financial mathematics

Bayes, Markov, and Conditional Probability in Finance Models

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Disclaimer: Not certain this is appropriate to EP. This is in the way of an introduction to some aspects of modeling and might be a bit arcane. It was inspired by a comment by RebelCapitalist and deals with econometric modeling. Enjoy.

Let's say we're interested in estimating the likelihood of some event x happening. x might be a loan default, upcoming regulations, getting hit by lightning, whatever. If we happen to know something about x, we can assign some probability P(x), play the numbers, and improve our chances of a good outcome. That's a big "if", and unless P = 1 we can still lose; still, that's the best we can do.

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

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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.