金融衍生产品的力学方法分析(Ⅱ)——期权市场价格基本方程

Analysis of Financial Derivatives by Mechanical Method(Ⅱ)——Basic Equation of Market Price of Option

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 :h v0 (t) =m1v- 10 (t) -n1v0 (t) +F ,式中h ,m1,n1,F为常数· 主要假设有 :期权市场价格v0 (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 ,为研究期货价vf对期权市价v0 (t)

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).