Black-Scholes-Merton model

In finance, the Black-Scholes-Merton model is a model for a financial market according to a set of parameters in the market (risk-free rate, option expiration, etc). It’s given by the partial differential equation:

$$\frac{\partial V}{\partial t}+\frac{1}{2}{\sigma }^2{S}^2\frac{{\partial }^{2}V}{\partial S^2}+rS\frac{\partial V}{\partial S}-rV=0$$

https://www.youtube.com/watch?v=A5w-dEgIU1M