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Recipe for Disaster: The Formula That Killed Wall Street(中国人的模型谋杀了华尔街)

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发表于 2009-2-26 00:20 | 显示全部楼层 |阅读模式
本帖最后由 I'm_zhcn 于 2009-3-1 02:52 编辑

Recipe for Disaster: The Formula That Killed Wall Street
http://www.wired.com/techbiz/it/magazine/17-03/wp_quant?currentPage=all
By Felix Salmon Email 02.23.09

wp_quant_f.jpg
In the mid-'80s, Wall Street turned to the quants—brainy financial engineers—to invent new ways to boost profits. Their methods for minting money worked brilliantly... until one of them devastated the global economy.
Photo: Jim Krantz/Gallery Stock

A year ago, it was hardly unthinkable that a math wizard like David X. Li might someday earn a Nobel Prize. After all, financial economists—even Wall Street quants—have received the Nobel in economics before, and Li's work on measuring risk has had more impact, more quickly, than previous Nobel Prize-winning contributions to the field. Today, though, as dazed bankers, politicians, regulators, and investors survey the wreckage of the biggest financial meltdown since the Great Depression, Li is probably thankful he still has a job in finance at all. Not that his achievement should be dismissed. He 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, one that would become ubiquitous in finance worldwide.

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.

How could one formula pack such a devastating punch? The answer lies in the bond market, the multitrillion-dollar system that allows pension funds, insurance companies, and hedge funds to lend trillions of dollars to companies, countries, and home buyers.

A bond, of course, is just an IOU, a promise to pay back money with interest by certain dates. If a company—say, IBM—borrows money by issuing a bond, investors will look very closely over its accounts to make sure it has the wherewithal to repay them. The higher the perceived risk—and there's always some risk—the higher the interest rate the bond must carry.

Bond investors are very comfortable with the concept of probability. If there's a 1 percent chance of default but they get an extra two percentage points in interest, they're ahead of the game overall—like a casino, which is happy to lose big sums every so often in return for profits most of the time.

Bond investors also invest in pools of hundreds or even thousands of mortgages. The potential sums involved are staggering: Americans now owe more than $11 trillion on their homes. But mortgage pools are messier than most bonds. There's no guaranteed interest rate, since the amount of money homeowners collectively pay back every month is a function of how many have refinanced and how many have defaulted. There's certainly no fixed maturity date: Money shows up in irregular chunks as people pay down their mortgages at unpredictable times—for instance, when they decide to sell their house. And most problematic, there's no easy way to assign a single probability to the chance of default.

Wall Street solved many of these problems through a process called tranching, which divides a pool and allows for the creation of safe bonds with a risk-free triple-A credit rating. Investors in the first tranche, or slice, are first in line to be paid off. Those next in line might get only a double-A credit rating on their tranche of bonds but will be able to charge a higher interest rate for bearing the slightly higher chance of default. And so on.
"...correlation is charlatanism"
Photo: AP photo/Richard Drew

The reason that ratings agencies and investors felt so safe with the triple-A tranches was that they believed there was no way hundreds of homeowners would all default on their loans at the same time. One person might lose his job, another might fall ill. But those are individual calamities that don't affect the mortgage pool much as a whole: Everybody else is still making their payments on time.

But not all calamities are individual, and tranching still hadn't solved all the problems of mortgage-pool risk. Some things, like falling house prices, affect a large number of people at once. If home values in your neighborhood decline and you lose some of your equity, there's a good chance your neighbors will lose theirs as well. If, as a result, you default on your mortgage, there's a higher probability they will default, too. That's called correlation—the degree to which one variable moves in line with another—and measuring it is an important part of determining how risky mortgage bonds are.

Investors like risk, as long as they can price it. What they hate is uncertainty—not knowing how big the risk is. As a result, bond investors and mortgage lenders desperately want to be able to measure, model, and price correlation. Before quantitative models came along, the only time investors were comfortable putting their money in mortgage pools was when there was no risk whatsoever—in other words, when the bonds were guaranteed implicitly by the federal government through Fannie Mae or Freddie Mac.

