The Art of Credit Derivatives: Demystifying the Black Swan

13

Correlation from Collateral to Tranches

When the rich wage war it’s the poor who die.

Jean-Paul Sartre

13.1 INTRODUCTION

In this chapter we show how variations on the correlation among the underlying collateral of an asset backed security (ABS) impacts the correlation among the tranches in a portfolio of ABSs. We also give evidence of the dependency on the time frame. This chapter should be read in conjunction with the framework described in Chapter 23 and in our earlier paper (Garcia et al., 2007) as a solution for the securitization business model of a financial institution.

This chapter is complementary to Chapters 22 and 23 in two ways. First, it shows how changes in correlation of the collateral underlying an ABS affects the correlation between ABS tranches. Second, it shows that this correlation changes with the investment horizon. The chapter brings support to the idea that the lowest possible cost of capital is associated with a short-term holding period, and as such the securities should be put on trading books and have their values monitored via the standardized credit indices. In the absence of time series of expected loss of ABS tranches we use a Monte Carlo simulation based on the widespread copula algorithm to generate data for the collateral and, consequently, the prices of the tranches.

The remainder of the chapter is organized as follows. In Section 13.2 we review the generic 1-factor model used for valuation of CDO tranches. The algorithm based on Monte ...