Convergence Rates Of Binomial Tree Algorithms For Option Pricing

Option is one of the most important financial derivatives, option pricing plays a key role in option trading. Theory of option pricing can do it back to Black and Scholes (1973) and Morton (1973), since then, there have been emerging extensive studies in option pricing theory. Binomial approach is one of the popular methods for pricing option. Recently, there are increasingly interests in proving the convergent rates of the binomial methods.In this thesis, we utilize stochastic analysis, combinatorial mathematics and other mathematical tools to prove the convergence rates of binomial tree algorithms for pricing European-style options and exotic options.This thesis provides comprehensive literature review for the theory of convergence rates for binomial tree methods, and proves the convergence rates of many variants binomial tree methods which are lack in the existent literature. Another contribution of this thesis is to prove the convergence rate of some exotic options (power options, gap options, etc.). Finally, the convergence rates for computing the Greeks of power options are proved.