On the efficacy of Fourier series approximations for pricing European options

This paper investigates several competing procedures for computing the prices of vanilla European options, such as puts, calls and binaries, in which the underlying model has a characteristic function that is known in semi-closed form. The algorithms investigated here are the half-range Fourier cosine series, the half-range Fourier sine series and the full-range Fourier series. Their performance is assessed in simulation experiments in which an analytical solution is available and also for a simple affine model of stochastic volatility in which there is no closed-form solution. The results suggest that the half-range sine series approximation is the least effective of the three proposed algorithms. It is rather more difficult to distinguish between the performance of the halfrange cosine series and the full-range Fourier series. However there are two clear differences. First, when the interval over which the density is approximated is relatively large, the full-range Fourier series is at least as good as the half-range Fourier cosine series, and outperforms the latter in pricing out-of-the-money call options, in particular with maturities of three months or less. Second, the computational time required by the half-range Fourier cosine series is uniformly longer than that required by the full-range Fourier series for an interval of fixed length. Taken together,these two conclusions make a case for pricing options using a full-range range Fourier series as opposed to a half-range Fourier cosine series if a large number of options are to be priced in as short a time as possible.

Effect of fourier domain quantization on matched filtering

It is shown that the use of a coarsely quantized binary digital hologram as a matched filter on an optical computer does not degrade signal-to-noise ratio (SNR) appreciably.

L-p-Integrability, Dimensions of Supports of Fourier Transforms and Applications

It is proved that there does not exist any non zero function in with if its Fourier transform is supported by a set of finite packing -measure where . It is shown that the assertion fails for . The result is applied to prove L-p Wiener Tauberian theorems for R-n and M(2).

Sign changes of Fourier coefficients of Hilbert modular forms

Sign changes of Fourier coefficients of various modular forms have been studied. In this paper, we analyze some sign change properties of Fourier coefficients of Hilbert modular forms, under the assumption that all the coefficients are real. The quantitative results on the number of sign changes in short intervals are also discussed. (C) 2014 Elsevier Inc. All rights reserved.

Cuspidality and the growth of Fourier coefficients of modular forms : A survey

In this paper, we present a survey of the recent results on the characterization of the cuspidality of classical modular forms on various groups by a suitable growth of their Fourier coefficients.

Lq estimates for rearrangements of Fourier series

This work is concerned with estimating the upper envelopes S* of the absolute values of the partial sums of rearranged trigonometric sums. A.M. Garsia [Annals of Math. 79 (1964), 634-9] gave an estimate for the L₂ norms of the S*, averaged over all rearrangements of the original (finite) sum. This estimate enabled him to prove that the Fourier series of any function in L₂ can be rearranged so that it converges a.e. The main result of this thesis is a similar estimate of the L_q norms of the S*, for all even integers q. This holds for finite linear combinations of functions which satisfy a condition which is a generalization of orthonormality in the L₂ case. This estimate for finite sums is extended to Fourier series of L_q functions; it is shown that there are functions to which the Men’shov-Paley Theorem does not apply, but whose Fourier series can nevertheless be rearranged so that the S* of the rearranged series is in L_q.

Theoretical analysis and experimental study of Fourier transformation of Franz-Keldysh oscillations in GaAs

Fourier transformation (FT) has been used in the theoretical line shape analysis of Franz-Keldysh oscillations (FKOs) in detail by numerical simulations. FKOs from the surface-intrinsic-n(+) GaAs structure were obtained in photoreflectance (PR) measurements with various modulation light intensities and with different strengths of bias light illumination, which were used to change the static electric field in the intrinsic layer of the sample. The FT spectra of the PR spectra, including the real part, imaginary part, and the modulus, were very consistent with the theoretical line shapes. The ratio of the square root of the reduced mass (root mu (L)/root mu (H)) and the ratio of transition strength of the electron heavy hole to the electron light hole were obtained from the PT spectra. In addition, the electric field in the intrinsic layer of the sample without and with bias illumination and the modulation field induced by photomodulation were also obtained. (C) 2000 American Institute of Physics. [S0021-8979(00)02123-X].

A study of isomeric diglycosyl flavonoids by SORI CID of Fourier transform ion cyclotron mass Spectrometry in negative ion mode

High-resolution Sustained off resonance irradiation (SORI) CID was employed to distinguish four pairs of isomeric diglycosyl flavonoids in the negative mode using the electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry (ESI FTICR MS). All of these isomers can be distinguished via MS/MS data. For these diglycosyl flavones and flavanones, the deprotonated alpha 1-->6 linkage diglycosyl flavonoids produce fewer fragments than the alpha 1-->2 linkage type compounds and the Retro-Diels-Alder (RDA) reaction in MS/MS only takes place when the aglycone is a flavanone and glycosylated with an alpha 1-->2 intersaccharide linkage disaccharide. The deprotonation sites after collisional activation are discussed according to the high mass accuracy and high-resolution data of tandem spectrometry. Some of these high-resolution SORI CID product ions from alpha 1-->2 linkage diglycosyl flavonoids involve multibond cleavages; the possible mechanism is discussed based on the computer modeling using Gaussian 03 program package at the B3LYP/6-31G level of theory. Unambiguous elementary composition data provides fragmentation information that has not been reported previously.

Mapping 2-D defects in a conductive half-space by eigenfunction expansions in K-space of Fourier-Laplace transforms

info:eu-repo/semantics/published

On the Computation of Fourier Coefficients

In this paper we derive an identity for the Fourier coefficients of a differentiable function f(t) in terms of the Fourier coefficients of its derivative f'(t). This yields an algorithm to compute the Fourier coefficients of f(t) whenever the Fourier coefficients of f'(t) are known, and vice versa. Furthermore this generates an iterative scheme for N times differentiable functions complementing the direct computation of Fourier coefficients via the defining integrals which can be also treated automatically in certain cases.

An analysis of real time implementation of Fourier transform-based frequency recognition algorithms

Frequency recognition is an important task in many engineering fields such as audio signal processing and telecommunications engineering, for example in applications like Dual-Tone Multi-Frequency (DTMF) detection or the recognition of the carrier frequency of a Global Positioning, System (GPS) signal. This paper will present results of investigations on several common Fourier Transform-based frequency recognition algorithms implemented in real time on a Texas Instruments (TI) TMS320C6713 Digital Signal Processor (DSP) core. In addition, suitable metrics are going to be evaluated in order to ascertain which of these selected algorithms is appropriate for audio signal processing(1).