Convergence-Rate Study Of Trinomial European Option Pricing Models

Lattice approach is a usual method in option pricing. It has received a lot of attention in the study of pricing options. The convergence rates of binomial methods have been well developed in the literature. Relatively, the convergence rates of trinomial methods are not been fully understood. Although trinomial convergence has been known, the convergence rates have not been proven. The aim of this thesis is to study the convergence rates of trinomial methods for pricing European options.In this thesis, two methods are developed:one is to extend the theory of Leisen (1995) which represents the error bound by moments and pseudo-moments. The other one is to develop a new method which expands the option price into the trinomial value plus high-order remainder and then the rates of the trinomial methods are proven after analyzing the order of the remainder. The last method provides a new idea for proving the rates of trinomial tree method.We have a rough assessment for the order of trinomial tree using moments method, and know that the order is one after finding either moments or pseudo-moments converge at a speed of one order. However, there are drawbacks in the proof of Leisen (1995) with an assumption. Therefore, we develop a new proof.