爱思英语编者按:诺贝尔经济学奖(The Prize in Economic Sciences),是由瑞典银行在1968年,为纪念诺贝尔而增设的并非诺贝尔遗嘱中提到的五大奖励领域之一,全称为“纪念阿尔弗雷德·诺贝尔瑞典银行经济学奖(The Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel)”,通常称为诺贝尔经济学奖(Nobel economics prize),也称瑞典银行经济学奖。经济学奖并非根据阿尔弗雷德·诺贝尔的遗嘱所设立的,但在评选步骤、授奖仪式方面,与诺贝尔奖相似。奖项由瑞典皇家科学院每年颁发一次,遵循对人类利益做出最大贡献的原则给奖。1969年(瑞典银行的300周年庆典)第一次颁奖,由挪威人弗里希和荷兰人扬·廷贝亨共同获得,美国经济学家萨缪尔森、弗里德曼等人均获得过此奖。

The Nobel prize for economics
The right option
正确的选择权
 
ECONOMISTS may sometimes seem about as useful as a chocolate tea-pot, but as this year's Nobel prize for economics shows, it isn't always so. On October 14th, the $1m prize was awarded to two Americans, Robert Merton, of Harvard University, and Myron Scholes, of Stanford University. Their prize-winning work involves precisely the sort of mind-boggling mathematical formulae that usually cause non-economists either to snooze or scream. That is too bad, for it ranks among the most useful work that economics has produced.
 
经济学家有时可能看起来中看不中用,但是,正如今年的诺贝尔经济学奖所示,这并非向来如此。10月14日,100万美元奖金被授予了两位美国人——哈佛大学的罗伯特·默顿(Robert Merton)和斯坦福大学的迈伦·斯科尔斯(Myron Scholes)。他们的获奖研究所涉及的正是那类通常让非经济学家昏昏欲睡或惊声尖叫的让人头大的数学公式。鉴于这个公式位列经济学所生产的最实用的研究,这太糟糕了。 
 
What Mr Merton and Mr Scholes did, back in 1973, was to put a price on risk. Their work on how to price financial options, carried out with the late Fischer Black, turned risk management from a guessing game into a science. The complex Black-Scholes option pricing model (“It should probably be called the Black-Merton-Scholes paper,” Mr Black once said) and its subsequent evolutions, led to explosive growth in stock options and other financial derivatives. It also opened the era of the Wall Street rocket-scientist, a strategist schooled in physics or mathematics who makes money crunching numbers rather than playing hunches.
 
回到1973年,默顿和斯科尔斯当时的所为就是为风险定价。他们与已故的费希尔·布莱克(Fischer Black)共同进行的有关如何为金融期权定价的研究,将风险管理从一种猜谜游戏变成了一门科学。复杂的布莱克一斯科尔斯期权定价模型(Black-Scholes option pricing model)(布莱克曾经表示:“它或许应当被叫做布莱克-默顿-斯科尔斯论文。”)以及随后的演进,导致了股票期权和其他金融衍生品的爆炸式增长。它还开启了华尔街分析师是专业为数学或物理学的高智力人才时代。
 
Although derivatives often come dressed up in fancy names, among them swaptions and quantos, they really boil down to two basic sorts of financial instrument: forward contracts and options. A forward commits the user to buying or selling an asset—say a Treasury bill, or dollars—at a specific price on a specific date in the future. It is rather easy to price. The main difficulty is working out the cost of carrying the asset until it changes hands.
 
尽管衍生品经常是披着五花八门的名字出现,如互换期权 (swaptions) 和汇率连动期权(quantos)等等。但是,它们归根结底是两类基本的金融工具:远期合约和期权。远期合约保证使用者可以在将来的某个特定日期以特定价格买卖某种资产,如财政部债券或美元。给它定价非常容易,主要困难是计算持有这种资产直至换手的成本。
 
An option gives the buyer the right, but not the obligation, to sell or buy a particular asset at a particular price, on or before a specified date. Pricing one is a trickier affair, as it involves putting a number on the probability that a buyer will exercise his option. Until 1973 that was largely a matter of guesswork—which is why, though options first arose centuries earlier, the market for them remained tiny. But the Black-Scholes formula was published in May 1973, just after the world's first options exchange had opened in Chicago. Within a year it was being used by every trader. The rest, as they say, is history.
 