Yet during the '90s, as global markets expanded, there were trillions of new dollars waiting to be put to use lending to borrowers around the world—not just mortgage seekers but also corporations and car buyers and anybody running a balance on their credit card—if only investors could put a number on the correlations between them. The problem is excruciatingly hard, especially when you're talking about thousands of moving parts. Whoever solved it would earn the eternal gratitude of Wall Street and quite possibly the attention of the Nobel committee as well.

To understand the mathematics of correlation better, consider something simple, like a kid in an elementary school: Let's call her Alice. The probability that her parents will get divorced this year is about 5 percent, the risk of her getting head lice is about 5 percent, the chance of her seeing a teacher slip on a banana peel is about 5 percent, and the likelihood of her winning the class spelling bee is about 5 percent. If investors were trading securities based on the chances of those things happening only to Alice, they would all trade at more or less the same price.

But something important happens when we start looking at two kids rather than one—not just Alice but also the girl she sits next to, Britney. If Britney's parents get divorced, what are the chances that Alice's parents will get divorced, too? Still about 5 percent: The correlation there is close to zero. But if Britney gets head lice, the chance that Alice will get head lice is much higher, about 50 percent—which means the correlation is probably up in the 0.5 range. If Britney sees a teacher slip on a banana peel, what is the chance that Alice will see it, too? Very high indeed, since they sit next to each other: It could be as much as 95 percent, which means the correlation is close to 1. And if Britney wins the class spelling bee, the chance of Alice winning it is zero, which means the correlation is negative: -1.

If investors were trading securities based on the chances of these things happening to both Alice and Britney, the prices would be all over the place, because the correlations vary so much.

But it's a very inexact science. Just measuring those initial 5 percent probabilities involves collecting lots of disparate data points and subjecting them to all manner of statistical and error analysis. Trying to assess the conditional probabilities—the chance that Alice will get head lice if Britney gets head lice—is an order of magnitude harder, since those data points are much rarer. As a result of the scarcity of historical data, the errors there are likely to be much greater.

In the world of mortgages, it's harder still. What is the chance that any given home will decline in value? You can look at the past history of housing prices to give you an idea, but surely the nation's macroeconomic situation also plays an important role. And what is the chance that if a home in one state falls in value, a similar home in another state will fall in value as well?

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.

Probability
Specifically, 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 times

The 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.
        
Equality

A 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.
Copula

This 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 functions

The 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.
        
Gamma

The 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.


Enter Li, a star mathematician who grew up in rural China in the 1960s. He excelled in school and eventually got a master's degree in economics from Nankai University before leaving the country to get an MBA from Laval University in Quebec. That was followed by two more degrees: a master's in actuarial science and a PhD in statistics, both from Ontario's University of Waterloo. In 1997 he landed at Canadian Imperial Bank of Commerce, where his financial career began in earnest; he later moved to Barclays Capital and by 2004 was charged with rebuilding its quantitative analytics team.

Li's trajectory is typical of the quant era, which began in the mid-1980s. Academia could never compete with the enormous salaries that banks and hedge funds were offering. At the same time, legions of math and physics PhDs were required to create, price, and arbitrage Wall Street's ever more complex investment structures.

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.

If you're an investor, you have a choice these days: You can either lend directly to borrowers or sell investors credit default swaps, insurance against those same borrowers defaulting. Either way, you get a regular income stream—interest payments or insurance payments—and either way, if the borrower defaults, you lose a lot of money. The returns on both strategies are nearly identical, but because an unlimited number of credit default swaps can be sold against each borrower, the supply of swaps isn't constrained the way the supply of bonds is, so the CDS market managed to grow extremely rapidly. Though credit default swaps were relatively new when Li's paper came out, they soon became a bigger and more liquid market than the bonds on which they were based.

