Economia
A fórmula que matou Wall Street - receita para o desastro
Recipe for Disaster: The Formula That Killed Wall Street - Felix Salmon
For five years, Li's formula, known as a Gaussian copula function, looked like an unambiguously positive breakthrough, a piece of financial technology that allowed hugely complex risks to be modeled with more ease and accuracy than ever before. With his brilliant spark of mathematical legerdemain, Li made it possible for traders to sell vast quantities of new securities, expanding financial markets to unimaginable levels.
Then the model fell apart. Cracks started appearing early on, when financial markets began behaving in ways that users of Li's formula hadn't expected. The cracks became full-fledged canyons in 2008—when ruptures in the financial system's foundation swallowed up trillions of dollars and put the survival of the global banking system in serious peril... In the world of finance, too many quants see only the numbers before them and forget about the concrete reality the figures are supposed to represent. They think they can model just a few years' worth of data and come up with probabilities for things that may happen only once every 10,000 years. Then people invest on the basis of those probabilities, without stopping to wonder whether the numbers make any sense at all.
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Here's what killed your 401(k) David X. Li's Gaussian copula function as first published in 2000. Investors exploited it as a quick—and fatally flawed—way to assess risk. A shorter version appears on this month's cover of Wired.
ProbabilitySpecifically, this is a joint default probability—the likelihood that any two members of the pool (A and B) will both default. It's what investors are looking for, and the rest of the formula provides the answer. | Survival timesThe amount of time between now and when A and B can be expected to default. Li took the idea from a concept in actuarial science that charts what happens to someone's life expectancy when their spouse dies. | EqualityA dangerously precise concept, since it leaves no room for error. Clean equations help both quants and their managers forget that the real world contains a surprising amount of uncertainty, fuzziness, and precariousness. |
CopulaThis couples (hence the Latinate term copula) the individual probabilities associated with A and B to come up with a single number. Errors here massively increase the risk of the whole equation blowing up. | Distribution functionsThe probabilities of how long A and B are likely to survive. Since these are not certainties, they can be dangerous: Small miscalculations may leave you facing much more risk than the formula indicates. | GammaThe all-powerful correlation parameter, which reduces correlation to a single constant—something that should be highly improbable, if not impossible. This is the magic number that made Li's copula function irresistible. |
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Os Limites Da Análise Financeira Quantitativa
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Links de artigos que examinam a contribuição de modelos estadísticos quantitativos de modelar risco e incerteza para a emergência da crise atual:
A dash of this integer and a dab of that regression
March 30, 2009 11:11 PM by Tim Swanson
Wondering...
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Modelo Errado
Financial meltdown blamed on risk models
Web posted at: 2/14/2009 9:20:18
Source ::: FINANCIAL TIMES
By Norma Cohen
The failure of banks to count, manage and hedge their risks over the past decade is responsible both for the fantastic growth before...
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Uma Proposta De Reforma Do Sistema Financeiro
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Economia