Arbitrage Pricing of Single-name Credit Derivatives

In existing pricing theories, pricing of single-name credit default swaps (CDSs) and their options makes no reference to the prices of defaultable bonds, the underlying assets of those derivatives. Such a pricing practice does not exclude possible arbitrage across bond and CDS markets. In this paper, we introduce a new theory that treats the two markets as one and thus ensures price consistency. The basic building blocks of our theory are risky zero-coupon bonds backed by the coupons of defaultable bonds. We develop a market model for credit derivatives, and the model bears high analogy to the LIBOR market model. Compared with other existing theories, our theory has two distinguished features. First, the recovery rate is no longer required as an input. Second, credit default swaps can be replicated statically by risky bonds and annuities. According to our theory, the introduction of CDSs eliminates recovery-rate risks in underlying defaultable bonds, leaving “early redemption” as the only residual risk.