The mean field market model revisited

Area of Science:

• Quantitative Finance
• Financial Modeling
• Risk Management

Background:

• The LIBOR market model (LMM) is a standard in interest rate derivatives pricing.
• Mean-field models offer theoretical advantages but often lack practical implementation.
• Transitioning from IBORs to risk-free rates (RFRs) necessitates adaptable modeling frameworks.

Purpose of the Study:

• To present a novel, practical mean-field LMM.
• To enable efficient control of term rate variances over long time horizons.
• To facilitate the modeling of in-arrear term rates based on RFRs like SOFR and ESTR.

Main Methods:

• Embedding a mean-field model within a classical financial framework.
• Developing a method to control term rate variances without nested simulations.
• Applying the framework to model in-arrear term rates derived from SOFR and ESTR.

Main Results:

• The proposed model maintains LMM practicability through efficient calibration and simulation.
• The framework successfully models in-arrear term rates derived from RFRs.
• Theoretical arguments and calibration studies provide insights into model stability and the probability of extreme rates.

Conclusions:

• The novel mean-field LMM offers a practical and efficient alternative for financial modeling.
• The framework's adaptability to RFRs addresses the ongoing market transition.
• The model enhances risk management by allowing for the estimation of extreme rate probabilities.