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## Fixed Income and Credit Risk

• Teacher(s):
• Course given in: English
• ECTS Credits: 6 credits
• Schedule: Spring Semester 2021-2022, 4.0h. course + 1.0h exercices (weekly average)
•  sessions
•  course website
• Related programmes:
Master of Science (MSc) in Finance, Orientation Corporate Finance

Master of Science (MSc) in Finance, Orientation Asset and Risk Management

Master of Science (MSc) in Finance : Financial Entrepreneurship and Data Science

### Objectives

There are two parts in this course: A) master the techniques that are required for option pricing in the Black-Scholes setting. This encompasses stochastic calculus and it leads to the fundamental partial differential equation which we solve with Feynman-Kac. B) In this part we discuss the techniques related to fixed income markets: types of interest rate quotes, rate curves, duration. Forward rates, Floating-Rate-Notes, Forwards and SWAPS. The course will cover in detail the following interest rate models: Merton, Vasicek, as well as Cox, Ingersoll and Ross and mention many others. We will also move on to the Libor Market Model where the tools developped in part A will be extensitvely used. In this part we also introduce techniques to deal with credit risk by discussing structural and intensity based models.

After attending this course, participants should have the knowledge so that advanced textbooks such as the one by Brigo and Mercurio: "Interest Rate Models - Theory and Practice" become accessible.

### Contents

The course is structured around the following list of topics:

1. Stochastic calculus

2. Overview of fixed income instruments and relevant notation

3. Bootstrapping the term structure of interest rates

4. No arbitrage valuation and replicating portfolios

5. Interest rate modeling for valuation and hedging

6. Pricing and hedging of interst rate futures and options

7. Taking into account credit risk: intensity based modeling and structural models

TA is Georgii Zvonka Extranef.

### References

The primary textbook references are:

Steven Shreve, "Stochastic Calculus for Finance II: Continuous-Time Models", 2004, Springer.

Pietro Veronesi, "Fixed Income Securities: Valuation, Risk, and Risk Management", John Wiley and Sons, 2010.

Darrell Duffie, Kenneth J. Singleton, "Credit Risk", Princeton University Press, 2003.

Brigo D. and F. Mercurio, "Interest Rate Models: Theory and Practice: With Smile, Inflation and Credit", Springer Finance, 2006. (Second Editon).

John C. Hull, "Options, Futures and Other Derivatives", 7th Edition, Prentice Hall, 2008. (Hull 2008)

### Pre-requisites

Mathematics for Economics and Finance

Empirical Methods in Finance

Programming for Finance

### Evaluation

#### First attempt

Exam:
Written 4h00 hours
Documentation:
Allowed
Calculator:
Allowed
Evaluation:

Exam is Multiple Choice on MoodleExam.

Students are allowed to use their documentation and also to use Excel.

Problems are displayed randomly with order of questions also being random. It is possible to go back and forth across problems. Wrong answers get -1 point independently of points attributed to a problem.

#### Retake

Exam:
Written 4h00 hours
Documentation:
Allowed
Calculator:
Allowed
Evaluation:

Same as main exam.

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