Binomial Tree Pricing Model Based On Interval Numbers

Since Cox,Ross,Rubinstein proposed the binomial tree model in 1979, due to its concise derivation process,the CRR model has been widely used in the option pricing theory,and by choosing certain parameters the CRR model can converge to the famous Black-Scholes formula for European call option.But the supposition in CRR that the rasing and decreasing range of the stock price are constants does not fit with the real situation of financial market,where exist a variety of uncertainty.In this paper,by introducing some uncertainty tools,we present the rasing and decreasing rang of the stock price in CRR model by interval numbers to fit with the real situation in financial market.The second part of the paper briefly introduces the basic knowledge of the interval numbers,the famous Black-Scholes formula of European call option and the traditional binomial tree pricing model;The third part of the paper establishes the binomial tree pricing model of European call option which bases on interval number,deduces the European call option price range in the multi-period model and the relationship between closed interval and price range is given; deduces the kind of Black-Scholes formula in the interval number cases.The innovation of this article is an extension of the traditional binomial tree pricing model, the interval number of binomial tree pricing model of European call option is obtained.Moreover,the pricing formulas for interval number binomial tree model is got on the basis of the risk neutral probability pricing theory and the scope of this formula is obtained.Finally,the interval number kind of Black-Scholes formula is obtained on the basis of the interval number binomial tree model.