Counterparty Credit Risk and Credit Value Adjustment: A Continuing Challenge for Global Financial Markets, 2nd Edition

10.3 Curve Mapping

In Section 10.1.5, we discussed the quantification of risk-neutral default probabilities from the credit spread of a counterparty. Such a credit spread may be derived in a variety of ways from the market prices of bonds, asset swaps and single-name CDSs. However, a key aspect in quantifying CVA is to obtain credit spreads for non-observable names, i.e., those counterparties for which there is no defined credit spread trading in the market.

Whilst using subjective mapping methods to determine a credit spread may seem rather non-scientific, it is generally a necessary process for banks to value illiquid assets, such as bonds and loans, held on their trading books. Furthermore, Basel III capital rules impose similar requirements for capital allocation against CVA, stating (BCBS, 2011): “Whenever such a CDS spread is not available, the bank must use a proxy spread that is appropriate based on the rating, industry and region of the counterparty.” Banks and authors (e.g., Gregory, 2010) have argued against this requirement on the basis that banks do not attempt to mark-to-market much of their illiquid credit risk (including CVA).

10.3.1 Basics of Mapping

The fundamental aim of credit curve mapping is to use some relevant points to achieve a general curve based on observable market data, as illustrated in Figure 10.13. This illustrates a case where a number of points can be used at various different maturities (as in the case of the secondary bond market). A best fit ...