# Feynman-Kac Theorem

*Quant & Pricing — Finicade finance glossary*

The Feynman-Kac theorem links PDEs to expectations of stochastic processes: a PDE solution equals the expected discounted payoff of a diffusion.

The Feynman-Kac theorem links partial differential equations to expectations of stochastic processes: the solution of a PDE equals the expected discounted payoff of a diffusion. This is the bridge that makes both pricing methods legitimate — it's why solving the Black-Scholes PDE and running a Monte Carlo simulation must give the same answer, and why a desk can choose whichever is cheaper to compute.

**Also known as:** Feynman Kac, Feynman-Kac formula

**Related terms:** [Black–Scholes PDE](https://finicade.com/glossary/black-scholes-pde), [Risk-Neutral Pricing](https://finicade.com/glossary/risk-neutral-pricing), [Monte Carlo Simulation](https://finicade.com/glossary/monte-carlo), [Martingale](https://finicade.com/glossary/martingale), [Stochastic Differential Equation](https://finicade.com/glossary/stochastic-differential-equation)

Source: https://finicade.com/glossary/feynman-kac-theorem