‘Single Name’ CDS
We saw in section 20.1 that, in the case of an F2D where the reference entities have uncorrelated spreads (hazard rates), the valuation formulas are relatively simple. We apply the similar arguments to a CDS with uncorrelated counterparty risk in section 25.1, and with 100% correlation in section 25.2.
We also saw in Part II section 9.8 that, even where name and counterparty hazard rates are correlated, the impact of high correlation and high spread volatility is minimal (except at high spreads and very long-life CDSs) if the hazard rate process is a diffusion without jumps. However, the default time model in Chapter 20 used to price baskets and CDOs, carries the implication that hazard rates follow a jump process. We also saw in Part III (section 22.4) that portfolio products exhibit significant default time correlation, therefore we cannot reasonably ignore the name and counterparty risk without more detailed investigation. Fortunately we can use the correlated default time model to value CDSs including counterparty risk (we shall illustrate some results in section 25.3).
We revisit the question of alternative Copulas in section 25.4. We look at the effects of collateralisation versus non-collateralised trades in section 25.5, and at CDSs on a counterparty to a CDS trade (CCDSs) in 25.6.
25.1 NON-CORRELATED COUNTERPARTY
If, under a default time correlation model, two names are uncorrelated, then the expected default time of one name conditional on the ...