Reduced-form models: curve construction and the pricing of credit swaps, options and hybrids

Leif Andersen

INTRODUCTION

In the analysis of credit risk, it is often assumed that a default event is triggered when firm assets fall to a sufficiently low level relative to the notional of outstanding debt. In this line of thinking, models of credit risk naturally involve joint assumptions of the stochastic evolution of the individual components of the firm capital structure – ie, assets, debt, and equity. Such an approach is clearly “deep” in the sense that the analysis aims not only to quantify the credit risk itself, but also to understand the causal factors behind it.

The description of credit risk through an analysis of balance sheet information and other fundamental factors is the domain of the so-called structural models. While such models have their uses (see Chapters 5, 7, 14 and 15), it is often more practical to work at a higher level of abstraction and simply treat credit events as point processes with parameters that can be inferred from observations. This approach is known as reduced-form modelling. While reduced-form models are, in a sense, less fundamental than structural models, they offer the financial engineer large advantages in terms of implementation, analytic