Convergence in probability of numerical solutions of a highly non-linear delayed stochastic interest rate model

ArXiv ID: 2510.04092 “View on arXiv”

Authors: Emmanuel Coffie

Abstract

We examine a delayed stochastic interest rate model with super-linearly growing coefficients and develop several new mathematical tools to establish the properties of its true and truncated EM solutions. Moreover, we show that the true solution converges to the truncated EM solutions in probability as the step size tends to zero. Further, we support the convergence result with some illustrative numerical examples and justify the convergence result for the Monte Carlo evaluation of some financial quantities.

Keywords: Stochastic Differential Equations, Interest Rate Models, Euler-Maruyama Method, Numerical Analysis, Monte Carlo Methods, Fixed Income

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats
• Why: The paper is heavily theoretical, focusing on proving the convergence of numerical solutions for a complex stochastic differential delay equation (SDDE) with super-linear coefficients, which involves advanced stochastic calculus and heavy mathematical derivations. The empirical support is limited to ‘illustrative numerical examples’ and a justification for Monte Carlo use, but lacks backtest-ready code, statistical metrics, or detailed implementation steps.

  flowchart TD
    A["Research Goal:<br/>Convergence of Numerical Solutions<br/>for Non-linear Stochastic Interest Rate Model"] --> B["Methodology: Develop New Mathematical Tools<br/>and Apply Euler-Maruyama Method"]
    B --> C["Inputs: Delayed Stochastic SDE<br/>with Super-linear Growth"]
    C --> D["Computational Process:<br/>Truncated Euler-Maruyama (EM) Solutions"]
    D --> E["Key Finding: True Solution converges<br/>in probability to EM solution as step size → 0"]
    E --> F["Validation: Numerical Examples &<br/>Monte Carlo Evaluation of Financial Quantities"]