Course Unit Page


This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.

Quality education

Academic Year 2021/2022

Learning outcomes

Upon successful completion of the course, you will be able to correctly map all the techniques adopted in interest rate models (from the one factor family to the HJM one and the market models) onto a unified theoretical framework assuring for the absence of arbitrage opportunities, appreciating the interconnections, and gaining a fresh perspective on the known techniques and the pricing of derivatives in every setting.

Course contents

1. Interest rates and related contracts

2. Arbitrage Theory

3. Short-Rate Models

4. HJM approach

5. Forward Measures

6. Market models


Term-Structure Models, D.Filipovic, Springer

Martingale methods in financial modeling, Musiela-Rutkowsky, Springer

Interest Rate Models - Theory and Practice, D.Brigo and F.Mercurio, Springer

Teaching methods

Theoretical lessons will be support by applied examples about the discussed models in order to incite students to find themselves the explicit solutions of the theoretical problems applying the correct mathematical instruments.

Assessment methods

The learning test consists in a written exam and the implementation of an assigned work enriched by the MatLab codes.

The written exam, to solve in 2 hours, is composed by 3 execises which are structured into 2 questions. During the exam it is permitted to use the calculator but it is not allowed to consult books or notes. It is attributed on average 10 points to each exercise. The students pass the exam with a score not lower than 18 points.

The subject of the assigned work concerns mainly the simulation of a particular contingent claim's price and its sensitivities to the model's parameters using the approaches analyzed during the course, with MatLab code in appendix. This work can be done on its own or in a group of maximum 3 students. The oral presentation of this work is valuated with a score (maximum equal to 30).

The final grade is the average of the witten exam's and the assigned work's score. The exam is passed with a final score greater than or equal to 18.

The student can ask also for an oral exam about all the programme of the course. In this case the final grade will be the average of the oral and the witten exam's grade and of the valuation of the assigned MatLab work.

Office hours

See the website of Silvia Romagnoli