NUM

Numerical methods

Root finding, interpolation and stability — with implied volatility as the worked case.

  1. 1

    Root finding

    Bisection, Newton–Raphson, secant and Brent; solving for implied volatility.

  2. 2

    Interpolation

    Splines, Runge’s phenomenon, and interpolating a curve or surface.

  3. 3

    Numerical integration

    Trapezoid, Simpson, Gauss–Legendre and adaptive quadrature.

  4. 4

    Linear algebra numerics

    LU, QR and Cholesky in practice, conditioning, and never inverting a matrix.

  5. 5

    ODE and PDE solvers

    Euler, Runge–Kutta, finite differences and stability conditions.

  6. 6

    Floating point

    IEEE 754, catastrophic cancellation, and why prices are stored as integers.