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Short sales have historically accounted for a small, though rising, percentage of shares outstanding Short interest on the New York Stock Exchange, about 02% two decades ago, is now about 16% Of course, only a portion of this interest is motivated by security selection; most short sales are undertaken by dealers supplying liquidity or investors shorting for risk-hedging, tax-deferral, or arbitrage purposes In a market characterized by diverse opinion and restricted short selling, then, inef ciencies might be concentrated in overpriced stocks In that case, short sales of the most overpriced stocks may be able to offer higher excess returns than long purchases of underpriced stocks When market inef ciency is greater on the short side of the market than the long side, the excess return to the short portfolio in Exhibit 3.

4 may be expected to be greater than the excess return to the long portfolio in Exhibit 33, and the returns to the long and short positions illustrated in Exhibit 32 will not be symmetric about the market return, but will be greater for short positions..

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But at the same time, something funny happened as a direct result of the crash. The currently ubiquitous volatility smile was born, a re ection of freshly developed crashophobia on the part of traders. After witnessing the massacre, it became clear to options pros that markets cannot be assumed to behave normally as the mathematics behind Black-Scholes (another big-time casualty of Black Monday) assumes, and that rare events do happen and can be truly criminal. In essence, traders realized that they had been hopelessly underestimating the value of crash protection. From then on, crash-protecting tools (such as out-of-the-money puts) would have to be priced upwards. Option traders very survival was at stake. To correct for the mathematical insanity of Black-Scholes and for the real-life dif culties of hedging an option book, now only too obvious, the volatility parameter that goes into the model (by de nition, the only manipulable input) was arti cially manipulated upwards so that the values of options with strikes at the extremes could be signi cantly pumped up, giving birth in the process to the smile. Prior to the 1987 crash, dealers had been content to charge the same volatility independent of the strike level, and the chart plotting implied volatility and strikes was more or less horizontally at, exactly as the pure version of Black-Scholes would dictate. This, now we know, hopelessly underpriced out-of-the-money puts, providing scant compensation for the risks that dealers were taking. After a 20-sigma event on Wall Street (something deemed impossible by the Normal distribution), option pros decided to change tack and take protective measures. The smile became such protection, and very graphically illustrated Black-Scholes s number one competitive advantage, the real reason why it is embraced and continues to be the most popular option

had known about him for a while, mostly through his very well written Black-Scholes and Beyond book, and was fully aware of Chriss standing within the quant community Even without the other accomplishments and accolades, his then current position, the number one reason why I got to share the same space as him for those brief moments almost a decade ago, by itself spoke volumes of his nancial engineering reputation As director of the math nance program at New York University s ultra prestigious Courant Institute of Mathematics, Chriss held the keys to attendance to any of the lectures on offer by the program (consistently among the global elite in its eld).

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Though I was a student at NYU s business school, I was doing a specialized degree focusing on derivatives and nancial mathematics and thus was very interested in attending a class at Courant (which, for those not in the know, sits just in front of the B-school) My own program s extraordinary exibility allowed me to do so, but I obviously also needed special permission from Courant In asking for such granting, I was crossing the short divide between both schools in the least popular direction, as by far many more math students seemed to want to roam around the B-school than vice versa I knocked on Neil Chriss s of ce door and got in I don t remember much, but the place was dark and small, de nitely unassuming.

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IPTV Security: Protecting High-Value Digital Contents David Ramirez 2008 Alcatel-Lucent. All Rights Reserved

i) = 0, for the SEE working covariance structure: SEEII-ORf(age): SEE with a working odds ratio modelled as a function of an individual s age group by log(

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