The Black Scholes Model and Use in Modern Financial Theory

The Black Scholes Model, which is also known as the Black-Scholes-Merton Model, is considered by many to be one of the most important concepts used in current financial theory. Developed by Fisher Black, Myron Scholes and Robert Merton in 1973, it is used to determine option pricing. Option pricing techniques are some of the most mathematically complex financial calculations. They are used to calculate the value of stock options accurately.

What is an Option?

Options have been used since the time of Ancient Romans and Greeks to determine the value of outgoing cargo ships. When this term is used in finance, it defines a contract between two parties. One party in the transaction must have the right to buy or sell an asset, but not the obligation to. This has a financial value that is defined as an option. These options are purchased by option holders, making them an asset. They are paid by an up-front fee called a premium. They can also be associated with bonds. When they are used with bonds, they are paid in installments over the life of the bond.

The History of the Black and Scholes Model

The Black Scholes Model was developed when Fisher Black began looking for a way to create a valuation model for stock warrants. This involved building a calculation that measured how the discount rate of a warrant varies based on a previous model by A. James Boness. The variant worked with time and stock price. This calculation resulted into a heat transfer equation. Myron Scholes joined Black and together they built an option pricing model that had a proof with an absence of assumptions on an investor's risk preferences.

The Assumption of Dividends

There are a few assumptions necessary for the Black Scholes Model to work. First is that the stock doesn't pay any dividends during the life of the option. Because many companies pay share holders by dividends, this might seem to be a serious limitation to the model. However, the model adjusts for this situation. This is done by taking the future stock dividend price and subtracting the discounted value.

Working with an Efficient Market Assumption

Another assumption of the Black Scholes Model is that the market is efficient. People cannot consistently predict which direction a stock or the stock market is heading. Share prices fluctuate through a continuous process. However, this process can be observed over time and a calculation can be determined based on the preceding observation. By looking at the continuous process a pattern can be discerned.

Since its inception, many other mathematical scholars have expanded upon the basic calculations of this model. Robert Merton and Jonathan Ingerson provided particularly noteworthy additions. Now this valuation model for stock options is one of the most commonly used and widely accepted methods of calculating stock options. While a few assumptions are necessary in order for this method to work, it can be adjusted for other factors as well to provide a highly accurate representation of the option market for investors.