Numerical Methods

Monte Carlo with variance reduction, finite difference schemes with convergence analysis, PSOR for American options, and Carr-Madan FFT pricing.

4 modules~92 min total

Prerequisites

Linear algebraAnalysis (convergence, Taylor expansion)Basic C++ or Python

Modules

01

Monte Carlo: Antithetic Variates, Control Variates, Quasi-MC

Medium
Numerical MethodsMonte CarloVariance ReductionQuasi-Monte Carlo
02

Finite Difference Schemes and Convergence Analysis

Hard
Numerical MethodsFinite DifferencesBlack-Scholes PDEConvergence Analysis
03

PSOR for American Options

Hard
Numerical MethodsAmerican OptionsPSORLinear ComplementarityFree Boundary
04

FFT and Carr-Madan Pricing

Hard
Numerical MethodsFFTCharacteristic FunctionsCarr-MadanFourier Pricing