Tuesday, April 24, 2007

How to price a CDS

As with any other derivative contract, the valuation of CDS is (was?) primarily based on replicate portfolio and no arbitrage argument. The picture below (from Merrill Lynch Credit Derivative Handbook 2003) depicts a portfolio that replicates a credit default swap:

  • A fix rate corporate bond is acquired by the investor. This exposes the investor to two major risks: interest rate risk and credit risk. The bond pays treasury rate plus a spread (Sc).

  • The bond purchase is repo financed. This is necessary because par CDS is unfunded transaction.

  • An interest rate swap transaction is then arranged. The investor pays fixed leg and receives LIBOR plus spread (Ss). This effectively eliminates the interest rate risk component.

  • A single counter-party would package the bond and swap into a single asset swap to minimize counter-party risk.

  • The investor is now holding only the credit risk of the bond issuer, which is the same for a CDS contract. Hence the "price" of this portfolio should be the same as a CDS with the same maturity (with adjustments on coupon interval, day count, yadayada...)
One thing to note is that this pricing framework is now mostly theoretical. With exponential growth in the credit market, CDS contracts have become more liquid than corporate bonds. CDS is considered a plain vanilla product and its spread quote is used to derive default probability and price other credit derivative products