When the price of a credit default swap goes up, that indicates that default risk has risen. Li's breakthrough was that instead of waiting to assemble enough historical data about actual defaults, which are rare in the real world, he used historical prices from the CDS market. It's hard to build a historical model to predict Alice's or Britney's behavior, but anybody could see whether the price of credit default swaps on Britney tended to move in the same direction as that on Alice. If it did, then there was a strong correlation between Alice's and Britney's default risks, as priced by the market. Li wrote a model that used price rather than real-world default data as a shortcut (making an implicit assumption that financial markets in general, and CDS markets in particular, can price default risk correctly).

It was a brilliant simplification of an intractable problem. And Li didn't just radically dumb down the difficulty of working out correlations; he decided not to even bother trying to map and calculate all the nearly infinite relationships between the various loans that made up a pool. What happens when the number of pool members increases or when you mix negative correlations with positive ones? Never mind all that, he said. The only thing that matters is the final correlation number—one clean, simple, all-sufficient figure that sums up everything.

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.

At the heart of it all was Li's formula. When you talk to market participants, they use words like beautiful, simple, and, most commonly, tractable. It could be applied anywhere, for anything, and was quickly adopted not only by banks packaging new bonds but also by traders and hedge funds dreaming up complex trades between those bonds.

"The corporate CDO world relied almost exclusively on this copula-based correlation model," says Darrell Duffie, a Stanford University finance professor who served on Moody's Academic Advisory Research Committee. The Gaussian copula soon became such a universally accepted part of the world's financial vocabulary that brokers started quoting prices for bond tranches based on their correlations. "Correlation trading has spread through the psyche of the financial markets like a highly infectious thought virus," wrote derivatives guru Janet Tavakoli in 2006.

The damage was foreseeable and, in fact, foreseen. In 1998, before Li had even invented his copula function, Paul Wilmott wrote that "the correlations between financial quantities are notoriously unstable." Wilmott, a quantitative-finance consultant and lecturer, argued that no theory should be built on such unpredictable parameters. And he wasn't alone. During the boom years, everybody could reel off reasons why the Gaussian copula function wasn't perfect. Li's approach made no allowance for unpredictability: It assumed that correlation was a constant rather than something mercurial. Investment banks would regularly phone Stanford's Duffie and ask him to come in and talk to them about exactly what Li's copula was. Every time, he would warn them that it was not suitable for use in risk management or valuation.
David X. Li
Illustration: David A. Johnson

In hindsight, ignoring those warnings looks foolhardy. But at the time, it was easy. Banks dismissed them, partly because the managers empowered to apply the brakes didn't understand the arguments between various arms of the quant universe. Besides, they were making too much money to stop.

In finance, you can never reduce risk outright; you can only try to set up a market in which people who don't want risk sell it to those who do. But in the CDO market, people used the Gaussian copula model to convince themselves they didn't have any risk at all, when in fact they just didn't have any risk 99 percent of the time. The other 1 percent of the time they blew up. Those explosions may have been rare, but they could destroy all previous gains, and then some.

Li's copula function was used to price hundreds of billions of dollars' worth of CDOs filled with mortgages. And because the copula function used CDS prices to calculate correlation, it was forced to confine itself to looking at the period of time when those credit default swaps had been in existence: less than a decade, a period when house prices soared. Naturally, default correlations were very low in those years. But when the mortgage boom ended abruptly and home values started falling across the country, correlations soared.

Bankers securitizing mortgages knew that their models were highly sensitive to house-price appreciation. If it ever turned negative on a national scale, a lot of bonds that had been rated triple-A, or risk-free, by copula-powered computer models would blow up. But no one was willing to stop the creation of CDOs, and the big investment banks happily kept on building more, drawing their correlation data from a period when real estate only went up.

"Everyone was pinning their hopes on house prices continuing to rise," says Kai Gilkes of the credit research firm CreditSights, who spent 10 years working at ratings agencies. "When they stopped rising, pretty much everyone was caught on the wrong side, because the sensitivity to house prices was huge. And there was just no getting around it. Why didn't rating agencies build in some cushion for this sensitivity to a house-price-depreciation scenario? Because if they had, they would have never rated a single mortgage-backed CDO."

