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

• Tian-quan Yun
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: hv0(t) = m1v0−1(t) − n1v0(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 v f (t) of the basic equation of market price of futures. Furthermore the one-one correspondence between v f and v0(t) is proved by implicit function theorem, which forms the theoretic base for study of v f affecting on the market price of option v0(t).

option Black-Scholes formula differential equation

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