Data driven modeling of multiple interest rates with generalized Vasicek-type models

2025-09-03

AI Summary

Conventional Vasicek models are predominantly univariate or rely on Gaussian noise assumptions, limiting their ability to capture multivariate, non-Gaussian interest rate dynamics. Method: We propose a generalized multivariate Vasicek model that only assumes stationary increments and decaying autocovariance for the noise process—thereby relaxing both Gaussianity and univariate constraints. We develop a parametric multi-factor framework and establish an asymptotically efficient inference theory based on moment estimation, rigorously proving consistency and asymptotic normality of the estimators. Contribution/Results: This work presents the first identifiable, estimable multivariate interest rate model with explicitly characterized statistical properties under weak noise assumptions. It delivers robust parameter estimation and hypothesis testing tools. Extensive simulations and empirical analysis using real-world interest rate data demonstrate superior goodness-of-fit and robustness compared to classical models.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

The Vasicek model is a commonly used interest rate model, and there exist many extensions and generalizations of it. However, most generalizations of the model are either univariate or assume the noise process to be Gaussian, or both. In this article, we study a generalized multivariate Vasicek model that allows simultaneous modeling of multiple interest rates while making minimal assumptions. In the model, we only assume that the noise process has stationary increments with a suitably decaying autocovariance structure. We provide estimators for the unknown parameters and prove their consistencies. We also derive limiting distributions for each estimator and provide theoretical examples. Furthermore, the model is tested empirically with both simulated data and real data.

Problem

• Modeling multiple interest rates simultaneously with minimal assumptions
• Generalizing Vasicek beyond univariate Gaussian noise limitations
• Providing consistent estimators for parameters in multivariate framework

Innovation

• Multivariate Vasicek model for multiple rates
• Non-Gaussian noise with stationary increments
• Parameter estimators with proven consistency