This paper describes an approach that is able to fix difference in multifractal behaviour of various World Stock Indexes. The approach is beneficial for the forecasting and simulations of the most European and Asian stock indexes. Multifractal analysis is provided using the so-called Wavelet Transform Modulus Maxima approach, which involves two basic aspects:
-Contacts between pantograph and catenary are the most critical parts in the transmission of electrical energy for modern high-speed trains. Contact wire oscillations change combined force between pantograph and catenary, and the contact may even get lost. Therefore special pantographs and catenaries have been developed and further constructive changes are under development. A design criterion includes the permanent contact of pantograph head and contact wire at high speed and the reduction of both aero acoustic noise and wear. Because of complicated dynamic behaviour and very high costs for prototypes, all modifications and new design concepts for the pantograph/catenary system are essentially based on dynamical simulation. Traditional approaches focus on the catenary, which is modelled as set of coupled strings and/or beams, whereas simplified lumped mass models are used to describe the pantograph. Nowadays increased computer power allows considering applications with more refined pantograph modes (e.g. the elasticity of the pantograph) and active control components in innovative pantograph concepts.Keywords -interaction pantograph-catenary, mechanical multibody system, high performance computing in MATLAB
-Very few models allow expressing European call option price in closed form. Out of them, the famous BlackScholes approach sets strong constraints -innovations should be normally distributed and independent. Availability of a corresponding characteristic function of log returns of underlying asset in analytical form allows pricing European call option by application of inverse Fourier transform. Characteristic function corresponds to Normal Inverse Gaussian (NIG) probability density function. NIG distribution is obtained based on assumption that time series of log returns follows APARCH process. Thus, volatility clustering and leptokurtic nature of log returns are taken into account. The Fast Fourier transform based on trapezoidal quadrature is numerically unstable if a standard cumulative probability function is used. To solve the problem, a dampened cumulative probability is introduced. As a computation tool Matlab framework is chosen because it contains many effective vectorization tools that greatly enhance code readability and maintenance. The characteristic function of Normal Inverse Gaussian distribution is taken and exercised with the chosen set of parameters. Finally, the call price dependence on strike price is obtained and rendered in XY plot. Valuation of European call option with analytical form of characteristic function allows further developing models with higher accuracy, as well as developing models for some exotic options.
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