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The last step of this refactoring is to compile, deploy, and test all of these changes to make sure that everything behaves as expected. If this is the case, then you have an excellent mechanism for gradually converting from your application CMP to BMP.

Proof. Using the same arguments as in the proof of Theorem 3.2, it is suf cient to prove that E (J ) =

wavelengths travel in different directions. The peak intensity at each wavelength depends on the number of slits in the grating. The transmission function of a grating is de ned by t x; y U x; y; 0 U x; y; 0 5:6-2

Such a practical, engineering-type approach is a testament to the fact that quantitative doctrinarism must take a backseat to pragmatic functionality when real cash is at stake Emanuel Derman once said that It s common to imagine that physicists on Wall Street spend their time predicting the future They rarely do Most of us work in quantitative haute couture, using models to create custom-tailored risk pro les from off-the-shelf products I vividly recall explaining to a fellow trading oor colleague the mathematical subtleties (based on academic papers, now long forgotten by me) involving the pricing of digital and barrier options (two types of exotic derivatives), only to be cut off by his pragmatism-dominated assertion that he couldn t care less about those equations, given that those kind of options can be replicated (and thus valued) through a combination of plain-vanilla contracts.

pre-BSM; that is, BSM architecture would be used to return to superior pre-BSM formulas.) So yes, the model would continue to be very enchanting to use and to allow traders to break free from unworldly tenets. Those nice things would continue to be nice. But not, as typically espoused, under the Black-Scholes umbrella. The smile is not smiling at Black-Scholes. It is proclaiming its death. This is one of the few topics in this book that require some graphical support, since visual reconnaissance is a must if we want to fully understand why the birth of the volatility smile (after October 1987, as will be detailed in a posterior section) renders BSM not-used. Figure 7.1 plots the relationship between implied volatility and different strike levels for equity options (in this case linked to the Nikkei, since the example is borrowed from Emanuel Derman, who reportedly rst heard of the smile while in Tokyo in the late 1980s; other international stock markets smile in similar fashion, typically a tad more enthusiastically so in the United States). The horizontal line depicts how things were before October 1987, in perfectly pure BSM-compliance: constant volatility for all options on the same underlying asset, independent of strike levels. The curved line represents the state of affairs post-October 1987, the volatility smile (actually a skew more than a matter-of-fact smile, but this is customary in equity markets, for a variety of reasons;

Potatoes are part of a healthy diet for people living with diabetes. (And they are part of a healthy living for many Canadian farmers, too. Canada is one of the largest potato producers in the world.) In addition to providing energy, potatoes are a good source of potassium and vitamins (including vitamin B6 and vitamin C), and potato skin provides fibre. Popular baking potatoes like russet are light, fluffy, and creamy and are ideal for baking, mashing, and French fries. Popular boiling potatoes like White, Red, and Ruby Crescent, are great for soups, casseroles, salads, roasting, and barbecuing because of their tendency to hold their shape. (They can be mashed, but will result in thick and lumpy potatoes.) These are some other types of potatoes: Yukon Gold potatoes are moister than the baking variety and will hold together during boiling. They can be used for roasting, pan frying, stews, soups, and gratins. They can be also used for baking, mashing, and frying, but will not produce the quality that baking potatoes can. New potatoes are immature, small potatoes of any variety. Sweet potatoes grow on a vine above the ground and actually have no real relation to the white potato. Sweet potato is rich in beta carotene, vitamin C, and vitamin E. Yams are native to Africa and are larger than sweet potatoes and have fewer nutrients. (Yams are often mixed up with sweet potatoes in the grocery store, but fortunately, both can be used interchangeably in recipes.)