BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Refined and enhanced FFT techniques\, with applications to pricing
  barrier options and their sensitivities - Sergei Levendorskii (Univeristy
  of Chicago)
DTSTART:20090224T153000Z
DTEND:20090224T163000Z
UID:TALK16834@talks.cam.ac.uk
CONTACT:HoD Secretary\, DPMMS
DESCRIPTION:Many mathematical methods of option pricing rely on one's abil
 ity to calculate the action of certain integro-differential operators and 
 convolution operators quickly and efficiently. In turn\, the latter comput
 ations are based on FFT techniques. However\, in many important cases\, a 
 straightforward application of FFT and iFFT leads to errors of several kin
 d\, which cannot be made simultaneously small (uncertainty principle) unle
 ss grids with too many points are used. We explain an approach to using FF
 T techniques that gives one more flexibility in controlling the aforementi
 oned errors\, and\, at the same time\, yields fast and efficient algorithm
 s. As applications\, using Carr's randomization\, we compute the prices an
 d sensitivities of barrier options and first-touch digital options on stoc
 ks whose log-price follows a Levy process. The numerical results obtained 
 via our approach are demonstrated to be in good agreement with the results
  obtained using other (sometimes fundamentally different) approaches that 
 exist in the literature. However\, our method is computationally much fast
 er (often\, dozens of times faster). Moreover\, our technique has the adva
 ntage that its application does not entail a detailed analysis of the unde
 rlying Levy process: one only needs an explicit analytic formula for the c
 haracteristic exponent of the process. Thus our algorithm is very easy to 
 implement in practice. Finally\, our method yields accurate results for a 
 wide range of values of the spot price\, including those that are very clo
 se to the barrier\, regardless of whether the maturity period of the optio
 n is long or short. A natural extension of the method gives similar result
 s for double-barrier options.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
END:VEVENT
END:VCALENDAR