Because quick decisions about derivative securities and other financial instruments are fraught with uncertainty — and monumental stakes — traders have often turned to the Monte Carlo method as a means of estimating probability.
After producing thousands of semirandom solutions to derivative valuation and hedging, this efficient computer algorithm can point market decision makers in the right direction, estimating exposure to risk and providing a degree of protection.
Now, thanks to new work by Professors Paul Glasserman (CBS) and Mike Giles (Oxford), these rapid calculations of hedge ratios can happen even faster. Their recent paper in Risk magazine describes how it can be done — through the application of adjoint methods more commonly found in engineering design and fluid dynamics.
The paper — “Smoking Adjoints: Fast Monte Carlo Greeks”(Click here to download the PDF) — won the two authors Risk magazine's 2007 Quant of the Year award.
Comments
I downloaded the PDF on "Smoking Adjoints: Fast Monte Carlo Greeks" and read the abstract and introduction to the concept. Many of the precepts discussed, particularly as they related to a bundle of securities, could likely be applied to other types of securities, in which derivatives are created and traded (perhaps a VIN, or variable interest entity, or SPV special purpose vehicle, consisting of several other publicly traded entities, regrouped via specific rules of consolidation, such as FIN 46 and FIN 46R as well as FAS140, if not, under other rules for GAAP accounting, depending on the market). Instinctively, I figured that fluid mechanics concepts would come into play as to how to most properly use them as hedging instruments, but was pleasantly surprised to see that others had already published extensively on the subject. I will read with much interest the remainder of the article.
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