Gaussian Copula

So how did Credit Default Swap (CDS) end up being the financial weapon of mass destruction? No one actually knows the number (since these trades are opaque to us), but we think this is what happened:

CDS is a derivative. That is to say, it is an insurance contract on "something"; this "something" being collateral debt obligations (CDO), the sliced-and-diced securities that take in a bunch of questionable loans and create AAA bonds out of them.

Now if you're a financial institution, then you are concerned about the risk of these CDOs, and the risk of these CDOs will determine their values. Very risky? then the price of these CDOs will be low, and vice versa [1].

Well, banks had no way of valuing this risk, because the underlying loans for these CDOs can number in the thousands- to model all that would have been too intractable. If you can't value them, then you can't buy them.

That's when Wall Street hit on this idea: why not use the value of the options made on the CDOs to value the CDOs themselves? In other words:

• Efficient market says that price encapsulates all the information available
• CDSs are insurance contracts made on CDOs
  
• These CDSs are traded are certain prices
• therefore, these prices tell you how to value these CDOs
  

Financial alchemy! Now that you know how to price these CDOs, then it's just another financial instrument that you can trade like cattle.

One slight problem. The assumption that these CDS derivatives are made in "efficient market" turned out to be horribly wrong. To see how badly you can abuse the market, consider this example:

• Bank A bought XYZ CDO at $100M
• Bank A creates two fake brokerage firms: Stool Pigeon LLC and Suckers Inc.
• Stool Pigeon LLC and Suckers Inc buy and sell CDS on XYZ CDO (derivatives) to and from each other at completely made-up prices. Since one subsidiary's loss and another subsidiary's gain, these sham transactions cost Bank A zero dollars.
• By manipulating CDS prices, Bank A just manipulated XYZ CDO valuation
  
• Bank A then sells XYZ CDO to Iceland at $110M. Profit!
  

Since CDS was completely unregulated (something that will no longer be true), we have no idea to what extent the CDS market was gamed in this fashion. However, the fact that the notional value of these contracts got up to $45 trillion in 2007 (in contrast, the GDP of planet Earth was about $54 trillion in 2007), there was some sense that something was wrong.

Something was wrong.

[1] The risk here is not just default risk, but its correlation risk. I'm going to gloss over that for the sake of expositional clarity.