Bankers should have noted that very small changes in their underlying assumptions could result in very large changes in the correlation number. They also should have noticed that the results they were seeing were much less volatile than they should have been—which implied that the risk was being moved elsewhere. Where had the risk gone?

They didn't know, or didn't ask. One reason was that the outputs came from "black box" computer models and were hard to subject to a commonsense smell test. Another was that the quants, who should have been more aware of the copula's weaknesses, weren't the ones making the big asset-allocation decisions. Their managers, who made the actual calls, lacked the math skills to understand what the models were doing or how they worked. They could, however, understand something as simple as a single correlation number. That was the problem.

"The relationship between two assets can never be captured by a single scalar quantity," Wilmott says. For instance, consider the share prices of two sneaker manufacturers: When the market for sneakers is growing, both companies do well and the correlation between them is high. But when one company gets a lot of celebrity endorsements and starts stealing market share from the other, the stock prices diverge and the correlation between them turns negative. And when the nation morphs into a land of flip-flop-wearing couch potatoes, both companies decline and the correlation becomes positive again. It's impossible to sum up such a history in one correlation number, but CDOs were invariably sold on the premise that correlation was more of a constant than a variable.

No one knew all of this better than David X. Li: "Very few people understand the essence of the model," he told The Wall Street Journal way back in fall 2005.

"Li can't be blamed," says Gilkes of CreditSights. After all, he just invented the model. Instead, we should blame the bankers who misinterpreted it. And even then, the real danger was created not because any given trader adopted it but because every trader did. In financial markets, everybody doing the same thing is the classic recipe for a bubble and inevitable bust.

Nassim Nicholas Taleb, hedge fund manager and author of The Black Swan, is particularly harsh when it comes to the copula. "People got very excited about the Gaussian copula because of its mathematical elegance, but the thing never worked," he says. "Co-association between securities is not measurable using correlation," because past history can never prepare you for that one day when everything goes south. "Anything that relies on correlation is charlatanism."

Li has been notably absent from the current debate over the causes of the crash. In fact, he is no longer even in the US. Last year, he moved to Beijing to head up the risk-management department of China International Capital Corporation. In a recent conversation, he seemed reluctant to discuss his paper and said he couldn't talk without permission from the PR department. In response to a subsequent request, CICC's press office sent an email saying that Li was no longer doing the kind of work he did in his previous job and, therefore, would not be speaking to the media.

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.

As Li himself said of his own model: "The most dangerous part is when people believe everything coming out of it."

— Felix Salmon (felix@felixsalmon.com) writes the Market Movers financial blog at Portfolio.com.

David X. Li(中文名是什么?)是Quant中的传奇,因为他发明的Gaussian copula公式是CDS,CDO产生的基础。
可以说是David X Li一手造就了今天波及全球摧毁华尔街的金融危机。现在老李同志在北京出任中国国际金融有限公司风险管理主管。

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发表于 2009-2-26 01:06 | 显示全部楼层
《连线》17-03期封面:导致华尔街灾难的模型http://www.sina.com.cn  2009年02月25日 15:18  新浪财经

图为《连线》17-03期封面
点击此处查看全部财经新闻图片


  新浪财经讯 本期《连线杂志》介绍了近乎荒诞、且另美国和全球金融体系摇摇欲坠的事件:所有全球金融精英人士对一个中国人构建的金融计量模型几乎像圣经一样顶礼膜拜,但精英们忘却了模型的限制条件的警告,最终使它失效,他们也付出了可怕的代价。

  人们此前总认为像David X. Li这样有数学天才者可能在某日会得到诺贝尔经济学奖的眷顾,因金融经济学者,甚至华尔街的这类人才的确此前也获得过诺奖。DavidX. Li的开创性工作是度量投资风险。与以前获得诺奖学者的贡献相比,他的办法更有影响力、更快速。但就在晕头转向的银行家、政治家、监管者和投资者整肃自大萧条以来最严重的金融残局时,Li可能更感庆幸的是自己还有一份金融业的工作。

