Stochastic Calculus

Itô's Lemma for Dummies

Why the chain rule breaks for randomness: Taylor to second order, because (dW)² = dt.

What to remember

  • Itô = Taylor to second order + (dW)² = dt.
  • d(W²) = 2W dW + dt; W² − t is a martingale.
  • d ln S = (μ − σ²/2) dt + σ dW: the source of volatility drag.
Read the lessonItô's Lemma, with a checkpoint at the end.