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Pricing-Hedging Duality For Credit Default Swaps And The Negative Basis Arbitrage

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  • JAN-FREDERIK MAI

    (XAIA Investment, Sonnenstr. 19, 80331 München, Germany)

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.

Suggested Citation

  • Jan-Frederik Mai, 2019. "Pricing-Hedging Duality For Credit Default Swaps And The Negative Basis Arbitrage," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(06), pages 1-17, September.
    • Handle: RePEc:wsi:ijtafx:v:22:y:2019:i:06:n:s0219024919500328
    DOI: 10.1142/S0219024919500328
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    References listed on IDEAS

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    1. Frank Gehmlich & Thorsten Schmidt, 2018. "Dynamic Defaultable Term Structure Modeling Beyond The Intensity Paradigm," Mathematical Finance, Wiley Blackwell, vol. 28(1), pages 211-239, January.
    2. Damiano Brigo & Agostino Capponi & Andrea Pallavicini, 2014. "Arbitrage-Free Bilateral Counterparty Risk Valuation Under Collateralization And Application To Credit Default Swaps," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 125-146, January.
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