Small Volatility Approximation and Multi-Factor HJM Models

ArXiv ID: 2506.12584 “View on arXiv”

Authors: V. M. Belyaev

Abstract

Here we demonstrate how we can use Small Volatility Approximation in calibration of Multi-Factor HJM model with deterministic correlations, factor volatilities and mean reversals. It is noticed that quality of this calibration is very good and it does not depend on number of factors.

Keywords: Heath-Jarrow-Morton (HJM) Model, Small Volatility Approximation, Calibration, Deterministic Volatility, Term Structure, Fixed Income

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: The paper is dense with advanced stochastic calculus, advanced PDEs, and multi-factor HJM derivations, fitting High Math, but it lacks backtesting, code, or specific data implementation details, resulting in Low Empirical Rigor.

  flowchart TD
    A["Research Goal:<br>Effective Calibration of Multi-Factor HJM"] --> B["Key Data/Inputs<br>Market Swap Rates & Volatilities"]
    B --> C{"Core Methodology:<br>Small Volatility Approximation"}
    C --> D["Computational Process:<br>Solve for Factor Loadings<br>Calibrate HJM Parameters"]
    D --> E["Key Finding 1:<br>Very Good Calibration Quality"]
    D --> F["Key Finding 2:<br>Quality Independent<br>of Number of Factors"]
    E --> G["Outcome:<br>Efficient Deterministic<br>Volatility HJM Framework"]
    F --> G