The Black-Scholes-Merton (BSM) formula holds the same weight in financial science as E = mc² does in physics. The formula revolutionized the development of the options market. Thanks to it, the authors received the Nobel Prize, and savvy investors earned substantial profits.

Substantively, the BSM is a transformation of the binomial method from a discrete distribution of outcomes to a continuous distribution. In the binomial method, increasing the number of steps makes the model more realistic but also more complex. In the BSM, we increase the number of steps to infinity and calculate using a single (not very complicated) formula.

The formula allows for accurate valuation of a wide range of options, and its precision is very high. However, in some cases, we still use the binomial model because the BSM does not account for the possibility of early exercise of the option. Additionally, sometimes it is necessary to consider the dividend portion, which the stock owner may take before the option is exercised.

You can find an options price calculator at this link:
Black-Scholes Calculator

Excel Model:

Black-Scholes-Merton Model – Excel

Adapted from:

Principles of Corporate Finance – by F. Allen, R. A. Brealey, & S. Myers