The Research of Black-Scholes’ Formula for Pricing European Options

The volatility is the key parameter in option pricing ,but Black-Scholes' formula makes no sense when the volatility is zero. This paper explains the financial means, and presents the pricing model and formula for European options by use of arbitrage-free principle when σ=0.Used hedging technique and Ito formula, the partial differential equation of option price is deduced. This paper proves that the Black-Scholes' formula also holds in the sense of limit when σ=0, and estimates the option price when the volatility is very small.