The Mean Field Market Model Revisited

ArXiv ID: 2402.10215 “View on arXiv”

Authors: Unknown

Abstract

In this paper, we present an alternative perspective on the mean-field LIBOR market model introduced by Desmettre et al. in arXiv:2109.10779. Our novel approach embeds the mean-field model in a classical setup, but retains the crucial feature of controlling the term rate’s variances over large time horizons. This maintains the market model’s practicability, since calibrations and simulations can be carried out efficiently without nested simulations. In addition, we show that our framework can be directly applied to model term rates derived from SOFR, ESTR or other nearly risk-free overnight short-term rates – a crucial feature since many IBOR rates are gradually being replaced. These results are complemented by a calibration study and some theoretical arguments which allow to estimate the probability of unrealistically high rates in the presented market models.

Keywords: Mean-field models, LIBOR market model, SOFR/ESTR, Term structure modeling, Stochastic volatility, Interest Rates

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: The paper is highly theoretical, featuring dense stochastic calculus, measure theory, and ODE derivations with minimal empirical data or backtesting results.

  flowchart TD
    A["Research Goal<br>Develop an efficient, realistic model<br>for LIBOR market replacement rates"] --> B["Key Methodology<br>Embed mean-field model in classical setup"]
    B --> C["Data Inputs<br>Historical data for SOFR/ESTR<br>and near risk-free rates"]
    B --> D["Computational Process<br>Calibration & simulation without<br>nested methods"]
    C --> D
    D --> E["Key Findings & Outcomes<br>• Retains volatility control<br>• Supports SOFR/ESTR modeling<br>• High-rate probability estimation"]
    E --> F["Impact<br>Practical, scalable term structure model<br>for replacing legacy IBOR rates"]