PRICING-HEDGING DUALITY FOR CREDIT DEFAULT SWAPS AND THE NEGATIVE BASIS ARBITRAGE

Jan-Frederik Mai ()
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Jan-Frederik Mai: XAIA Investment, Sonnenstr. 19, 80331 München, Germany

International Journal of Theoretical and Applied Finance (IJTAF), 2019, vol. 22, issue 06, 1-17

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∗∈ ℝ 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.

Keywords: Credit default swap; negative basis; bond-CDS basis; pricing-hedging duality; arbitrage (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1142/S0219024919500328

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