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Reading about CDOs and calibration to find the implied correlation, I came up with the following question.

Suppose we are pricing a CDO over a pool of $N=125$ names, using the usual Gaussian copula structure, with constant recovery rate, constant hazard rates and a unique value $\rho$ for the default times of the 125 names in the pool. This CDO has standard tranches $(l_k, u_k)$, with $k=1,\ldots n$. This is how the implied correlation algorithm is explained in several articles I read:

(1) The market quotes thefair spread $x^*_k$ for each CDO tranche, $k=1,\ldots n$.

(2) We can then plug these values $x^*_k$ in an algorithm and calculate an implied (base) correlation parameter $\rho_k$ corresponding to each tranche $(l_k, u_k)$.

Question: Now that I have found each tranche correlation $\rho_k$, how do I "use" it? What's its purpose? I mean, shall I use this parameter $\rho_k$ to price (for example) other CDOs on the same pool of 125 names, perhaps with different maturities/premium dates? Or what else?

My question came up because when we determine the implied volatility out of a set of vanilla call options, we shall use those implied volatilities to price more complex instruments (on the same underlying) having equal strike/expiry: then, implied volatility is "extracted" from one class of instruments (vanilla call options) to be "used" in other classes of instruments (e.g., exotic options, etc.).

But here? Do we also use implied correlation for pricing/evaluating any other imstruments? Which ones, exactly? How?

So, what is exactly the use of implied correlation of a CDO?? Thanks in advance for your help.

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  • $\begingroup$ Yes, like an implied vol, an implied correlation is supposed to tell you something about how the market prices the securities (that you could apply to other situations). But in practice i.c. has been found to vary a lot over time, probably because the underlying "copula model" is not very accurate. So I would not trust i.c. very much, too unstable and unreliable. $\endgroup$ – noob2 Mar 15 '17 at 12:55
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    $\begingroup$ @noob2 my question was: how exactly i.c. is determined for? Okay, I understand that it is not reliable, but what is its role? What are these "other situations"?? It is exactly this that I don't understand. $\endgroup$ – RandomGuy Mar 15 '17 at 13:20
  • $\begingroup$ You need a CDO expert, and I have never traded CDOs. My impression is ppl used ic as a rough and ready measure of valuation. Similar CDOs X,Y,Z have ic's of ix,iy,iz.. If situation comes along with ic different from this I conclude that this CDO is "cheap" or "expensive" in my judgmt. Also ppl used this kind of heuristic in pricing new CDOs. "we price this CDO at ic similar to other one that came out last week, buy now while supplies last". $\endgroup$ – noob2 Mar 15 '17 at 13:38
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    $\begingroup$ CDO is an investment vehicle (SPV). Assets are a pool of collateral; liabilities - tranches in capital structure. Each tranche is quoted using DM/spread/yield. When you back out implied correlation(IC) from quoted DMs (different tranches) you ultimately want an answer about characteristics of collateral pool. All these tranches are backed by the same collateral pool and theoretically when you convert quoted DMs into ICs these all should converge to a single const value. However that's just theory, in practice you'll get a skew. As @noob2 mentioned you can use it for relative value analysis $\endgroup$ – Nicholas Mar 18 '17 at 10:59
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    $\begingroup$ ^^ and relative value analysis is not limited by pricing new issuance; you could also make secondary trading decisions by buying "cheap" tranches and selling "expensive" tranches in the same CDO structure (i.e. popular trade was long mezzanine and short AAAs ...) $\endgroup$ – Nicholas Mar 18 '17 at 11:06

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