When the price of a credit default swap goes up, that indicates that default risk has risen. Li's breakthrough was that instead of waiting to assemble enough historical data about actual defaults, which are rare in the real world, he used historical prices from the CDS market. It's hard to build a historical model to predict Alice's or Britney's behavior, but anybody could see whether the price of credit default swaps on Britney tended to move in the same direction as that on Alice. If it did, then there was a strong correlation between Alice's and Britney's default risks, as priced by the market. Li wrote a model that used price rather than real-world default data as a shortcut (making an implicit assumption that financial markets in general, and CDS markets in particular, can price default risk correctly).
... "making an implicit assumption that financial markets in general, and CDS markets in particular, can price default risk correctly." Isn't it even worse than this? If I'm a CDS trader making a buy/sell decision about Alice (a decision that will help set the price of the CDS), I am most likely trying to use all available information, including Britney's behavior, into account when deciding whether to transact at a given price. Critical to my accurately pricing the risk would be the correlation between Alice's and Britney's default risks. If I'm going to price the default risk correctly, I must have a good way of coming up with this correlation.
But if I have a good way of accurately determining this correlation, why in the world did we need Li's copula formula? It's circular: I need accurate correlations to correctly price default risk, and Li's formula needs accurately priced default risk to back out the correlations. How could the financial services industry rely on a method that required accurate correlation estimates to determine accurate correlation estimates? Is this as monumentally stupid as it sounds, or am I missing something?
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