Mathematics of the Financial Markets: Financial Instruments and Derivatives Modelling, Valuation and Risk Issues

13

Credit derivatives

13.1 INTRODUCTION TO CREDIT DERIVATIVES

A credit derivative is a derivative product with credit risk as underlying. A credit risk is a risk about a payment default, partial or total, relative to any obligation of payments. Credit risk is also called counterparty risk (the counterparty to be understood as the debtor, or borrower), or default risk.

The major problem with credit derivatives is that, contrary to any other derivative, the underlying credit risk cannot be straight expressed as a number, nor straight measured on a spot market underlying. Hence the basic difficulty in pricing the derivative on an a priori “non-quantitative” underlying.

13.1.1 How to quantify a credit risk?

A non-quantitative measure as credit risk, could be indirectly quantified via:

• the rating of the debtor counterparty: at first sight, the rating attributed by rating agencies should reflect the soundness of the borrower, the risk that this debtor would default. In many cases, for a given borrower, such rating is refined for short or longer term debt maturities, even on each of specific debt issued by him.
• Unfortunately, such rating is not updated on a continuous basis, and even updates would be frequent enough, surveys indicate that the correlation is poor between the rating level and the percentage of observed defaults over time. Moreover, as usual (cf. previous chapters), such correlation is non-stationary over time;
• the interest rate paid by the borrower, practically speaking, ...