Ito's Lemma: The Cornerstone of Stochastic Calculus

Students frequently forget the second-order Ito correction term

\frac{1}{2} \sigma^2 f''

. They incorrectly apply the standard Chain Rule from deterministic calculus, ignoring the non-zero quadratic variation

d\langle W, W \rangle_t = dt

inherent to stochastic integrals.

Institutional Reference: Advanced Stochastic Processes