SIMULATION OF STOCK MARKET PRICING USING THE MODEL CEV

Authors

  • I.V. Burtnyak Vasyl Stefanyk Precarpatian National University Ministry of Education and Science of Ukraine, Department of Economic Cybernetics, Shevchenko str., 57, Ivano-Frankivsk, 76018
  • G.P. Malitska Vasyl Stefanyk Precarpatian National University Ministry of Education and Science of Ukraine, Department of Mathematical and functional analysis, Shevchenko str., 57, Ivano-Frankivsk, 76018

DOI:

https://doi.org/10.15330/apred.1.16.40-47

Keywords:

derivative pricing, stochastic volatility, local volatility, spectral theory, singular perturbation theory, regular perturbation theory

Abstract

This paper develops a systematic method for calculating approximate prices for a wide range of securities implying the tools of spectral analysis, singular and regular perturbation theory. Price options depend on stochastic volatility, which may be multiscale, in the sense that it may be driven by one fast-varying and one slow-varying factor. Price finding is reduced to the problem solving of eigenvalues and eigenfunctions of a certain equation.

The method of finding the approximate price for a wide class of derivatives whose volatility depends on two groups of variables has been improved, using the spectral theory and wave theory of singular and regular perturbations, Options for forecasting options generated by diffusion processes, where diffusion depends on two groups of variables, have been forecast. An algorithm for calculating the approximate price of derivatives and the accuracy of estimates has been developed, which allows to analyze and draw precautionary conclusions and proposals to minimize the risks of pricing derivatives that arise in the stock market. Methods for calculating the approximate price of options using the tools of spectral analysis, singular and regular wave theory in the case of fast and slow factors are developed. Combining methods from the spectral theory of singular and regular perturbations, it is possible to estimate the price of derivative financial instruments as a schedule by eigenfunctions. An algorithm for calculating the approximate price of derivatives and the accuracy of estimates has been developed, which allows to analyze and draw precautionary conclusions and proposals to minimize the risks of pricing derivatives that arise in the stock market

Author Biographies

I.V. Burtnyak , Vasyl Stefanyk Precarpatian National University Ministry of Education and Science of Ukraine, Department of Economic Cybernetics, Shevchenko str., 57, Ivano-Frankivsk, 76018

D. Sc. Econ., Professor

G.P. Malitska , Vasyl Stefanyk Precarpatian National University Ministry of Education and Science of Ukraine, Department of Mathematical and functional analysis, Shevchenko str., 57, Ivano-Frankivsk, 76018

Ph.D (Physical and Mathematica),  associate professor

References

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Published

2020-11-25

Issue

Vol. 1 No. 16 (2020): THE ACTUAL PROBLEMS OF REGIONAL ECONOMY DEVELOPMENT

Section

Development of financial-credit and insurance market of Ukraine

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