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Advanced · Self-paced2026 Edition

Numerical Methods for Finance

Where the maths meets the computer. The numerical-analysis toolbox a working quant uses to actually compute a price or a risk number — floating point, root-finding, interpolation, quadrature, finite differences for PDEs, Monte Carlo with variance reduction, and the LSM algorithm for American options. Ten modules pairing the algorithm with the production caveats.

10

Modules

~9h 15m

Reading time

Advanced

Level

Self-paced

Format

§

Syllabus

  1. 01

    Floating point, conditioning, and stability

    IEEE 754, machine epsilon, catastrophic cancellation. Condition number. The numerical traps that turn correct maths into wrong numbers.

    ~50 minModule 01
    →
  2. 02

    Root-finding — bisection, Newton, secant

    Inverting a bond price to a yield. Newton's method, convergence rates, robust hybrids (Brent), the practical algorithm a yield-to-maturity function actually calls.

    ~55 minModule 02
    →
  3. 03

    Interpolation and yield-curve construction

    Linear, cubic spline, monotone-preserving. Building a discount curve from a noisy set of bond prices. Bootstrapping the zero curve.

    ~55 minModule 03
    →
  4. 04

    Numerical integration

    Trapezoid, Simpson, Gauss-Hermite, Gauss-Legendre. Pricing a European option by integrating the risk-neutral density.

    ~50 minModule 04
    →
  5. 05

    Finite-difference methods for the BS PDE

    Explicit, implicit, Crank-Nicolson schemes. Stability conditions, boundary conditions, pricing American options by PSOR.

    ~65 minModule 05
    →
  6. 06

    Monte Carlo — the workhorse

    Simulating GBM paths. Standard error. Confidence intervals. Why MC is the only option for high-dimensional payoffs.

    ~55 minModule 06
    →
  7. 07

    Variance reduction

    Antithetic variates, control variates, importance sampling, stratification, quasi-Monte Carlo. The 100× speed-ups behind production MC engines.

    ~60 minModule 07
    →
  8. 08

    American options — Longstaff-Schwartz

    The least-squares Monte Carlo algorithm. Regressing continuation values, the optimal exercise boundary, why LSM democratised American option pricing.

    ~60 minModule 08
    →
  9. 09

    Binomial and trinomial trees

    Cox-Ross-Rubinstein. Backward induction. Why trees still earn their keep for path-dependent and early-exercise products.

    ~50 minModule 09
    →
  10. 10

    Numerics in production

    Reproducibility, regression tests, the pre-trade pricing sandbox, what a quant developer actually ships when they 'add a model' to a pricing library.

    ~55 minModule 10
    →

How to use this course

Start with module 01 if the material is new; skip ahead if you have prior exposure. Each module is self-contained but the arc is sequential — the projects in the final module assume the toolkit from modules 1-11. Every module ends with key takeaways and a curated further-reading list with primary sources.