98751 - ADVANCED MATHEMATICAL FINANCE

Learning outcomes

At the end of course students will be able to work with generalized stochastic modelling for pricing and hedging. Students will have knowledge about the main models proposed in literature for the representation of the term structure of interest rates.

Course contents

1. Interest rates and related contracts

2. Arbitrage Theory

3. Short-Rate Models

4. HJM approach

5. Forward Measures

6. Market models

7. The impact of climate variables on the interest rate curves

Readings/Bibliography

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. The implementation in MatLab (by simulation or market data) allows students to analyze the empirical feature of the different approaches.

Assessment methods

The learning assessment consists of a written exam. Students may also opt to take an oral exam and/or present a projecton an assigned topic, implemented in Python or MATLAB.

• The written exam lasts 2 hours and consists of 2 exercises, each subdivided into 2–3 questions. Use of a calculator is permitted, but books and notes are not allowed. Each exercise is typically worth 10 points, and the exam is passed with a minimum score of 18/30.

• The optional oral exam covers the entire syllabus, including proofs. A minimum score of 18/30 is required to pass the oral.

• The optional project work focuses on the simulation of a specific contingent claim’s price and the sensitivity analysis of the result with respect to model parameters, using techniques studied during the course. The project must include an appendix with Python or MATLAB code and can be completed individually or in groups of up to 3 students. The oral presentation of the project will be graded up to a maximum of 30 points.

The final grade is based on the written exam. If the student also completes the oral exam and/or the project, the final mark will be the average of the written exam and the additional component(s). The exam is passed with a final score of 18/30 or higher.

Teaching tools

Teaching tools will be blackboard and slides.

Office hours

See the website of Silvia Romagnoli