The Art of Credit Derivatives: Demystifying the Black Swan

19

1-factor Models for the ABS Correlation Market Pricing TABX Tranches

Follow the course opposite to custom and you will almost always do well.

Jean-Jacques Rousseau

19.1 INTRODUCTION

In Chapter 8 we discussed the corporate standardized credit indices and in Chapters 9, 10 and 11 we discussed pricing issues of those instruments. In Chapter 18 we described more recent standardized credit indices with focus on ABX.HE and TABX.HE, the standardized credit indices for subprime MBSs.

When pricing TABX we are confronted with three sorts of difficulties. First, the instruments underlying the contract are CDSs on ABSs and, contrary to the corporate CDS case, their prices are not readily available. Second, a more fundamental issue is that the notional underlying the contract is amortizing. The amortization schedule depends on the assumptions of prepayment on the mortgage pool and one possible estimation of the prepayment is available on the remittance report of the underlying ABS. Third, market participants have not (yet) agreed on a standard algorithm to price these indices.

The purpose of this chapter is to adapt the recursive algorithm, described in Chapter 9, to price the TABX tranches by using both the Gaussian copula and the Lévy base correlation methods. Additionally, the proposed approach takes into account the amortization schedule to price TABX. We will assume the prepayments are as given in the remittance reports.

The remainder of this chapter is organized as follows. In ...