NMAK22016U Term Structure Models

Volume 2024/2025

MSc Programme in Actuarial Mathematics

MSc Programme in Mathematics-Economics


This course gives the student an in depth overview of dynamic arbitrage free models of the term structure of interest rates in continuous time. The course will focus both on theoretical aspects as well as the practical implementation of the models.


Topics will include 

  • Pricing and risk managing interest rate derivatives i.e. swaps, futures, caps, swaptions etc. 
  • Affine Processes and Affine Term Structure Models.
  • The Heath-Jarrow-Morton framework
  • Multicurve Models
  • LIBOR Market Models
  • An overview of market and benchmark rates such as xIBOR, RFR and other money market rates


Selected topics (may change from year to year)

  • Estimation of term structure models using the Kalman filter 
  • xVA 
  • Credit, liquidity and roll-over-risk 
  • Jumps in interest rates 
  • LIBOR in transition
  • Commodity Derivatives
  • Pricing Kernel Models
  • Mortgage-Backed Securities
Learning Outcome

Knowledge of

  • The mathematical details of selected arbitrage free models of interest rates
  • Market structure and institutional details



  • Apply change-of-numeraire techniques for pricing interest rate derivatives 
  • Ability to implement pricing and risk management models in a high-level programming language e.g. Matlab, R or Python.
  • Applying Fourier methods, Monte-Carlo methods and solution of ordinary differential equations, with a view towards solving term structure models. 



  • Ability to read and understand the latest litterature in the field of mathematical term structure modelling
  • Assessing the strengths and weaknesses of mathematical financial model

Selected lecture notes and articles. See Absalon for a list of course literature

Knowledge of continuous time finance at the level of Finkont or Mathematical Finance
5 hours per week of lectures and tutorials.
  • Category
  • Hours
  • Lectures
  • 35
  • Preparation
  • 140
  • Project work
  • 30
  • Exam
  • 1
  • Total
  • 206
7,5 ECTS
Type of assessment
Oral examination, 25 minutes (no preparation time)
Type of assessment details
Oral examination with prepared slides
Exam registration requirements

One mandatory assignment must be approved to qualify for the exam. 

All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal examiners

Same as the ordinary exam.

If the mandatory assignment was not approved before the ordinary exam it must be (re)submitted and approved. It must be handed in four weeks before the beginning of the reexam week, in order to be approved three weeks before the beginning of the re-exam week.

Criteria for exam assesment

The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.