A Research On Option Pricing With Transaction Costs

In this paper we consider four problems on option pricing: the model of option pricing with transaction costs under CEVP , the model of option pricing with transaction costs under an ordinary process, the model of Asian option pricing with transaction costs and the pricing of multi-asset options with transaction costs.Firstly, we consider the model of Black-Scholes under CEVP, then add the transaction costs and take advantage of Leland's method to give the option pricing model under that case. Then we make some conditions simply to gain the option pricing formula of European Call.In the end,we discuss the solution of this model with definite difference.Secondly, we extend the process to an ordinary process and give an universal B-S formula on the base of the former.Moreover,it shows that the option's price isn't correlation to the float of stock.Finally, we also present the model of option pricing when the rate and the dividend rate are functions of time.Then we consider the Asian option and give the option pricing model when stock price under an ordinary process. Moreover, we give the option pricing formula under the Geometric Brown Motion.In the end, we discuss the situation of multi-asset options. On the foundation of former, we extend the rainbow option of two assets to the multi-asset options which base on many assets and give the formula of multi-asset options with transaction costs. Moreover, we use the foregoing discussion to promote the pricing formula under a general stochastic process.Through all above four aspect jobs, this paper extend these existing models furtherly. It believes that conclusions under these improvements are more conforming the reality and have some reference value.