Black Scholes Model Option Pricing

Fischer Black worked with Myron Scholes to develop the Black Scholes Model Options Pricing Model. However, Black began working on his own trying to develop a valuation model for stocks. The model he was working on focused on measuring the variations of the discount rate over time as well as the changes in stock price. After Black developed a calculation for stock warrants Scholes joined his efforts and the result was the Black Scholes Model Option Pricing, which is very accurate.

Inspiration for Black Scholes Model Option Pricing

The Black Scholes Model Option Pricing was not developed without some help from a previous model. In fact, A. James Boness developed a similar model, which was improved upon significantly by Black and Scholes, which resulted in the accurate Black Scholes Model Option Pricing that is used today.

Improvements to Black Scholes Model Option Pricing

The Black Scholes Model Option Pricing improved upon the Boness model by removing assumptions pertaining to the investors risk preferences and proving that the discount factor is the risk-free interest rate. These changes made the model incredibly accurate and are responsible for making this particular model popular.

Black Scholes Model Option Pricing Assumptions

One assumption is that no dividends are paid during the life of the option. This might appear to be a limitation of the model based on the fact that lower call premiums result from higher dividend yields. However, the model can adjust this by taking the stock price and subtracting a future dividend’s discounted value.

Efficient Market Assumption of Black Scholes Model Option Pricing

Another assumption for the Black Scholes Model Option Pricing is that the market or individualized stocks cannot be consistently predicted. Share prices follow a continuous process, which means the market is continuously operating and never stops.

No Commission Assumption for Black Scholes Model Option Pricing

The model can be distorted by including commissions. As a result, the Black Scholes Model Option Pricing assumes no commissions, which results in a more consistent and accurate model.
The risk free rate is used in the Black and Scholes model. There is no actual risk free rate; however it is frequently represented by the discount rate with 30 days until maturity on the US Government Treasury Bills. When interest rates are changing rapidly it is common for the 30 day rates to change as well. As a result, this would go against the model’s assumption that interest rates are known and constant.