The Black-Scholes model, which is widely used to price financial options, assumes that volatility is constant as a function of strike price. However when market option prices are used to infer the volatility that is implied by those prices, it often exhibits a marked dependence on strike price...

The publication of the Black-Scholes formula in 1973 appeared for the first time to put the pricing of financial options onto a rational and objective basis. While earlier option-pricing models relied on a subjective estimate of the stock’s uncertain future growth rate, the Black-Scholes model...