Quantitative Finance
Black–Scholes Equation
The PDE for pricing options.
∂V/∂t + ½σ²S²∂²V/∂S² + rS∂V/∂S − rV = 0
What it means
The Black–Scholes equation prices derivatives under geometric Brownian motion, a parabolic PDE solved across asset price and time.
Variables
| V | option value |
| S | asset price |
| σ | volatility |
| r | risk-free rate |
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