*This is a demanding second-semester lecture*

### 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 extensively 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 interest rate futures and options

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

### 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.

Additional textbook references:

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)

### Prerequisites

Mathematics for Economics and Finance

Empirical Methods in Finance

Programming for Finance