期权给与买方在某个特定日期或者该日期之前以特定价格买卖特定资产的权利,而非义务。为期权定价是一件较为棘手的事情,因为它涉及量化买方将来行使期权的可能性。直到1973年之前,它主要是猜测——这就是尽管期权早在几百年前就已出现而期权市场却一直很小的原因。但是,布莱克-斯科尔斯公式恰好是在世界首家期权交易所在芝加哥开张后被公之于众的。一年之内,它就被每一个交易员用上了。正如这些交易员所说,其余的[工具]已经成为历史。
 
The economists found what mathematicians call a “closed-form solution”. In essence this meant that sellers of options could bung in a number of variables and the model would churn out a price. The big advantage of the formula is that it does not require option sellers to take a view on which way the price of the underlying asset will move. It is not entirely fool-proof: some of the variables, such as the risk-free interest-rate and the volatility of the underlying asset, may change over time. Also, the formula does not deal well with very large price movements. Nonetheless, the Black-Scholes formula gave option sellers a far more precise way to work out what an option is worth.
 
经济学家发现了数学家所说的“封闭解”。从根本上来说,这意味着期权卖方能够代入众多变量,模型就会算出一个价格。这个公式的巨大优势在于,它不需要期权卖方对标的资产价格将来如何波动做出判断。它不是完全防傻的:有些变量,如零风险的利率和标的资产的波动性,可能会随时间而变化。同时,这个公式也不能很好地应对巨大的价格波动。尽管如此,布莱克-斯科尔斯公式还是给期权卖方提供了一种精确得多的办法,以计算期权的价值。
 
The option-pricing work of Messrs Black, Merton and Scholes was based on a clever and fundamental insight. This was that any asset, from a government bond to a bar of gold, is essentially a mixture of forward contracts and options. By, in effect, breaking down assets into constituent parts, it is possible to get rid of precisely those risks you do not want to keep and take on precisely those that you do. Breaking assets into their core bits allows the canny investor to spot cases where—hidden in, say, an Italian bond, or an American mortgage-backed security—certain sorts of risk are over-or underpriced relative to the market average. Arbitraging these price differences away has earned Wall Street a good deal of money.
 
布莱克、默顿和斯科尔斯的期权定价研究基于一种聪明而且根本的真知灼见。即,任何资产,无论是政府债券还是金条,本质上是一种远期合约和期权的融合物。实际上,通过将资产分割为多个组成部分,是有可能消除人们不想去维持的那些风险并使之具有人们愿意维持的那些风险的。分割资产直至其核心部分的办法能够让精明的投资者发现——比如说隐藏在某只意大利债券或是美国抵押贷款证券中的——那类风险相对于市场均值被过高或过低定价的情况。赚走这些价差的套利行为已经让华尔街挣了很大一笔钱。
 
This sort of arbitrage is precisely what Mr Merton and Mr Scholes are doing through Long-Term Capital Management, a hedge fund they helped create three years ago. Typically, the fund has around 20 highly diversified active investments in place around the world at any one time, with all but the precise risks the firm wants to bear hedged. The results have been impressive: high returns, with low volatility—every investor's dream. Already, the fund is said to have earned its founders profits of $1 billion. Thanks to the widespread use of their formula, however, such arbitrage opportunities are becoming rarer. Indeed, Long-Term Capital Management is returning to clients a large chunk of the $6 billion it manages because it cannot find enough opportunities in which to invest. Perhaps its begetters should have kept their bright idea to themselves.
 
这类套利正是默顿和斯科尔斯目前正通过他们3年前筹建的一只对冲基金——长期资本管理公司所做的事情。一般来说,这只基金无论何时通常都会在全世界各地有大约20个公司想要承担的风险已得到对冲的高度分散化的主动性投资。战果非同凡响:高收益,低波动——是每一位投资者的梦想。据说,这个基金已经为其创始人赚了10亿美元。不过,由于他们的公式的广泛运用,这类套利机会正变得愈发稀缺。事实上,长期资本管理公司正因为无法找到足够的投资机会而向客户归还它所管理的60亿美元中的大部分。或许,它的创始人应该把聪明才智留给自己。
 
Setting a price on the future
为未来定价
The mathematics of markets
市场的数学
The formula that changed finance
改变了金融的等式
 
Pricing the Future: Finance, Physics, and the 300-Year Journey to the Black-Scholes Equation. By George Szpiro. Basic Books; 298 pages; $28 and £18.99. 
《为未来定价:金融学、物理学以及到布莱克-斯科尔斯等式的300年之旅》作者:乔治·斯皮罗 
 
OPTIONS and futures are almost as old as trade itself. From the farmer who sold his crop before the harvest to the merchant who bought at a set price in the future, the forerunners of today's markets can be traced to ancient Greece and Rome. Yet for centuries these markets remained stunted because of a simple question of valuation. What is the right to buy next year's olive crop worth? Answering this question took centuries of study of physics, botany and mathematics. When solved, it changed finance for ever.
 
