# Black–Scholes PDE

*Quant & Pricing — Finicade finance glossary*

The partial differential equation every option price must satisfy, derived by hedging away all the risk. Solve it with a call's payoff as the boundary and out pops the Black–Scholes formula.

**Also known as:** the bs pde, black scholes pde

**Related terms:** [Black–Scholes Model](https://finicade.com/glossary/black-scholes), [Delta Hedging](https://finicade.com/glossary/delta-hedging), [Itô's Lemma](https://finicade.com/glossary/itos-lemma)

**Taught in:** Quant Quest — The Black–Scholes PDE, Derived

Source: https://finicade.com/glossary/black-scholes-pde