The Pricing Of Options On The Binomial Model With Proposed Long-range Dependence

China has gone into the era of options along with the successful listed abroad of Shanghai 50 ETF. As a kind of financial derivatives, option hedgers, speculators and arbitrageurs will achieve their own trading purposes through options trading. The launching of options to some extent can increase trading varieties, enrich financial products, improve trading ability and stabilize the stock market. During the transaction, the price of the option is crucial to traders, thus how to determine the price of option gives an important issue to industry and academia. Since 1973, the publication of the paper of Fisher Black and Myron Scholes option theory has been established. Many finance researchers have improved the option theory.This paper studies fully the long correlation of binary tree model of option pricing from theory and practice. During reading the literature of option-pricing, there are main models and methods as follows:(1) the traditional option-pricing method,(2) the binary tree, trigeminal tree option pricing method,(3) the B-S model pricing method,(4) the Monte-Carlo method,(5) the interval method and so on. But these methods have some disadvantages. In order to make for deficiency, this paper establishes a new model which is based on the classical binary tree with the length of correlation. In the process of research, it has precisely simulated the underlying asset price changes by using factorial carry, System, permutation, combination, martingale property, thus it can apply to option-pricing.During setting price, according to the actual movement process of underling asset price, the rising factor, decline factor and it corresponding probability of pricing model can be calculated. We can consider the problem by two assumptions: for one, we can calculate the risk-neutral probability by assuming that the rising factor and decline factor are the inverse of each other; for another, we can calculate rising factor and decline factor when the risk-neural probability is 0.5. Then we can use these two different assumptions to the same underlying assets. Next, with risk neutral principle, we can obtain corresponding derivatives(option) price by discounting the risk-free interest rate of maturity date derivatives. Finally, comparing with other models, we judge the pros and cons of this model through the results of empirical analysis, and the empirical sample verifies the effectiveness of the new model. This model provide an important theoretical a practical significance to all kinds of derivatives pricing.