Дослідження процесу Орнштейна – Уленбека методами спектрального аналізу

Abstract

The purpose of this paper is to develop methods for calculating the approximate prices for a broad class of securities with the tools of spectral analysis, singular and regular wave theory in the case of exposure to fast and slow-acting factors. Price options depend on stochastic volatility, depending on the route. Finding the price is reduced to the problem of finding own values and own functions of a certain equation. Combining the methods of the spectral theory of singular and regular perturbation working with the infinitesimal generators of the two-dimensional diffusion approximation the price of financial instruments as of own function expansion can be calculated. The study extended method of finding indicative prices for a wide class of derivative assets. One of the main advantages of our pricing methodology is that by combining the methods of the spectral theory of singular and regular perturbation; computing the price of the asset is reduced to solving the equation by finding the own values and own functions of the two solutions of the Poisson equation, reflecting the influence of various factors. Prospects for further research in this direction are the improvement and development of methods of spectral analysis for application in the study of stochastic volatility, depending on many heterogeneous factors taking place in the stock markets.