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. His method was adopted by everybody from bond investors and Wall Street banks to ratings agencies and regulators. And it became so deeply entrenched--and was making people so much money--that warnings about its limitations were largely ignored. 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. David X. Li, it's safe to say, won't be getting that Nobel anytime soon. One result of the collapse has been the end of financial economics as something to be celebrated rather than feared. And Li's Gaussian copula formula will go down in history as instrumental in causing the unfathomable losses that brought the world financial system to its knees.
His method was adopted by everybody from bond investors and Wall Street banks to ratings agencies and regulators. And it became so deeply entrenched--and was making people so much money--that warnings about its limitations were largely ignored.
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.
David X. Li, it's safe to say, won't be getting that Nobel anytime soon. One result of the collapse has been the end of financial economics as something to be celebrated rather than feared. And Li's Gaussian copula formula will go down in history as instrumental in causing the unfathomable losses that brought the world financial system to its knees.
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. David X. Li, it's safe to say, won't be getting that Nobel anytime soon. One result of the collapse has been the end of financial economics as something to be celebrated rather than feared. And Li's Gaussian copula formula will go down in history as instrumental in causing the unfathomable losses that brought the world financial system to its knees.
The risk was further systematized by the use of David X. Li's Gaussian copula model function to rapidly price Collateralized debt obligations based on the price of related Credit Default Swaps.[17][18] This formula assumed that the price of Credit Default Swaps was correlated with and could predict the correct price of mortgage backed securities. Because it was highly tractable, it rapidly came to be used by a huge percentage of CDO and CDS investors, issuers, and rating agencies.[18] According to one wired.com article[citation needed]: "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... Li's Gaussian copula formula will go down in history as instrumental in causing the unfathomable losses that brought the world financial system to its knees."
Another probable cause of the crisis -- and a factor that unquestionably amplified its magnitude -- was widespread miscalculation by banks and investors of the level of risk inherent in the unregulated collateralized debt obligation and Credit Default Swap markets. Under this theory, banks and investors systematized the risk by taking advantage of low interest rates to borrow tremendous sums of money that they could only pay back if the housing market continued to increase in value. The risk was further systematized by the use of David X. Li's Gaussian copula model function to rapidly price Collateralized debt obligations based on the price of related Credit Default Swaps.[17][18]
The risk was further systematized by the use of David X. Li's Gaussian copula model function to rapidly price Collateralized debt obligations based on the price of related Credit Default Swaps.[17][18]
Anyway, Li's formula doesn't systematise or quantify the risk. It prices it. And, under arbitrage pricing, the price of a credit instrument has nothing to do with the "actual" probability of default but is just related to a "market implied" probability of default.
In other words, they were pricing these things based upon magic? Conservatives want live babies so they can raise them to be dead soldiers. - George Carlin
For instance, under arbitrage pricing the price of a futures contract depends only on the spot price and the interest rates, not on the probability distribution of future price movements. Which explains this. Most economists teach a theoretical framework that has been shown to be fundamentally useless. -- James K. Galbraith
Also, CDO (or CDS) prices have nothing (a priori) to do with actual default probability. Most economists teach a theoretical framework that has been shown to be fundamentally useless. -- James K. Galbraith
I mean the banks' toxic assets. Most economists teach a theoretical framework that has been shown to be fundamentally useless. -- James K. Galbraith
without Li's formula or CDS prices the Bank's toxic assets cannot be priced.
WTF, over?
Cannot be priced? Are we talking "physically impossible in this Universe" or "we're too stupid to figure-out what the price is without a bogus mathematical statement to play with"?
The effect on the securitization market was electric. Armed with Li's formula, Wall Street's quants saw a new world of possibilities. And the first thing they did was start creating a huge number of brand-new triple-A securities. Using Li's copula approach meant that ratings agencies like Moody's--or anybody wanting to model the risk of a tranche--no longer needed to puzzle over the underlying securities. All they needed was that correlation number, and out would come a rating telling them how safe or risky the tranche was.
