Fixed Income OpenCourseWare

Fixed Income OpenCourseWare

Interest Rate Models

A rigorous, publicly available course on the mathematical structure of interest-rate modeling. Built primarily around Brigo & Mercurio’s Interest Rate Models: Theory and Practice and designed for serious students, quantitative analysts, and fixed-income practitioners.

This project follows the spirit of MIT OpenCourseWare — lecture notes, problem sets, solutions, and videos are released in weekly batches and made freely available. Theory and computational practice are developed in parallel.

Primary text: Damiano Brigo & Fabio Mercurio, Interest Rate Models: Theory and Practice, Springer Finance, 2nd ed. (ISBN 978-3-540-22149-4). Available through Springer and most university libraries.

Latest Batch

Lecture 09Brigo & Mercurio Sections 3.4–3.5
CIR Extensions & BK

Concluding classical one-factor short-rate models with CIR extensions and the Black–Karasinski model: positivity constraints, time-dependent parameters, lognormal short-rate dynamics, exact yield-curve fitting, conditional moments, trinomial tree calibration, and the tradeoffs between realism and tractability.

NotesLecture NotesProblem SetProblem SetSolutionsSolutions

Course Materials

Lecture Notes

Annotated notes for each lecture

Problem Sets

Weekly exercises and derivations

Solutions

Full worked solutions

Lectures

Video lectures with chapter references

Course Arc

Part I

Foundations

Discounting, zero-coupon bonds, spot and forward rates

Part II

Short-Rate Models

Vasicek, CIR, Hull-White, and related affine models

Part III

Heath-Jarrow-Morton Framework

Forward-rate dynamics and the HJM drift condition

Part IV

Market Models

LIBOR and swap market models, calibration

Part V

Credit and Extensions

Credit derivatives and further topics