# Does bond market trading price has recovery assumption in mind?

We all know fixed income seucirties have default risk which can be generated from CDS market. However, I am curious if the market trading price of a bond (say, $105) imposing any recovery assumption? Using recovery of 0 or 40%, the bond price could diff by more than 10 bucks. What is the real meaning out there from what we see on the screen or bid/ask of this$105? Should I price it without recovery assumption?

Quantitative Finance Asked by HoldBreath on November 11, 2021

The price of a defaultable bond is driven by 3 things:

• the observable interest rates

• the probability of default

• the price of the bond after a default (or, equivalently, the loss given default)

The price of an investment-grade bond reacts mostly to interest rates. Further into junk, the interest rates affect the price less, and the thoughs of what might happen after a default begen to affect the price more. For example, a few years ago, before Venezuela defaulted on its USD sovereign bonds, one of the bonds was much more expensive than the others - not because it was less risky (they all defaulted at the same time) but because traders thought it was better collateralized and would be more valuable after the imminent default.

Similar bonds might also trade differently because some have collective action clause (CAC) and others don't. For an IG bond it should not matter, but for junk, it may play a role.

Greatly oversimplying, imagine that the price of a defaultable bond that pays 1 with survival probability $$p$$ and alternatively pays recovery $$R<1$$ with probability $$1-p$$ is $$frac{1}{1+r} p + (1-p) R,$$ where $$r$$ is the interest rate. (People use much more complicated models but this is the general idea.) Clearly if $$p$$ is close to 1, then $$R$$ doesn't matter and $$r$$ drives the price. But as $$p$$ decreases and approaches 0, $$r$$ matters less, $$R$$ matters more, and eventually the price expresses the expectation of what the bond will be worth after the default.

Answered by Dimitri Vulis on November 11, 2021

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