Stochastic Calculus & SDEs

Itô calculus, Girsanov theorem, change of measure, and Feynman-Kac as pricing infrastructure — not as abstract mathematics.

4 modules~85 min total

Prerequisites

Measure-theoretic probability (σ-algebras, filtrations, conditional expectation)Real analysis (continuity, convergence)Basic ODEs

Modules

01

Brownian Motion and Quadratic Variation

Medium
Stochastic CalculusBrownian MotionQuadratic Variation
02

Itô's Lemma: Derivation and Applications

Hard
Stochastic CalculusItô's LemmaStochastic Differential Equations
03

Girsanov's Theorem and Equivalent Martingale Measures

Hard
Stochastic CalculusGirsanov's TheoremRisk-Neutral PricingChange of Measure
04

Feynman-Kac and the Connection to PDEs

Hard
Stochastic CalculusFeynman-KacPDEsBlack-Scholes