Phase 9
Stochastic Calculus
Phase 9 of the Quant Academy curriculum.
9.1Full Lesson
The Itô Integral
Why ordinary calculus fails for Brownian paths, and how to build an integral against them anyway.
9.2Full Lesson
Itô's Lemma
The chain rule of stochastic calculus, driven by the rule (dW)²=dt.
9.3Full Lesson
Stochastic Differential Equations and Geometric Brownian Motion
Solving dS = μS dt + σS dW and why stock models are lognormal.
9.4Full Lesson
Girsanov's Theorem and Change of Measure
Rewriting the drift of a Brownian motion by re-weighting probabilities.
9.5Full Lesson
The Feynman–Kac Theorem and the PDE Connection
How a conditional expectation solves a partial differential equation, and vice versa.
9.6Full Lesson
Risk-Neutral Pricing: Foundations
Why a derivative's price is a discounted expectation under a special probability measure.