Insegnamento a.a. 2019-2020

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

• Introduction to Fixed Income World: Examples of Structured products and Financial Engineering. Review of Basic elements of financial math and Interest Rate Conventions.
• Building Blocks: LIBOR, FRA, Eurofutures, Swap.
• Yield Curve Stripping: the Bootstrapping Procedure. Interpolating the yield curve: parametric and non-parametric methods.
• Pricing Floating Rate Notes.
• 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 foundations of risk-adjusted pricing in Fixed Income. The change of numeraire and pricing of interest rate derivatives.
• Understanding the different approaches to modelling: from short rates to HJM to the Libor Market Model. Short rate models. Merton, Vasicek, CIR. The Heath-Jarrow-Morton (HJM) Model. Gaussian HJM Models. Multivariate HJM models. The Libor Market Model: theory and fundamental formulas and techniques for pricing. Comparing different Term Structure Models: Market Models, Short Rate Models, HJM.
• Practical application, calibration and management of volatility and correlation.
• Fixed Income in the last decade: the multicurve market. Double discounting for collateralized Derivatives. Overnight Indexed Swaps. Bootstrapping the curves. Understanding how it emerges from credit and funding risk. Multicurve short rate models and multicurve Libor Market Model. The interaction of credit and interest rate risk - The XVAs - Collateral and OIS discounting.

• 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.

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 models and using them to value fixed income securities and fixed income derivatives.

• Face-to-face lectures
• Exercises (exercises, database, software etc.)
• Case studies /Incidents (traditional, online)
• Group assignments

This module is taught primarily through lectures and laboratories, making use of numerical 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 follows the initial six lectures and is based on the first part of the course. The second examination 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 Final examination (closed books) at the end of the course is planned, and is based on the entire course. 

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. 

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,  textit{Fixed Income Securities: Tools for Today's Markets}, 3rd Edition.
• L. BALLOTTA, FUSAI, GIANLUCA AND MARENA, MARINA, 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.