The Art of Credit Derivatives: Demystifying the Black Swan

10

Historical Study of Lévy Base Correlation

Doubt is the father of invention.

Galileo Galilei

10.1 INTRODUCTION

In Chapter 9 we described the concepts of implied compound correlation and base correlation used in the market for pricing purposes. We have shown that Lévy base correlation could be used as an alternative to the Gaussian copula approach. We also refer to our paper (Garcia et al., 2009). In this brief chapter we go into more details on the approaches and show numerical results of tests using both approaches for pricing and hedging purposes.

The chapter is organized as follows. The historical study is outlined in Section 10.2. We look at base correlation in these two models in Section 10.3. First, we show the evolution over time and, second, we consider the behavior across maturity and look at the base correlation surface. In Section 10.4 we compare hedge parameters in the different models. We focus on the deltas of the tranches with respect to the index. This is also done across maturity. Finally our conclusions are presented in Section 10.5.

10.2 HISTORICAL STUDY

In this section we describe our historical study. The dataset used is the iTraxx Europe Main data from 20 April 2005 until 16 March 2007. We look at index and tranche spreads for the 5-, 7- and 10-year maturity contracts. Figure 10.1 shows the historical evolution of the spreads for the 5-year maturity.

The key parameters in both models are the base correlation curves. First, we show the evolution over ...