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We know that, taken every discount curve, it's possible to calculate its forward rates according to our tenor preferences.

We know also that it's actually possible to extract an implied term structure from every discount curve simply using the appropriate forward rates.

This is indeed true for risk free discount curves, because the arbitrage-free assumption which returns the forward rates is fair.

Now let a risky discount curve, that is, every discount curve obtained from liquid issues' yields possibly interpolated and bootstrapped... and so on.

Questions:

  1. does it make sense to extract an implied term structure from it like we're used to do with a risk free zero rate curve?
  2. Is the implied term structure obtained in such a way an arbitrage-free forecast of the future yield curve shape?
  3. If not so, is the assumption that allows to calculate the forward rates valid for risk-free curves only?
  4. Does it make sense to obtain an implied term structure from, say, a CDS spread curve? Why?
  5. If the answer to 5. was affirmative, would that implied term structure be an arbitrage-free forecast of the issuer's default risk?
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  • $\begingroup$ not trying to be too investigative, but you find 50% of questions you asked and received multiple answers for not worthy commenting on or marking as sought after answer? Maybe a comment that you do not find any of the answers properly answered would help? $\endgroup$
    – Matt Wolf
    Commented Sep 22, 2013 at 15:46
  • $\begingroup$ Was this one the offending behavior of mine? $\endgroup$
    – Lisa Ann
    Commented Sep 22, 2013 at 16:50
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    $\begingroup$ Ok, in order to give a meaningful answer to your last question I took another look at all your questions where no answers were given. As part of most of such questions users added at least comments and you hardly responded/replied or added additional information in order to address the issues given by users in comments to your questions. If you seriously seek answers to your questions then maybe you want to interact with others that try to help but possibly did not understand your question or did not find it clear enough. Does that make more sense? $\endgroup$
    – Matt Wolf
    Commented Sep 23, 2013 at 5:26
  • $\begingroup$ I do not want to further clutter the comment section with this issue, I hope I made myself clearer about this issue and again, this is how I feel about it, maybe I am the only one. I prefer to answer questions where I know the asker is engaged and responsive because I believe I can then also learn and that the time, spent, is appreciated and will hopefully add value to other users also. $\endgroup$
    – Matt Wolf
    Commented Sep 23, 2013 at 5:30

2 Answers 2

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I think your questions above are all manifesto of a question on modeling assumption: should we assume a credit term structure in valuing risky/corporate bonds?

My personal opinion is yes. The framework I prefer to have is:

  1. Risk free rates/discounting curve from treasury bonds (or other assumptions you find valid)
  2. Credit curve from the risky bonds (using the discount curve from the 1st step)

Why does this matter to your question? You can certainly build a discount curve and compute forwards etc based on risky bonds. The question is what that means? When you compute forwards on the discount curve for example, you're basically doing interpolation using rates assumptions you derived from the discount curve.

But that could be "incorrect" if you buy in the credit assumption (as described above). In other words, with the credit assumption, the interpolations (say getting forward yield, etc) are all different. So to me, the answers to your questions are:

  1. Does it make sense to extract an implied term structure from it like we're used to do with a risk free zero rate curve? -- No
  2. Is the implied term structure obtained in such a way an arbitrage-free forecast of the future yield curve shape? -- No
  3. If not so, is the assumption that allows to calculate the forward rates valid for risk-free curves only? -- Well...technically no but that's my explanation above.
  4. Does it make sense to obtain an implied term structure from, say, a CDS spread curve? Why? -- Yes
  5. If the answer to 5. was affirmative, would that implied term structure be an arbitrage-free forecast of the issuer's default risk? -- Yes, at least implied by bond prices (assuming they have comparable liquidity premium, etc)
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1.Yes, for some bonds where you have enough issues to build a curve you are able to value them using the curve instead of just relying on the price per issue.

2.It's not a forecast of the future of the yield curve shape, it's a snapshot of the current markets view of the future.

3.No, see answer for Q1

4.Yes, to be able to value contracts on a curve instead of just on price (so you could see where a contract 'should' be)

5.I think the following post will point you in the right direction ( How to compute the implied probability of default from a CDS spread? ).

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