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Black-Scholes Formula

Introduction to the options history

Nowadays lots of investors who trade on stocks every day, have absolutely no idea about the stock option history. Where did it all start? How did it develop? Who was the founder? etc. If you are one of these people, then this short history of stock options is for you read.

2 Famous Mathematicians

In the history of options trading, there were 2 very significant mathematicians who contributed a lot to the options trading, first in the US and later their formula was used by the whole world.

To start with, Fischer Black and Myron Scholes are two mathematicians who wrote an article devoted to the calculating the premium of the option. In simple words, they gave a formula that got a name Black-Scholes based on physics and finances with the help of which a price for options could be calculated.

Because at that time, options trading started developing rapidly thanks to Brokers as well as Dealers Association. Both parties were trying to match option-buyers with sellers. Despite all this, there were problems connected with absence of standardized prices. Each contract between the seller and buyer had to have its price. So, Black-Scholes formula became a real help for this type of business.

Moreover, having done that, they won a Nobel Prize in Economics for this amazing contribution that keeps working even nowadays.

Here are the factors that affect the premium according to the Black-Scholes formula (the main distinction between the premium and the strike price, is that strike price is always fixed whereas the premium varies from high to low on a day-to-day basis):

  1. expiration date;
  2. strike price;
  3. underlying stock price;
  4. interest rates;
  5. divided status;
  6. implied volatility;

Of course, the Black-Sholes formula isn’t the only one to calculate an option’s theoretical price. For example, options that have American style are computed with the help of bi-nomial model.

The stock direction is always unpredictable yet these formulas do really help to make the right prediction. Also traders have a chance to adjust inputs manually to demonstrate the movement of the stock or implied volatility (fluctuation) changes etc.

Despite all this, no matter how perfect a formula could seem, the market will always determine the actual premiums. Therefore, it sometimes happens that the price “behavior” is extremely unpredictable and inexplicable.

In order to avoid such unpredictable situations, some investors use pricing models to “foresee” an option’s premium in the nearest future.