UDC 004.94
DOI: 10.36871/2618-9976.2021.10.004
Authors
Kuzmina H.V.
Ph.D. in PhysicoMathematical
Sciences, Associate Professor, Belarusian State University, Minsk, Republic
of Belarus
Ivanov M.N.
Candidate of Economics Sciences, Financial University under the Government of the Russian Federation,
Moscow, Russia
Abstract
The paper discusses the capabilities of the R language for the visualization
in modeling Levy processes – processes that currently
most closely correspond to the nature of the evolution of stock
price movements. R is a programming language and a free software
environment for statistical data processing and graphics.
Due to the possibility of direct access from R to stock values
stored in the Oracle database, modeling Levy processes in the R
language is an urgent task.
Levy processes are used as processes describing the evolution
of the logarithmic returns of financial assets in the exponential
Levy model. The article proposes modeling algorithms for some
Levy processes that significantly reduce the modeling time
of these processes compared to previously known Levy process
modeling algorithms. A significant reduction in the simulation
time of the indicated processes is confirmed experimentally.
A mathematical justification is presented for representing
the CGMY process as the difference of two slowly growing stable
independent random Levy processes. The efficient algorithm
of the CGMY process simulation as a difference of the tempered
stable independent Levy is processed and programmed at R language.
The efficient algorithm of variance gamma process simulation
using variance gamma random variables is processed and
programmed at R language.
Keywords
Levy processes
CGMY process
Variance gamma process
R language
