Friday, June 13, 2008

Black-Scholes and Heat Equation

Author: raj
Category: Finance

The Black-Scholes PDE is a “Wick rotated” Schrodinger
equation for a charged particle in an electromagnetic field, where the
risk-free rate plays the role of a gauge connection.

What’s more –

The gauge connection for the Black-Scholes PDE is given by

A = (r+frac{r<sup>2}{2sigma</sup>2}) dt – (frac{r}{sigma^2}) dx” />.</p>
  <p>Inserting the corresponding gauge factor</p>
  <p><img src=PDE results in

partial_t W = -frac{sigma<sup>2}{2} partial_x</sup>2 W” />,</p>
  <p>which is simply the heat equation from physics!</p><br />
</blockquote>

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