Applied Mathematics and Mechanics

, Volume 22, Issue 9, pp 1004–1011

# Analysis of financial derivatives by mechanical method (II)—Basic equation of market price of option

• Yun Tian-quan
Article

## Abstract

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: 0 (t)=m 1υ0 (t)+F, where h, m1, n1, F are constants. The main assumptions are: the ups and downs of market price v0(t) are determined by supply and demand of the market; the factors, such as the strike price, tenor, volatility, etc. that affect on v0(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 vf(t) of the basic equation of market price of futures. Furthermore the one-one correspondence between vf and v0(t) is proved by implicit function theorem, which forms the theoretic base for study of vf affecting on the market price of option v0(t).

### Key words

option Black-Scholes formula differential equation

F224.9 F830.9

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