期权和期货几乎同交易本身一样古老。从收获前将收成卖给将来以商定价格购买的商人的农民开始,当今市场的先行者可以上溯至古希腊和罗马。然而,几个世纪以来,这些市场却因为简单的估价问题而仍旧不健全。购买下个年度的橄榄收成的权力价值几何?对这个问题的回答花去了物理学家、植物学家和数学家长达几百年的研究。一朝得解,它永远地改变了金融。
 
The tale includes a fascinating succession of people who tried doggedly to master probability and markets. It is engagingly told by George Szpiro, a mathematician- turned-journalist, who flits between biographies and formulae. He begins with the futures and options markets of the tulip bubble of the 1630s. He looks at Napoleon's attempt to regulate trading with a modern-sounding ban on futures contracts and short sales. And he explores those whom history has forgotten, such as Jules Regnault, a self-taught broker's assistant who started working on the Paris Bourse in 1862. After seeing how share prices changed over time, he wrote a book on the subject and made a fortune trading shares. Regnault's writings have been largely forgotten, but his work foreshadowed modern financial theory.
 
故事包括一众相继不屈不挠地试图去掌握可能性并主宰市场的令人心动之人。它被游走与传记和公式之间的乔治·斯皮罗(George Szpiro),这位由数学家转行而来的记者,娓娓地讲了出来。他从17世纪30年代的郁金香泡沫时期的期货和期权市场讲起,说到了拿破仑试图用一种具有现代意味的期货合约和卖空禁令去监管交易的尝试,梳理了那些历史已被遗忘的人物,如1862年开始在巴黎证券交易所开始工作的自学成才的股票经纪人助手朱利·荷纽(Jules Regnault)。在看到股价如何随时间变动后,他就这个主题写了一本书并依靠买卖股票发了财。荷纽的文章大部分已被忘记,但是,它的研究昭示了现代金融理论。
 
Another great mind whose work was lost was Wolfgang Döblin. The son of a prominent German novelist of Jewish descent, Döblin fled Berlin to Paris in the 1930s. He obtained his PhD in mathematics at the Sorbonne, where he soon established himself as a pioneering mathematician and innovator in the field of probability. With war approaching, Döblin joined the French army in a gesture of gratitude to the country that had sheltered him. In his billet on the front-lines, he scribbled on a cheap school notebook, sketching out a formula that he sealed in an envelope and posted to the Académie des Sciences in Paris. Soon after, with his regiment surrounded and the French army in retreat, he burned his personal papers and, fearing what would happen if was captured by German soldiers, shot himself.
 
另一位研究成果已经丢失的大人物是沃尔夫冈·德布林(Wolfgang Döblin)。德布林是一位杰出的犹太裔德国小说家的儿子。20世纪30年代,他脱离柏林,去了巴黎。他在索邦大学获得了数学博士学位。之后不久,他在那里奠定了自己作为可能性领域的先驱数学家和创新者的身份。随着战争临近,德布林带着对这个庇护了他的国家的感激之情加入了法国军队。在前线兵营中,他在一本廉价的笔记本上写写画画,草拟了一个将其封在一个信封中并寄给了在巴黎的法国科学院的公式。不久之后,由于他所在的部队被包围,加之法国军队节节败退,他烧毁了他的个人文件,并且因为生怕被德国士兵俘虏而吞枪自杀。
 
The envelope lay sealed in archives until May 2000, when it was found to contain the mathematical tools to describe the random movements of particles. Calculations such as these transformed people's understanding of physics and provided an important building block of the so-called Black-Scholes equation.
 
