Stochastic Differential Equation

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.