Phase 13
Monte Carlo Methods
Phase 13 of the Quant Academy curriculum.
13.1Full Lesson
Random-Number Generation and Sampling
From a stream of uniforms to any distribution: inverse transform, acceptance–rejection, and Box–Muller.
13.2Full Lesson
Monte Carlo Estimation and Error Analysis
Unbiasedness, the \(1/\sqrt{N}\) standard error, and honest confidence intervals.
13.3Full Lesson
Variance Reduction: Antithetic, Control Variates, Stratification, Importance Sampling
Same accuracy, far fewer paths - shrink \(\sigma\) instead of paying the \(1/\sqrt N\) tax.
13.4Full Lesson
Simulating Sample Paths and Discretization (Euler–Maruyama)
Turning an SDE into a computable path, and the difference between strong and weak accuracy.
13.5Full Lesson
Monte Carlo Option Pricing, Greeks, and Quasi-Monte Carlo
Discounted risk-neutral expectations, sensitivities by pathwise and likelihood-ratio methods, and low-discrepancy sequen