Insegnamento a.a. 2024-2025

The main topics covered in the course are detailed here below:

• Review of Basic elements of financial math and interest rate conventions.
• Yield Curve Stripping: the Bootstrapping Procedure. Interpolating the yield curve: parametric and non-parametric methods.
• Pricing FRA, Floating Rate Notes and Interest Rate Swaps. Credit risk.
• Interest Rate Options: Caps, Swaptions and Bond Options.
• Use and transformations of the central Black Formula. The Black Model and the volatility surface
• Allowing for negative rates: Bachelier and Shifted Black model.
• Application to pricing structured products and their use for hedging interest rate risk.
• The change of numeraire and pricing of interest rate derivatives.
• Understanding the different approaches to modelling. The different approaches from short rates to HJM to the Libor Market Model.

• Classic Interest Rate models: applying short rates to plain vanilla interest rate derivatives. From Vasicek to Hull & White two factor.

• Modern rate models: BGM (Libor Market Model) for structured derivatives. Theory and fundamental techniques for pricing, calibration and management of volatility and correlation.

• The financial crisis and the consequences for fixed Income: spreads, collateral, negative rates and multicurve modelling until the Libor reform.

• The impact of technology on fixed income. The evolution of money from banks to digital currencies, and the application of innovation from cryptography to smart contracts.

• Decentralized finance: blockchains and applications to derivatives, exchanges, collateral and lending.

• Have a foundation in a crucial area of financial markets and quantitative finance.
• Complement the general derivatives course with specific instruction in a key derivatives area.
• Be acquainted with the main modelling streams in fixed income securities.
• Be able to use models in this area in practical applications.
• Be able to deal with fundamental mathematical modelling techniques underpinning the subject.
• Understanding the impact of fintech on fixed income products

Knowledge and understanding:

• Show knowledge of the some of the main models used in the mathematical modelling of fixed income.
• Understand how models are applied in practice.
• Understand the key differences between different modelling approaches.

Skills:

• Performing basic fixed income computations.
• Building the term structure of interest rates.
• Valuing interest rate swaps.
• Setting up hedges for fixed income portfolios.
• Implementing  the main term structure models and using them to value fixed income securities and fixed income derivatives.

• Lectures
• Practical Exercises
• Collaborative Works / Assignments

This module is taught primarily through lectures and laboratories, making use of numerical (mainly using Excel 365) and analytic examples with the support of case studies.

Written exam with numerical and theoretical questions, according to two possibilities:

1. Two partial examinations (closed books) are planned. The first mid-term exam follows the initial six lectures and is based on the corresponding content. It will be open books and will require the solution of numerical (using advanced functionalities in Excel 365) and theoretical questions. The student must show a personal understanding of the main topics and the ability to perform analytical and numerical calculations.  The second partial (closed books) occurs at the end of the course and is based on the second part of the course.   Grades are assigned as follows: 55% for the part having highest mark and 45% for the part having lowest score.
2. A general examination (closed books) at the end of the course is planned, and is based on the contents presented during the course. Numerical and theoretical questions will be the content of the exam. 

In addition, a not-compulsory group coursework (maximum 3 persons per group) on pricing a structured product is possible.  The usual deadline for the take home examination is around mid-January. The use of Excel VBA/Matlab/R/Pyhton will be required. The coursework gives the possibility of adding a maximum of 3 points to the written mark. 

There is no difference between students attending or not attending the lectures. Both can take the partials and submit the coursework. 

Textbook and course material:

1. Lecture Slides provided by the teachers.
2. Chapters from the following sources:

• D. BRIGO, F. MERCURIO, Interest Rate Models - Theory and Practice: With Smile, Inflation and Credit, Springer Finance, 2007, 2nd ed.
• P. VERONESI, Fixed Income Securities: Valuation, Risk, and Risk Management, Wiley, 2009.
• B. TUCKMAN, A.SERRAT,  Fixed Income Securities: Tools for Today's Markets, 3rd Edition.
• L. BALLOTTA, FUSAI, G. and MARENA, M., A Gentle Introduction to Default Risk and Counterparty Credit Modelling, available at SSRN http://ssrn.com/abstract=2816355.
• A complete suggested reading list is distributed at the beginning of the course and of each part.