**Black-Scholes**
One of a wide family of

mathematical models that are used today in

finance to determine the so-called

*fair value * of

options contracts.

An options contract - be it a

call or a

put, of the

American or

European variety - is a very simple example of what is more commonly known as a

*derivative*; that is, a

financial instrument that has no value on its own, instead it

derives its value from another,

*underlying* instrument.

The so-called

*Black-Scholes * model, originally developed in 1973, is intended to allow traders and

investors to calculate the fair value of an options contract. It was considered

earth breaking *(and in fact led to a Nobel Prize)* since this problem

*(the valuation of options)* had been attempted by various parties since the turn of the century.

It wasn't until the

differential equations underlying the problem were recognized to be similar to the well known

*heat transfer* problem from

physics that sufficient progress was made.

In its basic form the Black-Scholes differential equation is able to value American and European options on

non-dividend paying stocks.

During the intervening years since it's introduction, it has been

extended to value other underlying instrument; for example,

stock market indices *(e.g., the Dow Jones Industrials, or the S&P 500)* or various

commodities.