Credit Derivatives: Trading, Investing and Risk Management, Second Edition

9

Valuation and Risk: Basic Concepts and the Default and Recovery Model

Sections 9.2 and 9.3 develop a mathematical framework for the modelling of credit risk aimed at the valuation of CDSs and bonds. The model presented is largely the industry standard among the banking community. Section 9.4 generalises this model and shows under the circumstances in which the simpler model of 9.3 applies. In Chapter 8 we saw some of the major factors of relevance to the pricing of credit instruments. In this chapter we introduce a simple arbitrage model to help to identify the key driving factors in the valuation of CDSs, and to give a sound basis for the intuitive pricing of CDSs.

9.1 THE FUNDAMENTAL CREDIT ARBITRAGE - REPO COST

If BT debt is trading at 7% and risk-free (government) rates are 4%, what is the correct CDS premium for BT?

Let us assume that there is a 5-year FRN carrying a coupon (LIBOR plus a fixed spread S) such that the bond price is par. Let us also assume that default risk is constant on BT, so that the bond will always be priced at par, or at the recovery level in the default event. Suppose we buy a CDS on BT, to the same maturity as the bond, into which the bond - and that bond only - is deliverable and pays par plus accrued interest on the bond. In order to have a zero cost (self-financing) position we can lend the bond out on repo, receive cash collateral equal to the price of the bond, and pay the repo rate on the BT bond. We assume that the repo rate curve is ...