Fast Fourier Transform for Option Pricing

By Sajib Barua

Abstract:

The Fast Fourier Transform (FFT) has
been used in many scientific and
engineering applications. The use of FFT
for financial derivatives has been
gaining momentum in the recent past. In
this thesis, i) we have improved a
recently proposed model of FFT for
pricing financial derivatives to help
design an efficient parallel algorithm.
The improved mathematical model put
forth in our research bridges a gap
between quantitative approaches for the
option pricing problem and practical
implementation of such approaches on
modern computer architectures. The
thesis goes further by proving that the
improved model of fast Fourier transform
for option pricing produces accurate
option values. ii) We have developed a
parallel algorithm for the FFT using the
classical Cooley-Tukey algorithm and
improved this algorithm by introducing a
data swapping technique that brings data
closer to the respective processors and
hence reduces the communication overhead
to a large extent leading to better
performance of the parallel algorithm.
We have tested the new algorithm on a 20
node SunFire 6800 high performance
computing system and compared the new
algorithm with the traditional
Cooley-Tukey algorithm. Option values
are calculated for various strike prices
with a proper selection of strike-price
spacing to ensure fine-grid integration
for FFT computation as well as to
maximize the number of strikes lying in
the desired region of the stock price.
Compared to the traditional Cooley-Tukey
algorithm, the current algorithm with
data swapping performs better by more
than 15% for large data sizes. In the
rapidly changing market place, these
improvements could mean a lot for an
investor or financial institution
because obtaining faster results offers
a competitive advantages.

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