Many investors in options trading keep on searching for some good relevant guide to Black-Scholes Formula also called option pricing formula or derivatives pricing theory. Here we have tried to provide a complete useful guide on the same.

Bachelier, the inventor of Brownian motion, also invented the Black-Scholes Formula. This is considered as a risk-free approach that is also in some way responsible for invention of other alternatives of valuation methods including the Monte Carlo method and model future asset values.

With the help of the Black-Scholes theory, investors can deal with all financial assets as having anticipated returns that are equivalent to the risk neutral rate. But it is a fact that no trade can be risk neutral. Thus, the risk neutral technique is not a real or true reflection of the real world. But if dealt carefully and smartly, this theory can calculate correct option prices.

Initially, Cox and Ross mentioned the risk neutral valuation method. It was released in 1976. After three years, when they realized how important this technique is, they grouped with Mark Rubinstein and started publishing a paper that uses risk neutral valuation to develop the technique of binomial trees.

The Black Scholes theory is also called the differential equations approach. The reason being that the theory uses partial differential equations.

The Black Scholes Formula helps the options traders to compare the current option price in the exchange with the theoretical value taken with the help of the Black-Scholes formula so as to analyze whether a particular option contract is over or under valued, eventually helping the investors to take decisions regarding various options. Primarily, this formula was created for the pricing and equivocation of European Call and Put options. The difference in the European and American pricing is that the European options pricing do not contemplate the possibility of early exercising. Thus, American options have higher rate as compared to European options and the traditional Black-Scholes Model does not consider this extra rate in the calculations.

Before the invention of the Black-Scholes formula, no standard options pricing method was there to calculate the options value. Thus, no one was able to put a reasonable price for options. But the invention of the Black-Scholes formula converted the dream of investors to mathematically calculate the options value into reality. This turned the options market into a profitable business opportunity for investors.

Black-Scholes Model Assumptions

A lot of assumptions are there at the core of the Black-Scholes model of calculating options pricing. The six basic assumptions of the Black-Scholes Model include the following:

1. No dividend is paid on stocks

2. The use of options can only be before expiration

3. Market is unpredictable. Therefore, walk arbitrarily

4. Transactions don’t involve commissions

5. Interest rates are stable

6. The returns on stocks are distributed normally. Hence, instability is invariable over time. Always keep in mind that the values calculated from the Black-Scholes Model are just a guide for comparison and not an exact indication of the nature of a stock option values.