The Art of Credit Derivatives: Demystifying the Black Swan

2

Default Models

Genius, that power that dazzles mortal eyes, is oft but perseverance in disguise.

Henry Austin

2.1 INTRODUCTION

A credit derivative is a derivative whose payoff depends on the credit risk of an underlying reference. In several places in this book we show that the market for credit derivatives has grown enormously in recent years since its formal inception in the mid 1990s. As a consequence of this growth there has been a demand for default models to be used for the evaluation of those instruments. The increased level of sophistication of the credit instruments, as evidenced by the credit crunch of June 2007, brought up the necessity for credit risk systems and models for default probabilities for credit risk purposes. These models do not need to be the same.

There is already a lot of literature available on this subject and we do not intend to repeat it here. We will give a very brief description of what is behind the modeling approaches in a way that the reader can follow through the remaining chapters. Two traditional references are Schönbucher (2003) and de Servigny and Renault (2004). Additional references will be given at the appropriate place. The chapter is structured as follows. In Section 2.2 we discuss what is called a default. In Section 2.3 we present the two approaches most used to model the default process.

2.2 DEFAULT

Generally speaking, an obligor is said to be in default when she cannot honor her legal contractual obligation in a debt instrument. ...