Analysis of Financial Derivatives by Mechanical Method (Ⅰ)——Basic Equation of Price of Index Futures
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摘要: 类似连续介质力学方法,将期指价格变化看成是连续、有规律可寻的。根据期指特点,建立期指价格变化的基本方程。这是一个微分方程,其解显示时间与价格呈对数圆形关系。若将时间理解为相应价格的概率,则这一关系与基于统计理论分析的、著名的诺贝尔经济学奖(1997)获得者的期权定价Black-Scholes公式中主要假设——基础资产(在此为期指)价格呈对数正态分布——完全一致。表明了依据完全不同的两种分析方法,也会得到相同的结果。只是Black-Scholes是用假设给出,而作者则从微分方程的解推出。
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关键词:
- 金融衍生产品 /
- 期货 /
- 股票指数期货(期指) /
- Black-Sholes模型 /
- 微分方程
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. -
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