Black-Scholes – SMART Trading Strategies https://smarttradingstrategies.com Statistical and Mathematical Approach to Retail Trading Fri, 10 Sep 2021 06:16:50 +0000 en-US hourly 1 https://smarttradingstrategies.com/wp-content/uploads/2021/08/logo-150x150.png Black-Scholes – SMART Trading Strategies https://smarttradingstrategies.com 32 32 Converting the Black-Scholes Equation to the Diffusion Equation https://smarttradingstrategies.com/converting-the-black-scholes-equation-to-the-diffusion-equation/ https://smarttradingstrategies.com/converting-the-black-scholes-equation-to-the-diffusion-equation/#respond Fri, 10 Sep 2021 04:59:30 +0000 https://smarttradingstrategies.com/?p=455 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 = 0

Diffusion Equation:

\frac{\partial u}{\partial \tau} - \frac{\sigma^2}{2}\frac{\partial^2 u}{\partial x^2} = 0

Note: In the images below, tau (τ) is written as l.

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