We want the formula, we want the formula, the actual equation of CDOs

Like the scene from the The Return of the Secaucus 7, earlier I was asking for details on the actual mathematics upon which derivatives, CDOs (Collateralized debt obligations) are based.

Wired Magazine has answered the call in the article Recipe for Disaster. This article outlines the actual mathematical formula, a Gaussian copula, upon which so many derivatives are based.

In 2000, while working at JPMorgan Chase, Li published a paper in The Journal of Fixed Income titled "On Default Correlation: A Copula Function Approach." (In statistics, a copula is used to couple the behavior of two or more variables.) Using some relatively simple math—by Wall Street standards, anyway—Li came up with an ingenious way to model default correlation without even looking at historical default data. Instead, he used market data about the prices of instruments known as credit default swaps.

You must read the entire article, yes they mention mathematics, but they are explaining it all in layman's terms.

One thing I did not know, pointed out in the article, is that there are no limits on the number of CDS (credit default swaps) that can be issued against one borrower. CDSes are literally unconstrained by are subject to mark-to-market.

Back to the formula it appears that it was not based at all on historical data of actual mortgage defaults. It is purely based on the assumption that credit default swaps are correctly priced and accurate.

In other words, credit default swaps are little insurance policies on the possibility of default. One can issue multiple little insurance policies on just one data point (i.e. one borrower). So, this formula based it's risk assessment by claiming the final total price on another variable, i.e. a CDS, which has no bounds on issuance and is traded in an open market, is in perfect equilibrium. In other words, the gaussian copula used assumed the CDS is correctly valued.

Pause for a moment. See a major assumption flaw yet? Now, in our bubble world does anyone believe anywhere, the open market is correctly priced to the actual real values or risk? Maybe in a 11-dimensional universe during a delta function.

Even worse, CDSes are a new vehicle as well, only in existence about a decade. Nice historical track record, empirical data there too!

So where is the bad math? The bad math is trying to boil down the world as having a scalar, or just one correlation multiple. It just don't work that way, the world is not static and of course one cannot derive correlation from yet another vehicle, which of itself is not proved to historical data or even correlated in quantity to the actual underlying variable. Call it a mathematicians pipe dream or look at it as trying to reduce the universe to a 1 dimensional time invariant point on a pin.

The actual paper is here. The abstract:

This paper studies the problem of default correlation. We first introduce a random variable called "time-until- default" to denote the survival time of each defaultable entity or financial instrument, and define the default correlation between two credit risks as the correlation coefficient between their survival times. Then we argue why a copula function approach should be used to specify the joint distribution of survival times after marginal distributions of survival times are derived from market information, such as risky bond prices or asset swap spreads. The definition and some basic properties of copula functions are given. We show that the current CreditMetrics approach to default correlation through asset correlation is equivalent to using a normal copula function. Finally, we give some numerical examples to illustrate the use of copula functions in the valuation of some credit derivatives, such as credit default swaps and first-to-default contracts.

Can't be blamed? The formula creator, David Li, ran back to China and won't can't talk to the press. As I wade through the mathematics for myself, I'll probably post more later. Other math geeks reading this, please post your insights.

There is also an audio podcast on the mathematics, but with the same Wired author.

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Comments

this is the base concept

So, this is the base formula for many other models..
which is why they are going after this particular one.

I noticed they also said testing systems were black box.

Black box means no one has any idea of what is in side.

So, you could have inside accurate mathematical modeling...
or you could have a little gnome in there flipping a coin and spitting out a number.

That is seriously not good in terms of accuracy.

So, it's like so many did not understand the mathematics and models, did not bother to try to understand the mathematics or models and it sure appears like....
they did not get other mathematicians (this is mathematics, not physics...in the press they even get the expertise area wrong!) to review and validate these concepts.

It's like there is no peer review or something going on and when a new concept comes out, it should be peer reviewed and if they have any scientific integrity, well challenged.

I'll find out more but it sure seems like this guy wrote up this paper and a bunch of other guys who should have known better said "hell yeah" and took this and came up with a host of new "structured financial products".

I'm getting the impression there are trillions out there invested in fictional mathematical formulas that are not valid....

But this post are more like thoughts out loud. I have to go study much more for I do NOT have a PHD in structured financial, risk assessment, actuarial science, etc.

But upon first read, some of the assumptions just appear to be pure absolute caca. I mean basing a probability distribution on the pricing of another vehicle that is only 10 years old instead of actual historical data...

ok, that's from 1997 until now. What was happening in 1997? The housing bubble was assuredly seeded.

I figure if we can see the assumption flaws in a first pass...

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Are we sure David Li wasn't a plant?

I'm beginning to suspect that China has succeeded where Japan failed- in weaponizing trade to the point of being able to take down an entire country.

Are we sure David Li isn't a foreign spy meant to inject instability into western markets?

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Moral hazards would not exist in a system designed to eliminate fraud.

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Maximum jobs, not maximum profits.

And who/what does this so-called "pricing"???

"It is purely based on the assumption that credit default swaps are correctly priced and accurate."

And that corporate entity which determines the so-called value:

Markit, originally Markit Parnters, originally financed by JP Morgan Chase, Goldman Sachs, Citigroup and BankofAmerica.

What two guys were the primary traders in derivatives used in oil/energy, commodities and precious metals trading on their InterContinental Exchange: Goldman Sachs & Morgan Stanley.

What three banks handle 90% of the North American derivatives market?

Why, of course, JP Morgan Chase, Citigroup and BankofAmerica (50% with JP Morgan, and the other 50% split between Citigroup and BankofAmerica).

What is the crux of AIG's problem and why will their downfall cause the global economy (not to mention America's) to unravel in a most destructive manner? An infinite number of credit default swaps written against an incredibly shrinking number of borrowers.

And, oh yes, that electronic exchange where the bulk of credit default swaps are traded: Markit Wire (owned, of course, by Markit -- formerly SwapsWire).

See the connections? See also why capitalism is dead (you were sooo correct Mr. Covington and Mr. Marx) and why the economy is over?

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Multiple CDSs

Yes, there are no regulations on CDSs. I can buy 1 fire insurance policy on my house, and you may not buy any. If I could buy 10 on my own house, I would have a conflict of interest.

You can buy 10 CDSs on my bonds. This is the equivalent of you buying 10 fire insurance policies on my business. This is a bad idea.

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you bet your life

What an amazing house of cards with no intrinsic value, an escalating series of betting on the outcome of bets. Sad that when all this imaginary value collapsed, it ultimately crushed the underlying entities with actual intrinsic value.

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