Several New Methods Of Black-Scholes Modeling And Their Analyses

Black-Scholes equation is an important model in option pricing theory of financial mathematics, and it is very significant in practical applications to study its numerical results. In this paper, we give several new numerical methods for solving B-S equation, and the numerical experiments show the feasibility of these methods.In chapter 1, a specific statement of option pricing theory is made. In chapter 2, we establish a new two-order numerical scheme for solving Black-Scholes modeling, and its stability and convergence are also discussed. In chapter 3, we construct a new fully discrete universal difference scheme of an equivalent initial value problem transformed from Black-Scholes equation via variable-substitutions, and the schemes of stability proof and convergences are presented. Then, the numerical experiments verify the correctness and the practicability. In chapter 4, we give a detailed process of the binomial tree method of the Asian options, and then the analyses and simple examples indicate the efficiency.