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BOND MATH: The Theory Behind the Formulas by Donald J. Smith

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Implied Probability of Default on Coupon Bonds

In Chapter 2, we worked through the calculation of the implied probability of default on a zero-coupon corporate bond. We assumed that the amount the investor would be able to recover is a constant fraction of the risk-free value at the time of default. For a coupon bond, it is more common to set the recovery rate to be a constant fraction of the par value. But these are all arbitrary assumptions that can be changed to fit the circumstances; what matters for us is the approach to the bond math problem.

Suppose that the appropriate risk-free yield curve is flat at 3.50%. Then our 4-year, 4% annual payment corporate bond would be worth 101.837 (percent of par value) if there was no risk of default. ...

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