Sat, 09 Jul 2011

The Formula That Killed Wall Street is Alive and Well

The Gaussian Copula which used to be the standard model for valuing CDOs has been described as the The Formula That Killed Wall Street. After the crisis, several alternatives to the Gaussian copula have become popular for CDO valuation.

But there are many other areas where Gaussian copulas still hold sway. Last month, the Basle Committee on Banking Supervision published Operational Risk Supervisory Guidelines for the Advanced Measurement Approaches. The paper notes that the most common method of dealing with dependence in modelling operational risk is by use of copulas; and “Of the banks using Copulas, most (83%) use a Gaussian copula.” In addition about 17% of banks, used a correlation matrix which is even worse than a Gaussian copula.

Faced with this clearly unsatisfactory situation, the BCBS pushes back against this in the mildest possible way:

Assumptions regarding dependence should be conservative given the uncertainties surrounding dependence modelling for operational risk. Consequently, the dependence structures considered should not be limited to those based on Normal or Normal-like (eg T- Student distributions with many degrees of freedom) distributions, as normality may underestimate the amount of dependence between tail events. (para 229)

Not only is the Gaussian copula alive and well, the regulators do not seem to feel any sense of urgency in changing this state of affairs.

Posted at 22:26 on Sat, 09 Jul 2011     4 comments     permanent link

Comments...

Vivek wrote on Sun, 10 Jul 2011 11:22

Re: The Formula That Killed Wall Street is Alive and Well

Sir, could you kindly mention the other alternatives that have become popular for CDO valuation? Thanks!

• Prof. Jayanth R. Varma wrote on Mon, 11 Jul 2011 10:35

  Re: Re: The Formula That Killed Wall Street is Alive and Well
  

  Within the copula framework, non Gaussian copulas like the variance gamma and the normal inverse which were suggested pre-crisis have become more popular now. There is also greater interest in reduced form models which add a systemic default intensity to the standard (correlated) individual default intensities.

Dinesh Chaudhary wrote on Thu, 11 Aug 2011 14:12

Re: The Formula That Killed Wall Street is Alive and Well

Dear Sir,

RBI draft IRB guidelines have come. Gaussian copula is an integral part of IRB capital equation. While in CDO pricing, we are looking at unconditional portfolio loss distribution (by calculating conditional port loss at various economic states and then using gaussian quadrature to find the unconditional loss dist); for IRB capital, the regulator calculates conditional loss at a specific economic state (worst 0.01% to be precise). But the formula remains the same. So we can expect default dependence b/w borrowers to be understated (though BIS has increased correlation assumption of large banks by 25% in B-III), as gaussian copula by construct would not capture simultaneous tail events b/w asset values of borrowers (this is on top of various other weaknesses of IRB, major one being assuming infinitely granular portfolio, even when most of the bank failures may be attributed to concentration risk: Table 6 in http://www.bis.org/publ/bcbs_wp13.pdf).

Regards

Trambak Banerjee wrote on Thu, 24 May 2012 00:30

Re: The Formula That Killed Wall Street is Alive and Well

Among the non gaussian copulas, there are these archimedean copulas which can handle simultaneous occurence of tail events better (for example the Gumbel copula especially in AMA Operational Risk modeling). However the challenege here is that there is no straightforward way of implementing these copulas in a multidimensional framework. I believe the theory still needs to be developed.