Wednesday, April 1, 2009

Hiding the Copula and Other Tales

Well, very late, I've read about the formula at the center of the storm.

It's supposed to have hidden risk. I'm looking at Chart 5 - does this hide risk? It doesn't look like it (although I'm not sure why it is not symmetric about zero or why the risk appears linear with changes in "correlation", off hand). I mean, the author is clearly showing a sensitivity to correlation.

The insight is a pretty straight-forward application of the properties of a Markov process. From what I can tell, the mathematics of modeling survival rates (hazard rates) did two things. It generalized the mathematical problem AND it allowed people to use different estimates/estimators for the model inputs. The latter may have been more critically important, because it's not at all clear how much information is in credit spreads to begin with, right?

Anyway, Paul Wilmott thinks Gaussian Copula is not robust, but Black-Scholes is. Off hand, it's not easy to see what they are after with that. Both have Gaussian assumptions. You might argue that covariances are more sensitive to leptokurtosis than, say, standard deviation estimates, or something; but, given the Wilmott-Taleb emphasis on outliers, you'd think they would welcome that (if it were true).

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