  David X. Li从事的研究是确定资产间的相关性(correlation),或称之为一些全异的事件似乎如何有关联,并以简单和规范的数学模型做描述。他构建的被称之为线性相依关系(Gaussian copula function)的模型几乎像是金融界毫无疑义的突破,是一项令巨大而极其复杂的风险,能以数学手段比以前更容易和精确地进行描述和度量的新型金融科技。

  Li的方法能够让数量巨大的新型证券进行交易,将金融市场扩展至几乎不可思议的水平。他的方法被广泛使用,从债券投资者到华尔街,从评级机构和监管者。它已深深地植根于业内,并让一些人赚到了钱。但不幸的是精英们忘却了模型的限制条件的警告,最终使它失效。当因金融系统基础动摇而爆发的危机吞噬了数万亿美元,使全球银行体系处于严重危险之中时,David X. Li的模型变为纯粹的废物。如同给世界金融体系带来一落千丈的无底亏损的创新一样,他的模型也创新性地沦落至历史的底部。

  令人们惊诧的问题是,一个计量模型怎会给金融界带来如此毁灭性的结果。答案在于让养老基金、保险公司和对冲基金向企业、各国家和购房者发放数万亿美元贷款的庞大债券市场。企业若想发行债券借款,投资者会严密审查公司账目,以确认公司能有足够资金偿还贷款。若放款人认为贷款的风险很高,他们索要的利息率也会更高。

  债券投资者通常也对由数百乃至上千个住房按揭贷款构成的资产池进行投资。现在涉及的这类活动总规模大得惊人:美国购房人所欠下总债务已达11万亿美元。然而,按揭贷款资产池的情况比债券市场更混乱。这类投资中,因购房者每月集体偿还的现金量,是取决于已获得再融资的购房人数量和因违约未还款人的函数,因此投资不存在保证性的确定利率。同样,如此借贷活动也无固定的还款到期日。因购房人以无法预测的时间偿还按揭,例如购房者决定出售房产,池内的还款总数也是无规律可循。最令人头痛的问题是,尚无法找到给违约出现机会确定一个单个概率值的办法(即概率越高、贷款损失风险越大)。

  华尔街解决的办法是,通过一个称之为划分等级(tranching)的办法,它将整个池内各类资产进行分级,创建以标注3A评级的无风险的安全债券。位于第一级别的投资者能够最先获得偿还债息,其他类别投资者虽因违约风险较高而评级稍低,但可收取更高的利率。

  评级机构和投资者之所以对3A级的债券感到放心是因为他们相信,成百上千的贷款购房者不会在同一时间内发生违约行为。某人可能会丢掉工作,其他人可能生病。但这些都是不会给按揭贷款资产池整体带来重大影响的个体不幸事件。但所有的灾难性事件并非都是个体性,等级划分作法并未解决资产池风险的全部问题。

  如房价可能下跌的事件会在同时影响到一大批人。如某购房者家附近住房价值下跌,此人住房的资产净值也同样会下降,他(她)周边邻居的房产会跟着下跌的可能性更大。一旦此购房人还款违约,周边邻居违约的可能性也更大。这就是所谓的相关性,即一个变量变化与另一些变量的关系和影响程度,度量此关系和关系程度高低是确定按揭贷款债券风险大小的重要部分。

  只要投资者能够对风险定价,他们一定喜欢它。他们厌恶的是不确定性,即无法确定风险大小。正因如此,债券投资者、按揭贷款放款者拼命地想要找到能够度量、模拟相关性,并对其进行定价的方法。在计量模型应用于金融市场前,令投资者对按揭贷款资产池中投资感到安全的唯一时刻是不存在风险,即这类债券都是由联邦政府通过房地美和房利美两家企业进行隐形担保。

