Black-Scholes Equation

            In the early 1970s, Fischer Black, Myron Scholes, and Robert Merton made a major mathematical breakthrough in the pricing of stock options by developing what has been know as the Black-Scholes model.  This model has an enormous influence on the way trader price and hedge options.  It has also affected the growth and success of financial engineering.  Because of the success of the model Myron Scholes and Robert Merton were awarded the Nobel Prize for economics in 1997.  Fisher Black died in 1995, this is why he did not receive the Nobel Prize also.

            Black-Scholes model can be used for multiple purposes in finance but, we are only going to cover the model for valuing a European call and put options on a non-dividend paying stock.  The reason for covering European options is they expire on particular dates which is when they are traded, making calculations much easier.  Volatility can either be estimated from historical data or implied from option prices through the use of the model.