Black Scholes and Heat Diffusion

It is something of an interest that the Black Scholes equation can be converted into a diffusion equation. At first glance this seems very strange and fantastic, however, the more I look into it does not seem that special.

Both diffusion and Black Scholes have the basic assumption of Brownian motion. The difference is only a matter of boundary conditions. This is a point of interest in that it demonstrates the abstract nature of mathematics. The equation in themselves abstract from the qualitative matters of what the quantities are “about.” Some variable may equally represent density as much as stock returns.

In fact this should be as no surprise, given that the underlying assumption is the same process then we should see the same evolution of the system.

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