Application of the method of separation of mixtures of probability distributions in financial analysis problems

Recieved: 04/11/2023

Accepted: 05/15/2023

Published: 09/20/2023

Keywords: stochastic differential equations, finite mixtures of normal distributions, optimization method for separating mixtures of probability distributions, volatility, Value at Risk estimation

To cite this article

Lagno A.O., Kuzmin I. S. Application of the method of separation of mixtures of probability distributions in financial analysis problems. // Moscow University Journal. Series 15. Computational Mathematics and Cybernetics. 2023. N 3, p.33-48 https://doi.org/10.55959/MSU/0137–0782–15–2023–47–3–33–48.

This work is licensed under a Сreative Commons Atribiution - NonCommercial 4.0 International (CC BY-NC 4.0)

Lagno A.O. (Lomonosov Moscow State University (MSU))
Kuzmin I. S. (Lomonosov Moscow State University (MSU))

Abstract

This paper is devoted to the problem of separation of mixtures of probability distributions. An optimization method is proposed as an alternative to the EM-algorithm (Expectation-Maximization) for statistical estimation of mixture parameters. The idea of approximating the distribution of increments (logarithms) of financial data by a mixture of normal laws is considered. The practical application of such an approximation to the problems of calculating and predicting volatility, as well as to the problem of calculating the risk measure (Value at Risk), is presented. The results obtained allow us to conclude that the application of mixtures of normal distributions to the description of financial data is adequate.