Abstract: A detailed investigation into the option pricing process is presented in this paper from the angle of mathematical deduction. Every deductive reasoning procedure in both stochastic partial differential equation approach and probabilistic approach are described. The paper also reveals generally that how the mathematical techniques are applied to modern financial theories, especially to the valuation of derivatives. The author take European call option as the example, dissecting the conventional assumptions in Black-Scholes formulation.

Key words: option pricing, Black-Scholes formulation, mathematical deduction