Pricing-hedging duality for credit default swaps and the negative basis arbitrage

Abstract

Assuming the absence of arbitrage in a single-name credit risk model, it is shown how to replicate the risk-free bank account until a credit event by a static portfolio of a bond and infinitely many credit default swap (CDS) contracts. This static portfolio can be viewed as the solution of a credit risk hedging problem whose dual problem is to price the bond consistently with observed CDSs. This duality is maintained when the risk-free rate is shifted parallel. In practice, there is a unique parallel shift x -that is consistent with observed market prices for bond and CDSs. The resulting, risk-free trading strategy in case of positive x - earns more than the risk-free rate, is referred to as negative basis arbitrage in the market, and x - defined in this way is a scientifically well-justified definition for what the market calls negative basis. In economic terms, x - is a premium for taking the residual risks of a bond investment after interest rate risk and credit risk are hedged away. Chiefly, these are liquidity and legal risks.