That would be the Gaussian copula formula, see graphic, invented by David X. Li while working at JP Morgan Chase and articulated in his (2000) paper: ‘On Default Correlation: A Copula Function Approach” (For those unaware, a “copula” is a statistical device employed to couple the behavior of two or more variables) and blamed for “wrecking your 401k” according to an article ('A Formula for Disaster’) appearing in WIRED in 2009.
First, examine the Gaussian copula equation itself for which I have pointed out (in previous earlier posts) the key defects: simply copying equation fragments or quantitative components, e.g. from physics or discrete mathematics, plugging them into artificially contrived expressions and extrapolating from these in an indiscriminate way. Thus, one obtains more of an intellectual Frankenstein monster that never should have seen the light of day any more than a four-headed baby with a pointed tail.
In normative mathematics, equations are derived from a self-consistent basis and a pre-existing modus operandi and history. For example, the Riemann Zeta function, or the Euler Gamma function.
Consider, for example, the probability density equation for locating a particle between x1 and x2 (for which the quantities to the right of the integral sign are the wave function (y) and its complex conjugate (y*).
This important equation of quantum mechanics can be compared with Li’s Gaussian copula probability expression earlier. Now – what allows or enables us to pose an equal sign between the probability density(P) and the integral of the two wave functions? (After all, it is illegitimate to simply toss and equal sign into an equation as a fait accompli with no rational basis!)
What allows us to do this is the foreknowledge that the wave function is normalized so that effectively the probability that a given particle is somewhere along the x-axis is 1. (Fig. 2b)
I submit no such similar normalization applied to the Pr[T_A, T_B] of Li’s copula formula. More over, his misuse of the distribution functions (F_A(1)) and (F_B(1)) would appall any genuine mathematician.
Each is actually based upon significant uncertainties via survival law distributions which can vary enormously. There is no way to normalize any probability based on (T_A, T_B so there is no way to equate Pr[T_A, T_B] to anything on the left side. The equal sign is dangerous recklessness masquerading as math. And the copula (PHI2: first variable on the right side) makes it even more an abomination, since ostensible survival law uncertainties are “coupled” to try to arrive at a single number (usually the correlation parameter). This is insanity!
The hideous Gaussian copula equation has then mixed chalk and cheese to new and hitherto unbelievable levels. Functions from human actuarial tables, generic survival distribution laws, a “probability” function based on coupling two financial entities as “humans” in an actuarial table – then tossing in a correlation coefficient which nearly every Wall Street quant would likely be orgiastic over. (Since he can pin it down to one number, simplifying his financial analysis routines).
Can you imagine a quantum physicist performing an analogous desecration of the probability density equation by incorporating standard Gaussian distributions (not normalized) and mixing electrons with macroscopic entities like marbles – then deeming the wave function is capable of capturing the survival probabilities of both marbles and electrons? And – to add injury to insult, fabricating a “correlation coefficient” to relate (couple) survivable marbles to electrons? That quantum physicist would be run out of his lab so quickly he wouldn’t know what happened!
But David X. Li got away with it because too many banks and money grubbing capitalists were salivating to make money off the home owners, roped into third rate mortgages. Thereby a quant - too clever by half nearly brought the entire financial system crashing down in 2008, by creating a pseudo-mathematical fabrication that never should have emerged in the real world. And certainly not used to operate on CDOs, CDS or anything else, then sold to unwary investors - with the added fraud of fake credit ratings - by the likes of Moody's, Standard & Poor's.. See e.g.
My suggestion for what it’s worth? We need to get all these “quants” out of their finance ivory towers and back to doing REAL physics and mathematics for a change. Our financial futures may well depend on it, especially if rigid regulation doesn’t emerge to control their semi-quantified phantasmagorias.
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