# Stochastic Differential Equation

*Quant & Pricing — Finicade finance glossary*

A stochastic differential equation describes how a quantity evolves with both a predictable drift and a random shock, written as dX = drift·dt + volatility·dW. It's the native language of asset pricing: geometric Brownian motion, mean-reverting rates and stochastic volatility are all SDEs. Because the random term has infinite variation, ordinary calculus fails and Itô's lemma takes its place.

**Also known as:** SDE, stochastic differential equations

**Related terms:** [Brownian Motion](https://finicade.com/glossary/brownian-motion), [Itô's Lemma](https://finicade.com/glossary/itos-lemma), [Geometric Brownian Motion](https://finicade.com/glossary/gbm-model), [Stochastic Process](https://finicade.com/glossary/stochastic-process), [Monte Carlo Simulation](https://finicade.com/glossary/monte-carlo)

Source: https://finicade.com/glossary/stochastic-differential-equation