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The Mathematics of the Relationship between the Default Risk and Yield-to-Maturity of Coupon Bonds

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  • Sara Cecchetti
  • Antonio Di Cesare

Abstract

The paper analyzes the mathematics of the relationship between the default risk and yield-to-maturity of a coupon bond. It is shown that the yield-to-maturity is driven not only by the default probability and recovery rate of the bond but also by other contractual characteristics of the bond that are not commonly associated with default risk, such as the maturity and coupon rate of the bond. In particular, for given default probability and recovery rate, both the level and slope of the yield-to-maturity term structure depend on the coupon rate, as the higher the coupon rate the higher the yield-to-maturity term structure. In addition, the yield-to-maturity term structure is upward or downward sloping depending on whether the coupon rate is high or low enough. Similar qualitative results also holds for CDS spreads. Consequently, the yield-to-maturity is an indicator that must be used cautiously as a proxy for default risk.

Suggested Citation

  • Sara Cecchetti & Antonio Di Cesare, 2012. "The Mathematics of the Relationship between the Default Risk and Yield-to-Maturity of Coupon Bonds," Papers 1203.6723, arXiv.org.
    • Handle: RePEc:arx:papers:1203.6723
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    References listed on IDEAS

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    1. Edwin J. Elton & Martin J. Gruber & Deepak Agrawal & Christopher Mann, 2001. "Explaining the Rate Spread on Corporate Bonds," Journal of Finance, American Finance Association, vol. 56(1), pages 247-277, February.
    2. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
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    1. De Sola Perea, Maite & Dunne, Peter G. & Puhl, Martin & Reininger, Thomas, 2019. "Sovereign bond-backed securities: A VAR-for-VaR and marginal expected shortfall assessment," Journal of Empirical Finance, Elsevier, vol. 53(C), pages 33-52.

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