Эфект 'Северо-Восточного ветра волатильности' в разрезе бегущих волн. Спиральная структура коэффициентов Фурье волн волатильности

Пучков Андрей Александрович,

магистр экономики, докторант Рижского технического университета.

North-East Volatility Wind Effect in Traveling Wave Perspective. Helical Structure of Volatility wave Fourier Coefficients

Andrejs Puchkovs,

Economist, Mg. oec., PhD student of Riga Technical University.

            This article describes new properties of North-East Volatility Wind Effect. In current article North-East Volatility Wind Effect is analyzed from traveling wave perspective.

            After Volatility evolution matrix is obtained, by averaging volatility evolution matrix in a complex plain. Volatility evolution matrix at fixed time is considered as a function of interlayer volatility radius. Additional transformation is done by using (1) equation.

                                                                   (1)

            Transformation results are illustrated for Dow Jones Industrial Index next:

Fig. 1. Visualization of Transformation.

Fig. 2. Untransformed volatility evolution matrix.

Fig. 3. Transformed volatility evolution matrix.

            Implemented transformation brings out North-East Volatility Wind Effect understanding from traveling waves perspective. Volatility evolution function at fixed timeto be considered as analyzed signal. Let's call function as 'volatility pie' (at fixed time-). This function is represented in frequency domain by using Fast Fourier Transform.

                                                                                              (2)

            Fourier coefficients are represented in 4 a). Fig (top left corner).

            Consider function which also is represented in frequency domain.

                                          (3)

            Fourier coefficients are represented in 4 b). Fig (top right corner).

            Function (at fixed time - ) is shown in 4 c). Fig (bottom left corner).

            Overall volatility function is shown in 4 c). Fig (bottom right corner). Suppose time is fixed at time .

Fig. 4. Volatility pie as traveling wave in time.

a) Volatility pie in frequency domain(top left corner); b) Function(top right corner); c) Volatility pie (bottom left corner); d) Overall volatility function  (bottom right corner)

            The same picture is obtained in fixed time , Results are represented in next figure.

5. Fig. Volatility pie as traveling wave in time

a) Volatility pie in frequency domain(top left corner); b) Function(top right corner); c) Volatility pie (bottom left corner); d) Overall volatility function (bottom right corner).

            4. Fig. Is illustrating The Dow Jones Industrial Average index volatility pie at time which is correspondent to 2006 year. (before financial crisis 2007). According results Volatility pie in frequency domain anddid not have clear structure. The same conclusions are done about function.But in time (during financial crisis 2007 peak) the picture has been changing and functions aandacquired clear helical (spiral) structure. This effect is explored by less number of explicit harmonics (harmonics with higher magnitude). After market crisis 2007, clear clear helical (spiral) structure was lost.

            This effect can be used for stock market stability research. As a measure of structure could be used minimal total distance between all points in and/or or similar metrics. That measure can be used as measure of risk alternative to volatility measure.

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Поступила в редакцию 11.07.2014 г.