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Suppose a bond has annual coupon of \$1 and face value of \$100 and matures in two years. If recovery rate is $50\%$ and the bond defaults before the first coupon payment. How should we receive the recovery? Is it \$50 at year 2 or \$0.5 at year 1 and \$100.5 at year 2?

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the recovery rate is of the par value, which is \$100 in your case. So you'd receive \$50 in case of default. The time of receiving the recovery value could vary.

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  • $\begingroup$ So there is no recovery for coupons in any way? Some said to me that recovery is on present value of the bond so that would implicitly include coupons. Can you point out a source for this I can cite? Thank you! $\endgroup$ – Daniel Li Apr 1 '18 at 16:32
  • $\begingroup$ @DanielLi investopedia.com/terms/r/recovery-rate.asp this investopedia page states it pretty clear. On the other hand, recovery rate times present value doesn’t make sense. In case of default, the present value already has recovery rate embedded into it. Besides, coupons are interest. The debt issued only “promises” to give you back your par, not interest $\endgroup$ – Will Gu Apr 1 '18 at 18:42
  • $\begingroup$ Totally agree with all Will Gu says EXCEPT the very last line. Interest payments ARE contractual promises too. Recovery rate includes the interest payments (as per your Investopedia link) but recovery rate is defined as a percentage of the face (again, as per link above). $\endgroup$ – Spen Jan 2 '19 at 15:01
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Generally, the developed markets convention is that all the coupon that has been accrued and not paid yet just disappears, but the remaining notional is accelerated - becomes due immediately. To illustrate, suppose for concreteness that the issuer has two bonds. One pays 6% coupon, and matures in 2 years, bullet. The other pays 7% coupon, matured in 10 years, and has amortized, so the current factor is 75%. If the issuer defaults, then the coupons don't matter, the maturities don't matter. The current interest rate levels don't matter. The recovery is on face value of the bullet bond and 75% of face value of the amortized bond. Now, if instead of a bond you issue a bespoke credit-linked note, then you can specify anything you like on the term sheet. In particular, you can say that in case of a credit event, the coupon accrues until the day of default (like running spread of a credit default swap). You can also link the recovery to interest rates in some way. Although this is very seldom done, a good analytics library should have the flexibility to support this.

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