This book is an introductory guide to using Lévy processes for credit risk modelling. It covers all types of credit derivatives: from the single name vanillas such as Credit Default Swaps (CDSs) right through to structured credit risk products such as Collateralized Debt Obligations (CDOs), Constant Proportion Portfolio Insurances (CPPIs) and Constant Proportion Debt Obligations (CPDOs) as well as new advanced rating models for Asset Backed Securities (ABSs). Jumps and extreme events are crucial stylized features, essential in the modelling of the very volatile credit markets - the recent turmoil in the credit markets has once again illustrated the need for more refined models. Readers will learn how the classical models (driven by Brownian motions and Black-Scholes settings) can be significantly improved by using the more flexible class of Lévy processes. By doing this, extreme event and jumps can be introduced into the models to give more reliable pricing and a better assessment of the risks. The book brings in high-tech financial engineering models for the detailed modelling of credit risk instruments, setting up the theoretical framework behind the application of Lévy Processes to Credit Risk Modelling before moving on to the practical implementation. Complex credit derivatives structures such as CDOs, ABSs, CPPIs, CPDOs are analysed and illustrated with market data.

We develop a switching regime version of the intensity model for credit risk pricing. The default event is specified by a Poisson process whose intensity is modeled by a switching Lévy process. This model presents several interesting features. Firstly, as Lévy processes encompass numerous jump processes, our model can duplicate sudden jumps observed in credit spreads. Also, due to the presence of jumps, probabilities do not vanish at very short maturities, contrary to models based on Brownian dynamics. Furthermore, as parameters of the Lévy process are modulated by a hidden Markov chain, our approach is well suited to model changes of volatility trends in credit spreads, related to modifications of unobservable economic factors.

This paper presents a switching regime version of the Merton's structural model for the pricing of default risk. The default event depends on the total value of the firm's asset modeled by a Markov modulated Lévy process. The novelty of our approach is to consider that firm's asset jumps synchronously with a change in the regime. After a discussion of dynamics under the risk neutral measure, we present two models. In the first one, the default occurs at bond maturity if the firm's value falls below a predetermined barrier. In the second version, the company can bankrupt at multiple predetermined discrete times. The use of a Markov chain to model switches in hidden external factors makes it possible to capture the effects of changes in trends and volatilities exhibited by default probabilities. Finally, with synchronous jumps, the firm's asset and state processes are no longer uncorrelated.