| "Financial Mathematics, Financial Engineering and Financial Managing (NO.79790130)"is one of the important items during the ninth Five-Year-Plan in China, and option pricing is being studied heartily in this item. Binomial tree is widely used in option pricing, and it can be used to solve almost all the option pricing problems which have no closed solution and it also can be used to exotic options.In the research, we find that there is some coincidence in the way of choosing the C.R.R binomial's up factor and down factor and there is no effective program in the different underlying asset model. In chapter three, we try to disperse Ito process and get a new binomial model which has a valid way in choosing up factor and down factor. After that, we use C-M-G theorem to change the measure and it show the relationship between the C.R.R binomial tree and the new one. In the meantime we prove that the dispersed Ito process binomial tree's limit is the B-S formula in the European option. Finally, we give the extension of the way and sight in dispersing Ito process.However, in practical, the error between real trade price and price predicted by the B-S formula is not unacceptable, although it can't be ignored. It's unwise to abandon the B-S formula which has three decades history during which many researches have clarified that it has a good ability in explaining average option pricing. Thus, in chapter four, we take the B-S formula as main factor in option pricing. Meanwhile, we add a new factor to compensate and correct the error, and linear predict the factor's value. Similarly, for American option, we linear predict the error between the calculation values and practical data after get its price by binomial tree based on Ito process.In chapter five, we examine above methods using practical market trading data by using the numerical methods in chapter three to price option, and local linear prediction methods in chapter four to correct it. |
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