The BS Formula
Pricing of an option requires building a portfolio in shares and a loan in such a manner that its payoffs are equivalent to the payoffs from the option. We also know that there are five factors which influence the value of option: current share price, exercise price, risk free rate of interest, time to expiration on the option and price volatility of share (measured in terms of variance),
The BS model/formula makes, inter-alia, use of the above propositions and factors to determine the value of call option. The additional/redeeming feature of the BS model is that it takes into account the changes in the price of shares at shorter and shorter intervals, with each interval showing two possible changes in share; eventually a situation is reached in which price of the share is changing continuously and generating a continuum of possible share prices, and, therefore, to replicate option investors must continuously adjust their holdings in the shares. Though in practice, it is not feasible, the BS formulas (explained below) performs remarkably well in the real world where shares trade only intermittently and prices jump from one level to another. In fact, it has become the standard model for valuing options and is used by dealers on the options exchange.