Work

Computational Linearization of Nonlinear Kolmogorov Equations via the Generalized Newton Method in LSV Models

Year: 2026

Type: article

Abstract: This study develops a generalized Newton method to address the nonlinear Kolmogorov forward equation (KFE) under the local stochastic volatility (LSV) framework. Analytical convergence conditions are derived via the geometric series theorem, and empirical validation is conducted using 15 years of monthly crude oil spot price data (2011–2025), with the parameters set using maximum likelihood estimation. Sensitivity analyses confirm the stable convergence of the iterative scheme under realistic scenarios while also identifying parameter ranges that may lead to divergence. These findings demonstrate that the proposed methodology provides a tractable and accurate approach to probability density estimation in commodity markets, with a clear potential for extension to multi-dimensional settings and richer datasets.

Source: Mathematics

DOI: 10.3390/math14030555

Authors: Mehran Paziresh, Karim Ivaz, Mariyan Milev

Institutions: University of Tabriz, Sofia University "St. Kliment Ohridski"

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Bulgarian National Science Fund