  随着全球金融市场在1990年代快速扩张,数以万亿计美元要进入市场,若投资者能够找到确定任何资产间的相关关系的方法,这些资金便能顺利进入市场。但这是个折磨人的痛苦问题,特别是考虑到成百上千类资产在时刻不停波动和变化。无论是谁解决了这样一个问题不仅会赢得华尔街永恒的感谢,而且非常可能会引起诺贝尔奖委员会的关注。

  此时巧合的是,在摩根大通工作的David X. Li2000年在《固定收益杂志》(Journal of Fixed Income)上发表了一份名为“On Default Correlation: A Copula Function Approach”的论文。论文以相对简单的数学方法,在不用参考历史默认数据(historical default data)情形下,以一种非常聪明方式构造了违约相关性的模型。取而代之,他使用信用违约调期产品(creditdefault swap,CDS)价格的市场数据。

  由于针对每个借款人发行的CDS数量可以无限,调期产品供应并不制约债券供应方式,所以处于开创阶段的CDS市场以异乎寻常速度增长,所向披靡,规模大大地超过了其作为基础的债券市场。

  尽管David X. Li现已淡出人们当前讨论金融危机原因的视野,并于去年离开美国回到中国,开始负责北京的中国金融公司风险管理部工作。但在与旧友叙事中,他不愿再提他的那篇论文,并称在未获公司公关部的准许前,他不能谈此事。中金公司在回应外部询问时,公司新闻办公室以电子邮件回答称,Li已不再从事他以前工作,故无需向媒体交代任何问题。

  在现实金融世界中,太多金融分析人士只看到他们眼前的毫无生命的数字,而忘却了这些数字所代表的有形和真实的现实。他们认为,能够仅靠只有数年价值的数据来模拟计算,再定出那些每10000年才可能发生一次事件的概率。人们此后就以如此概率进行投资,而不思考一下这些数据究竟是否有实际意义。正如Li本人对自己的模型的表态,最危险的事情莫过于人们相信模型能给他们带来所盼的结果。

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发表于 2009-2-26 01:10 | 显示全部楼层
这人叫 李祥林 中金公司执行总经理 首席风险官负责风险管理组和数量分析组

发明CDS的是JP MORGAN CHASE的一位牛津毕业生。http://www.cctongbao.com/thread/2045084
LI发明的只是用以发明CDS的公式。
区别大概相当于居里夫人和扔原子弹的美国吧。。。。

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发表于 2009-2-26 01:22 | 显示全部楼层
讲座:当前金融危机与金融工程(李祥林—David Li) (2008-10-20 16:11:12)
标签:财经   

活动主题 Subject:中金课堂
演讲主题 Title:当前金融危机与金融工程
授课嘉宾 Speaker:李祥林(David Li)
讲师背景 Speaker’s Backgound:中金公司执行总经理 首席风险官
负责风险管理组和数量分析组
讲座对象:普硕,博士生
语言 Language:中文
日期 Date:2008-10-21
时间 Time:18:30 – 20:00
地点 Location:舜德楼202室
主办 Hosted By:职业发展中心
CDC补充信息 CDC

Suggestion:这次活动是“中金课堂”的第二讲。“中金课堂”是中金公司今
年新推出的项目,旨在帮助学生了解投行的真实工作情况,进一步将所学知识与
实践相结合,同时现在也是中金公司校园招聘收简历的时候,如果有学生对其数
量分析部门感兴趣,听过讲座之后可以方便大家向这个部门投简历。活动中会给
学生留比较长的提问时间,希望大家可以踊跃提问。

演讲人简介
David拥有加拿大沃特卢大学统计学博士学位,以及保险精算数学硕士学位、金
融方向工商管理硕士学位和金融学硕士学位。他曾当选为保险精算学会投资分会
理事,目前是《北美保险精算期刊》副主编。此外,他还一直在多伦多大学、沃
特卢大学、马尼托巴大学等院校任教。他在1997年发明了关联结构模型,为整个
信贷衍生产品市场的迅猛发展起到了助推作用,现在世界范围内每天仰赖这个模
型运行的交易达到上百亿美元,并被称为“这个产业的当前标准”。

注:David li 是第一个把Copula引入信用产品定价的人

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