Black and Scholes Option Price Model


Option Price Model estimates fair value


The 1997 Nobel Prize in Economics was awarded to Robert C. Merton and Myron S. Scholes for their work, along with Fischer Black, in developing the Fischer-Black options pricing model. (Black, who died in 1995, would undoubtedly have shared in the prize had he still been alive.)

Black and Scholes derived a stochastic partial differential equation governing the price of an asset on which an option is based, and then solved it to obtain their formula for the price of the option.

How does it work?

They showed that the fair price today of any financial instrument is determined by time, uncertainty, and the risk-free rate of return.

The Black and Scholes Option Pricing Model is a valuation model for stock options. This work involved calculating a derivative to measure how the discount rate of an option varies with time and stock price.

The first part of the model derives the expected benefit from acquiring a stock outright. This is found by multiplying stock price by the change in the call premium with respect to a change in the underlying stock price.

The second part of the model, gives the present value of paying the exercise price on the expiration day.

The fair market value of the call option is then calculated by taking the difference between these two parts.

Trading Signals

The Black-Scholes Formula is a way to determine how much an option is worth at any given time.


Australia and New Zealand Banking Group (ANZ) on the 14/11/2003 was trading at $16.32. The $18.50 Call Option expiring on 18 December 2003 was trading at $0.045, however the Black and Scholes Option Price Model had fair value at $0.036

Note: To use this go to Derivatives > Options Black Scholes Model

Note: To attain implied volatility go to the Option in the Options market and select the Volatility indicator, which will give you a historical and implied volatility.