这封信一直未被打开地躺在档案中直到2000年5月。当时,它被发现含有描述粒子随机运动的数学工具。众多诸如此类的计算彻底改变了人们对物理学的理解,为所谓的布莱克-斯科尔斯等式提供了一种重要的构件。
 
That equation, which Robert Merton, Myron Scholes and Fischer Black worked out in 1973, turned out to be a breakthrough that promised accurate assessments of the value of options, which are the right (but not the obligation) to buy or sell something at a particular price on some future date. Mr Merton and Mr Scholes were awarded the Nobel prize for their work on this in 1997. Black, who died in 1995, was also credited for his contribution.
 
事后证明,罗伯特·默顿、迈伦·斯科尔斯和费希尔·布莱克在1973年得出来的这个等式是一个昭示了期权——即在未来某个时日以特定价格进行买卖的权利(不是义务)——价值之精准评估的重大突破。1997年,默顿和斯科尔斯因为这方面的研究而被授予了诺贝尔奖。在1995年去世的布莱克也因为他的贡献而荣誉加身。
 
The equation's publication led to a flowering of options markets and an explosion of trading on them. It also transformed investment banking and stockbroking. The affable trader who calculated prices and odds by the seat of his pants on the trading floor, much as a gambler did at the poker table, was supplanted by the “quant”, a mathematician with a room full of computers and reams of data.
 
这个等式的公布带来了期权市场的一次大繁荣和期权市场交易的一场大爆发。它还彻底改变了投资银行业务和股票经济业务。那些在交易大厅中如同牌局上的赌徒那样凭借经验和直觉计算价格和概率的热情的交易员被“数量分析专家”(quant),即拥有满屋子计算机和海量数据的数学家,所取代。
 
Yet the model has deep failings. Black-Scholes assumes that movements in share prices, like those of particles suspended in liquid, can be plotted using a Gaussian, or bell curve, distribution. Yet finance is filled with “fat tailed” events that occur far more frequently than predicted by this model of the physical world. Black-Scholes reached its zenith in 1998, just before the collapse of Long-Term Capital Management (LTCM), an investment firm backed by the two Nobel prize-winning economists.
 
然而,这个模型有着深深的缺陷。布莱克-斯科尔斯模型认为,股价的走势,如同悬浮在液体中的粒子一样,利用某种高斯分布或者钟形曲线分布,,是能够被绘制出的。然而,金融充满了远较由这种物理世界的模型所预测的更为频繁发生的“厚尾”事件。1998年,就在得到两位诺贝尔奖得主的经济学家支持的投资公司——长期资本管理公司崩溃之前,布莱克-斯科尔斯模型达到了顶峰。
 
LTCM failed when the yields on bonds issued by countries such as Russia and America began to diverge, something the models said was virtually impossible. A decade later the great financial crisis was ushered in by the simultaneous collapse of house prices across America, another event that the mathematical models said was virtually impossible. In both instances, financial firms quickly found themselves racking up daily losses that the computers said should occur only once in millions of years.
 
当时,长期资本是在俄美等国发行的债券的收益率开始发散——即这种模型认为是绝对不可能是事情——之际失败的。十年后,伟大的金融危机因为另一件这个数学模型认为是绝对万不可能的事件——全美房价的同步崩溃而爆发。在这两个例子中,金融企业都很快就发现了自己每天都在大量累积那种计算机认为是几百万年只应当发生一次的损失。
 
“Pricing the Future” is at its best when it skips through the parallel developments in physics, mathematics and economics that led to the equation, a development that Mr Szpiro compares to the discovery of the structure of DNA or Isaac Newton's laws of motion. Unfortunately, Mr Szpiro's narrative dodges some important questions that it ought to have delved into in detail. In just four pages the book describes, almost as an afterthought, the failings of the Black-Scholes model and the history of the past decade since the collapse of LTCM. Black-Scholes may well have been a great achievement, but histories of the financial crisis will treat it less than kindly. The quest to tame risk and price the future is far from over.
 
《为未来定价》一书在跳过导致了这个等式的物理学、数学和经济学的并行发展,也就是斯皮罗认为可与DNA结构的发现或牛顿运动定理的发现相提并论的发展时,可谓是完美之极。不幸的是,斯皮罗的叙述绕开了一些本应追根究底的重要问题。这本书只用了4页的篇幅来描述布莱克-斯科尔斯模型的失败以及长期资本崩溃之后的那10年的历史,就好像是后来添加进去的。布莱克-斯科尔斯模型本来极有可能成为很一项伟大的成就,但是,金融危机的历史将会不那么友好地对待它。驯服风险并为未来定价的追求远未结束。