Stochastic Calculus: Itô's Formula

This lecture covers Stochastic Calculus, focusing on Itô's Formula and Stochastic Differential Equations. It explains the core formula of stochastic calculus, the sketch of proof for Itô's Formula, the stochastic exponential, and the covariation revisited. The lecture also delves into the uniqueness lemma, martingale properties, and the geometric Brownian motion. Furthermore, it discusses stochastic differential equations, the solution methods, and the Black-Scholes model for option pricing. Linear SDEs, Ornstein-Uhlenbeck processes, mean-reversion, the Gauss property, and stationarity are also explored.