Sebastian Pokutta's Blog

Mathematics and related topics

The impact of estimation errors on CDO pricing

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Another interesting, nicely written paper about valuating and pricing CDOs is “The Economics of Structured Finance” from Coval, Jurek, and Stafford which just appeared in the Journal of Economic Perspectives. It nicely complements the paper of Arora, Barak, Brunnermeier, and Ge titled “Computational Complexity and Information Asymmetry in Financial Products” (see also here). The authors argue that already small estimation errors in correlation and probability of default (of the underlying loans) can have devastating effect on the overall performance of a tranche. Whereas the senior tranches remain quite stable in the presence of estimation errors, the overall rating of the junior and mezzanine tranches can be greatly affected. Intuitively this is clear, as the junior and the mezzanine tranches act as a cushion for the senior tranches (and in turn the junior tranches are a protection of the mezzanine tranches). What is not so clear though at first is that this effect is so pronounced, i.e., smallest estimation errors lead to a rapid decline in credit quality of these tranches. In fact, what happens here is that the junior and mezzanine tranches pay the price for the credit enhancement of the senior tranches. And the stability of the latter with respect to estimation errors comes at the expense of highly sensitive junior and mezzanine tranches.

This effects becomes even more severe when considering CDO^2, where the loans of the junior and mezzanine tranches are repackaged again. These structures possess a very high sensitivity to slightest variations or estimation errors in the probability of default or correlation.

In both cases, slight impressions in the estimation can have severe impacts. But also, considering it the other way around, slight changes in the probability of default or the correlation due to changed economic conditions can have devastating effect on the value of the lower prioritized tranches.

So if you are interested in CDOs, credit enhancement, and structured finance you should give it a look.

Written by Sebastian

December 6, 2009 at 4:32 pm

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  1. […] ultimately limit the amount of rationality that we can get, into account (I wrote about this before here, here, and here). In fact, I am convinced that these aspects will play an important role in the […]

  2. […] (a) Rents: Landlords face the problem that the tenant’s credit quality is basically unknown. Often, a statement about the tenant’s income and liabilities should help to better estimate the risk of default. But this procedure can, at best, serve as an indicator. So why not using the same process to securitize the rent cash flows and sell the corresponding tranches back to the landlords. This would have several upsides. First of all, the landlord obtains a significantly more stable cash flow and depending on the risk appetite could even invest in the more subordinated tranches. This could potentially reduce rents as the risk premium charged by the landlord due to his/her potentially risk averse preference could be reduced to the risk neutral amount (plus some spreads, e.g., operational and structuring costs). The probability of default could be significantly easier estimated for the pooled rent cash flows as due to diversification it is well approximated by the expected value (maybe categorized into subclasses according to credit ratings). Of course, one would have to deal with problems such as adverse selection and the potentially hard task to estimate the correlation – which can have a severe impact on the value of the tranches (see my post here). […]

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