Credit Models and the Crisis: A Journey into CDOs, Copulas, Correlations and Dynamic Models

2

Market Quotes

For single names our reference products will be credit default swaps (CDSs). The most liquid multi-name credit instruments available in the market are instead credit indices and CDO tranches (e.g. DJ-iTraxx, CDX). We discuss them in the following.

The procedure for selecting the standardized pool of names is the same for the two indices. Every six months a new series is rolled out at the end of a polling process managed by Markit, where a selected list of dealers contributes the ranking of the most liquid CDSs. All credit references that are not investment grade are discarded. Each surviving credit reference underlying a CDS is assigned to a sector. Each sector is contributing a predetermined number of credit references to the final pool of names. The rankings of the various dealers for the investment grade names are put together to rank the most liquid credit references within each sector.

2.1 CREDIT INDICES

The index is given by a pool of names 1, 2, . . . , M , typically M = 125, each with notional 1/M so that the total pool notional is 1. The index default leg consists of protection payments corresponding to the defaulted names of the pool. Each time one or more names default, the corresponding loss increment is paid to the protection buyer, until final maturity T = T_b arrives or until all the names in the pool have defaulted.

In exchange for loss increase payments, a periodic premium with rate S is paid from the protection buyer to the protection seller, ...