Black-Scholes-Merton Model

What is Black-Scholes-Merton Model?

Black-Scholes was the first widely used option pricing model, commonly known as Black-Scholes-Merton (BSM). The price of a European-style call option is calculated using the premise that assets such as stock shares or futures contracts will have a lognormal distribution of values following a random walk with constant drift and volatility and other essential characteristics.

The Black-Scholes-Merton model assumes that the return from a non-dividend-paying stock is normally distributed over a short time. If μ is the mean return and is the volatility, then the return in time $ \Delta $ t is assumed to be normal with mean μ $ \Delta $ t and standard deviation $ \sigma \sqrt{t} $ . In theory, we only assume this is true in the limit as $ \Delta $ tends to zero. In practice, it is approximately true for a small $ \Delta $ .

Why is BSM Model important?

This sums up the significance of the black-Scholes model. The fundamental relevance of this model, which is used to establish fair pricing of options, is that it assists an investor in hedging the financial instrument while ensuring minimal risk.