Steady States Transitions and Correlated Noise: Rethinking Interest Rate Model Stability

Abstract

This study explores the effects of incorporating colored noises into stochastic financial models, replacing traditional Brownian motion, to analyze how they influence change-point detection. Our focus lies in understanding how correlated noises alter volatility patterns in time series data and impact critical transition points within both synthetic model and actual financial models. For the latter, we employ the Vasicek model, commonly used to model interest rate dynamics, as a core component of our investigation.
The paper offers a background on the dynamics of complex systems, specifically in financial and economic contexts, where multiple stable states and sudden transitions are prevalent. In this paper, we dissect interest rate models, scrutinize their market influence, and illuminate how they respond to underlying economic fluctuations. We survey relevant literature and examine the Vasicek model's capabilities in financial modeling, including its potential for identifying critical shifts.
Our analysis centers on replacing Brownian motion with colored noises such as pink and red. The Euler-Maruyama method aids in obtaining numerical solutions for the modified model. We further address the processes of parameter estimation, integration step calibration, and change-point identification using the efficient Pruned Exact Linear Time (PELT) algorithm.
Crucially, we investigate the ability of both deep learning and conventional machine learning models to recognize transitions between stable states induced by fluctuations within the data.