Overview
The Black Scholes equation is a differential equation which specifies the dynamics of a derivatives price as the price of the underlying changes and as time progresses.
{% \frac{\partial V}{\partial t} + \frac{1}{2} \sigma ^2 \frac{\partial^2 V}{\partial S^2} + rS \frac{\partial V}{\partial S} -rV = 0 %}
- {% S %} is the underlying price
- {% V %} is the derivative price
- {% t %} is time
- {% r %} is the interest rate
Topics
- Derivation - shows the steps to derive the Black Scholes equation.
- Equivalence to the Heat Equation - shows that the Black Scholes equation can be transformed into the heat equation