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CATEGORIES:Probability
SUMMARY:Refined and enhanced FFT techniques\, with applica
tions to pricing barrier options and their sensiti
vities - Sergei Levendorskii (Univeristy of Chicag
o)
DTSTART;TZID=Europe/London:20090224T153000
DTEND;TZID=Europe/London:20090224T163000
UID:TALK16834AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/16834
DESCRIPTION:Many mathematical methods of option pricing rely o
n one's ability to calculate the action of certain
integro-differential operators and convolution op
erators quickly and efficiently. In turn\, the lat
ter computations are based on FFT techniques. Howe
ver\, in many important cases\, a straightforward
application of FFT and iFFT leads to errors of sev
eral kind\, which cannot be made simultaneously sm
all (uncertainty principle) unless grids with too
many points are used. We explain an approach to us
ing FFT techniques that gives one more flexibility
in controlling the aforementioned errors\, and\,
at the same time\, yields fast and efficient algor
ithms. As applications\, using Carr's randomizatio
n\, we compute the prices and sensitivities of bar
rier options and first-touch digital options on st
ocks whose log-price follows a Levy process. The n
umerical results obtained via our approach are dem
onstrated to be in good agreement with the results
obtained using other (sometimes fundamentally dif
ferent) approaches that exist in the literature. H
owever\, our method is computationally much faster
(often\, dozens of times faster). Moreover\, our
technique has the advantage that its application d
oes not entail a detailed analysis of the underlyi
ng Levy process: one only needs an explicit analyt
ic formula for the characteristic exponent of the
process. Thus our algorithm is very easy to implem
ent in practice. Finally\, our method yields accur
ate results for a wide range of values of the spot
price\, including those that are very close to th
e barrier\, regardless of whether the maturity per
iod of the option is long or short. A natural exte
nsion of the method gives similar results for doub
le-barrier options.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:HoD Secretary\, DPMMS
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