What is the Black Scholes Model?

Black-Scholes model, also known as the Black-Scholes-Merton model, is a mathematical model used for pricing financial derivatives, most commonly options contracts. It was developed by Fischer Black, Myron Scholes, and Robert Merton in the early 1970s and has become a widely used tool in finance.

Black-Scholes formula calculates the theoretical price of European-style options, which can only be exercised at expiration. It provides a means to determine the fair value of an option at a given point in time based on factors such as the current stock price, the option’s strike price, time to expiration, risk-free interest rate, and volatility of the underlying asset.

Assumptions of Black-Scholes Model

The model makes several key assumptions:

• No Dividends: The underlying asset does not pay any dividends during the option’s life.
• Efficient Markets: Market movements are random and follow a geometric Brownian motion with constant drift and volatility.
• Risk-Free Rate: The risk-free interest rate is constant and known.
• Constant Volatility: The volatility of the underlying asset’s returns is constant and known.
• Log-Normally Distributed Returns: The returns on the underlying asset are normally distributed.

The potential cost of European-style options is determined using a mathematical model called the Black-Scholes Model. With Robert Merton’s help, economists Fischer Black and Myron Scholes created it in 1973, revolutionizing options pricing and laying the groundwork for contemporary quantitative finance. The concept is widely used in financial markets to value options on stocks, commodities, currencies, and other types of assets.

In this article, we will discuss the formula that helps us calculate the prices of options using the Black-Scholes Model and also see some solved examples for it.