Abstract: Similar to the method of continuum mechanics,the variation of the price of index futures is viewed to be continuous and regular.According to the characteristic of index futures,a basic equation of price of index futures was established.It is a differential equation,its solution shows that the relation between time and price forms a logarithmic circle.If the time is thought of as the probability of its corresponding price,then such a relation is perfectly coincided with the main assumption of the famous formula of option pricing,based on statistical theory,established by Black and Scholes,winner of 1997 Nobel.prize on economy.In that formula,the probability of price of basic assets(they stand for index futures here)is assummed to be a logarithmic normal distribution.This agreement shows that the same result may be obtained by two analytic methods with different bases.However, the result,given by assumption by Black-Scholes,is derived from the solution of the differential equation.