金融衍生产品的力学方法分析（Ⅱ）—期权市场价格基本方程

类似固体力学建立基本方程方法,根据期权特点,采用一些假设,建立期权市场价格基本方程：hv0(t)=m1vo^-1(t)-n1vo(t) F,式中h,m1,n1,F为常数,主要假设有：期权市场价格vo(t)的升降由市场供求决定;影响v0(t)的因素如行使价,期限,波幅等用正或反比关系;买和卖用相反规律。文中给出不同情况下基本方程的解,并和期货市场价基本方程的解vf(t)相比较,以及用隐函数存在定理证明vf与v0(t)存在一一对应关系,为研究期货vf对期权价vo(t)的影响提供理论依据。

Analysis of Financial Derivatives by Mechanical Method (

The basic equation of market price of option is formulated by taking assumptions based on the characteristics of option and similar method for formulating basic equations in solid mechanics: h 0(t)=m 1v -1 0(t)-n 1v 0(t) F, where h,m 1,n 1,F assumptions are: the ups and downs of market price v 0(t) are determined by supply and demand of the market; the factors, such as the strike price, tenor, volatility, etc. that affect onv 0(t) are demonstrated by using proportion or inverse proportion relation; opposite rules are used for purchasing and selling respectively. The solutions of the basic equation under various conditions are found and are compared with the solution v f(t) of the basic equation of market price of futures. Furthermore the one_one correspondence between v f and v 0(t) is proved by implicit function theorem, which forms the theoretic base for study of v affecting the market price of option v 0(t).