Several Problems On European Option Pricing With Transaction Costs

In this paper three problems on European option pricing are mainly discussed: European option pricing with transaction costs about stock price's dual influences of continuous wave and abnormal wave, Binomial tree and triple tree method's further promotion and extension, And several exotic option pricing on many B-S modified conditions.Firstly, under an arbitrage-free framework, we consider European option pricing with stock price's proportional transaction costs in the process of stock trading,and stock price's dual influences of continuous wave and abnormal wave(described by Brownian motion and poisson motion).And an explicit expression of option pricing formula is given. Then the solution to the model is given out by using some knowledge of stochastic differential equation. A more generally pricing formula is obtained.Secondly, pricing formula and numerical solution for above model are obtained by using a new kind of binomial tree method. And an example is used to verify this method's rationalization.Then the mutual relations between stochastic differential equation's solution and binomial tree method's solution is discussed.And on the basis of binomial tree matrix form algorithm method, triple tree matrix form algorithm is obtained,one kind of new method to study option pricing problem is provided.Finally, we consider four variation options which are combined and derived by standard options:Rainbow option; Multi-factor option; Asian option; Lookback op-tion;And these options's stochastic differential equations are given on the conditions of transaction costs,stock price's dual influences of continuous wave and abnormal wave and constant elasticity of variance.These results enrich and develop the theory of option pricing, and from the stand-point of application, which are suitable for more complicated real financial market.