This post discusses three transformations that convert the Black-Scholes Equation to the Diffusion Equation.
Black-Scholes Equation:
\frac{\partial V}{\partial t} + \frac{1}{2}\sigma^2S^2\frac{\partial^2 V}{\partial S^2} + rs\frac{\partial V}{\partial S} - rV = 0Diffusion Equation:
\frac{\partial u}{\partial \tau} - \frac{\sigma^2}{2}\frac{\partial^2 u}{\partial x^2} = 0Note: In the images below, tau (τ) is written as l.
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