From the Modern Portfolio Theory of Markowitz to the capital equilibrium pricing theory of Sharpe、 Lintner and Mossin, and the following Option Pricing Theory of Black- Scholes, and the Arbitrage Pricing Theory of Ross, all is under EMH or closely-related with it.
Whether we can not use capital pricing model, then avoid joint hypothesis in the empirical process, arbitrage the kernel of finance theory becomes the breach of the problem.
In the first place the paper educes preparation theorem by the tool of martingale: no arbitrage equilibrium is the necessary condition of capital market efficiency.
Then introducing the concept of statistical arbitrage that put forward newly, it is the extended form of standard arbitrage. By comparing standard arbitrage and statistical arbitrage, educes that statistical arbitrage is standard arbitrage under the condition that expected return is positive;
We obtain a Black-Scholes formula for the arbitrage-free pricing of European Call options with constant coefficients when the underlying stock generates dividends.
The arbitrage free pricing of the option is determined via a series of partial differential equations, which is derived at the view point of backward stochastic differential equation (BSDE).