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.