Overview — Numerical Methods and Calibration

Market prices quote bond yields and option volatilities implicitly: recovering them is root-finding. Expectations and Greek bumps are integrals and derivatives that rarely admit closed forms: recovering them is quadrature and finite differences. Fitting a model to a strip of quotes is an inverse problem that inherits every ill-conditioning lesson from earlier topics. This topic closes the programme with the numerical toolkit and an explicit calibration reading, then a seeded Python lab that wires solve / Cholesky / Newton together.

By the end of this note you should be able to:

• run bisection and Newton for a bond yield or similar monotone root;
• approximate an integral (trapezoid) and a Greek by finite differences, with truncation vs roundoff trade-offs;
• formulate calibration as a (possibly regularised) least-squares inverse problem and diagnose non-uniqueness;
• implement a small lab checkpoint that reproduces a known numerical value.

1. Contents
2. The big picture