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
MediumStochastic CalculusBrownian MotionQuadratic Variation
18 min
02
Itô's Lemma: Derivation and Applications
HardStochastic CalculusItô's LemmaStochastic Differential Equations
22 min
03
Girsanov's Theorem and Equivalent Martingale Measures
HardStochastic CalculusGirsanov's TheoremRisk-Neutral PricingChange of Measure
25 min
04
Feynman-Kac and the Connection to PDEs
HardStochastic CalculusFeynman-KacPDEsBlack-Scholes
20 min