly or even oscillate significantly. This paper introduces a novel tree model, the bino-trinomial tree (BTT), that can price a wide range of derivatives efficiently and accurately. The BTT reduces the nonlinearity error sharply by adapting its structure to suit the derivative’s specification; consequently, the pricing results converge smoothly and quickly. Moreover, the pricing of some European-style options on the BTT can be made extremely efficient by combinatorial tools, which are not available to most other tree models. Therefore, the BTT can efficiently reduce the distribution error by picking a large number of time steps. Finally, the BTT can be easily adapted to efficiently model a stock process with a complex dividend regime. This paper uses a variety of options to demonstrate the effectiveness of the BTT. Extensive numerical experiments show the superiority of the BTT to many other popular and/or much more sophisticated numerical models.