Currently, simple instruments of .shares and commodities traded at today’s price are considered ‘vanilla’ trading compared to future derivative products, also known as Options.

These are generally defined as a "contract between two parties in which one party has the right but not the obligation to do something, usually to buy or sell some underlying asset". In 1973, the tandem team of Fischer Black and Myron Scholes had written the first draft of a paper that outlined an analytic model that would determine the fair market value for European type call options on non-payout assets. Basically, the fundamental insight from the Black and Scholes model comes out to be that the call option is always given a price value if the stock is to be traded (Wikipedia, 2005).

Over time, the formula and the model itself have become ingrained in the financial markets of the world and due to their usefulness and applicability. This model itself is one of the basic tenants for any stock trader to understand and apply while dealing with stock options in the modern financial world. Merton and Scholes shared the 1997 Nobel Prize for their study. Unfortunately, Black himself could not be a part of the winning team since he had already expired in 1995 and thus become ineligible for the prize (Wikipedia, 2005).

The Black-Scholes model today is used in everyday pricing of options and futures and almost all formulas for pricing of exotic options such as barriers, compounds, and Asian options take their foundation from the Black-Scholes model. Keeping the aim of this paper in mind, we’ll be mainly looking at simple European and American Call Options.

This supposition is a major drawback of the model as in the real world, most companies pay dividends to their shareholders. To account for this assumption and to make the model more accurate, a common alteration to the model is to subtract the discounted present value of future dividends from the stock price depending on the bylaws and articles of .incorporation of the company.