As a result, just about anything could be bundled and turned into a triple-A bond--corporate bonds, bank loans, mortgage-backed securities, whatever you liked. The consequent pools were often known as collateralized debt obligations, or CDOs. You could tranche that pool and create a triple-A security even if none of the components were themselves triple-A. You could even take lower-rated tranches of other CDOs, put them in a pool, and tranche them--an instrument known as a CDO-squared, which at that point was so far removed from any actual underlying bond or loan or mortgage that no one really had a clue what it included. But it didn't matter. All you needed was Li's copula function. The CDS and CDO markets grew together, feeding on each other. At the end of 2001, there was $920 billion in credit default swaps outstanding. By the end of 2007, that number had skyrocketed to more than $62 trillion. The CDO market, which stood at $275 billion in 2000, grew to $4.7 trillion by 2006.
The CDS and CDO markets grew together, feeding on each other. At the end of 2001, there was $920 billion in credit default swaps outstanding. By the end of 2007, that number had skyrocketed to more than $62 trillion. The CDO market, which stood at $275 billion in 2000, grew to $4.7 trillion by 2006.
The context of the document is that a professional credit rater has told his superiors that he needs to examine the mortgage loan files to evaluate the risk of a complex financial derivative whose risk and market value depend on the credit quality of the nonprime mortgages "underlying" the derivative. A senior manager sends a blistering reply with this forceful punctuation:Any request for loan level tapes is TOTALLY UNREASONABLE!!! Most investors don't have it and can't provide it. [W]e MUST produce a credit estimate. It is your responsibility to provide those credit estimates and your responsibility to devise some method for doing so.
Any request for loan level tapes is TOTALLY UNREASONABLE!!! Most investors don't have it and can't provide it. [W]e MUST produce a credit estimate. It is your responsibility to provide those credit estimates and your responsibility to devise some method for doing so.
To be more precise:
the price and [price-]implied creditworthiness of a CDO have precious little to do with the underlying securities. Most economists teach a theoretical framework that has been shown to be fundamentally useless. -- James K. Galbraith
I've heard of creating markets, but this is ridiculous, no? Conservatives want live babies so they can raise them to be dead soldiers. - George Carlin
I've heard of creating markets, but this is ridiculous, no?
"Expected value" pricing is exceedingly difficult. "Arbitrage pricing" much less so. A similar phenomenon occurred with "vanilla" derivatives (such as ordinary call options) - before Black-Scholes-Merton pricing was "expected value pricing" and people had to carefully consider the actual probabilities of future stock price movements. After Black-Scholes-Merton pricing became decoupled from market forecasting and the market for "vanilla" derivatives exploded.
But vanilla equity derivatives are continuously hedgeable in a way that credit derivatives are not. What happened with CDS and CDO was qualitatively (and now visibly in their consequences) very different. Most economists teach a theoretical framework that has been shown to be fundamentally useless. -- James K. Galbraith
Hedging against changes in the implied volatility of options is standard fare in options trading. Why not hedging against changes in the correlation given by CDS prices?
Then again, it is possible that credit risk cannot be hedged but only insured... Most economists teach a theoretical framework that has been shown to be fundamentally useless. -- James K. Galbraith
Then again, it is possible that credit risk cannot be hedged but only insured...
One result of the collapse has been the end of financial economics as something to be celebrated rather than feared.
I find the very existence of "financial economics" offensive, quite honestly. If people want to study finance, they should go study finance.
I'd celebrate its collapse if it were clear to me the lessons has been learned. Maybe trying to marry economics and mathematics into a field dedicated to educating tomorrow's Bernie Madoffs, instead of a field that's supposed to explain how households and businesses make decisions about money and goods, wasn't such an awesome idea?
Stick a bunch of yokels from accounting and finance and other B-school silliness -- people who think Jude Wanniski drawing pictures on a napkin for Dick Cheney constitutes academic research -- into a social science. What could go wrong?
Nobody could've predicted.... Conservatives want live babies so they can raise them to be dead soldiers. - George Carlin
we need departments of political economy and instead we get departments of mathematical finance
[Li] took a notoriously tough nut--determining correlation, or how seemingly disparate events are related--and cracked it wide open with a simple and elegant mathematical formula ...
The unfortunate truth is:
It appears that the empirical input needed to apply Li's formula was CDS price data. Most economists teach a theoretical framework that has been shown to be fundamentally useless. -- James K. Galbraith
Worse, the process the equation describes is not reversible. The transactions based on the equation can not be uncopulated. The markets are well and truly "copulated!" As the Dutch said while fighting the Spanish: "It is not necessary to have hope in order to persevere."
