Fourier and Wavelet Analysis

Options are believed to contain unique information on the risk-neutral moment generating function (MGF) or the risk-neutral probability density function (PDF) of the underlying asset. This paper applies the wavelet method to approximate the implied risk-neutral MGF from option prices.Monte Carlo simulations are carried out to show how the risk-neutral MGF can be obtained using the wavelet method. With the Black-Scholes model as the benchmark, we offer a novel method to reveal the implied MGF, and to price in-sample options and forecast out-of-sample option prices with the estimated MGF.JEL Classification: C02, C63, G13

show abstract

“…A more formal and thorough treatment on wavelet theory can be found in Daubechies (1992) and Bachman et al (2002).…”

Section: The Wavelet Methodsmentioning

confidence: 99%

Revealing the implied risk-neutral MGF from options: The wavelet method

Haven

Liu

et al. 2009

Journal of Economic Dynamics and Control

View full text Add to dashboard Cite

show abstract

“…Analyzing (8), we can see that the function F : Z l → R is a convolution (see e.g., [10], [7]) of two discrete functions A and I. Let us recall that F contains the F -transform components F k , k = 0, .…”

Section: F-transform As a Convolutionmentioning

confidence: 99%

“…There are used the Gaussian kernel with k = 2 and the linear generating function with h = 2. For the generating function, we can write without 0 borders with respect to (10).…”

Section: Comparisonmentioning

confidence: 99%

F-transform and discrete convolution

Vlašánek

Perfilieva

2015

Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

View full text Add to dashboard Cite

Discrete convolution is commonly used operation in the image processing field. The technique modifies an input image in various ways by scalable and easy computation. We are able to achieve many applications such as edge detection, noise reduction or artistic filtering, by selection of the proper kernel. The technique of the F-transform investigated in few last years also modifies an input image in the certain ways. Following paper introduces image processing based on the convolution operation and F-transform approximation with emphasis on similarities and negotiability of the both techniques. As an illustration, we will use the Gaussian convolution kernel and appropriate F-transform basic function for simple noise reduction.

show abstract

“…Its applications have been considered in different fields such as criminology, epidemiology, and economy, social and conducted sciences [15,16]. It has been shown that FD is a promising method in transient detection [11][12][13][14][15][16]. In addition, in this approach there is no need to have a prior knowledge about the attributes of the transient.…”

Section: Fractal Dimensionmentioning

confidence: 99%

Network Traffic Deviation Detection Based on Fractal Dimension

Shaabany

Jamshidi

2012

CIT

View full text Add to dashboard Cite

In this paper we examine aggregate network traffic for deviation detection. The precise and fast detection of network traffic deviation is crucial to improve the efficient operation of a network. It is often difficult to detect the time when the defects occur in a network. In this article, a new algorithm is presented to supervise the aggregate network traffic to fast detect the time deviation transpires in a network. This is performed by supervising the statistical attributes of the time series representing the network conduct. The method examines the network conduct using fractal dimension and discrete stationary wavelet transform. In the proposed method, after applying discrete stationary wavelet transform on the signal representing the network traffic, the fractal dimension of the disintegrated signal is computed in a sliding window. Then, variations of signal fractal dimension are considered for deviation detection. Performance of the proposed method is compared with that of three other existing methods using synthetic signal. The results show superiority of the proposed method in terms of accuracy compared to existing methods.

show abstract

Fourier and Wavelet Analysis

Cited by 135 publications

References 13 publications

Revealing the implied risk-neutral MGF from options: The wavelet method

Revealing the implied risk-neutral MGF from options: The wavelet method

F-transform and discrete convolution

Network Traffic Deviation Detection Based on Fractal Dimension

Contact Info

Product

Resources

About