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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.

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File URL: http://arxiv.org/pdf/1203.6723
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Paper provided by arXiv.org in its series Papers with number 1203.6723.

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Date of creation: Mar 2012
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Handle: RePEc:arx:papers:1203.6723

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Web page: http://arxiv.org/

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  1. Edwin J. Elton, 2001. "Explaining the Rate Spread on Corporate Bonds," Journal of Finance, American Finance Association, vol. 56(1), pages 247-277, 02.
  2. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
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