SABR Type Libor (Forward) Market Model (SABR/LMM) with time-dependent skew and smile

Paper: arXiv 2603.07616

Authors: Osamu Tsuchiya

Abstract

Volatility Skew and Smile of Interest Rate products (Swaption and Caplet) are represented by SABR (Stochastic Alpha Beta Rho model). So, the Interest Rate derivatives model for pricing the callable exotic swaps should be comparable to the SABR volatility surface. In the interest rate derivatives models, Libor Market Model (LMM) (in a post-Libor world, Forward Market Model (FMM)) is one of the most popular models used in the market. So, there are many attempts to develop LMMs that are comparable to the SABR surface. It is called SABR/LMM. There are many references for SABR/LMM, but most of them only treat SABR/LMM, which is not flexible enough to be used practically in global banks. The purpose of this paper is to provide a comprehensive definition of SABR/LMM and a complete description of how it is to be implemented.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 2.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a dense mathematical derivation for mapping a complex SABR/LMM framework to an uncorrelated SABR model using skew averaging and perturbation techniques. However, it lacks empirical backtesting, market data implementation, and validation against real trading desks, making it primarily a theoretical modeling contribution.

Research Flowchart

  flowchart TD
    A["Research Goal: Practical SABR/LMM with time-dependent skew & smile for callable exotics"] --> B["Inputs: Market SABR surfaces (Caplet/Swaption) & Initial Forward Curves"]
    B --> C["Methodology: Comprehensive definition of extended SABR/LMM framework"]
    C --> D["Computation: Parameter calibration & Monte Carlo simulation engine"]
    D --> E["Key Findings: Practical, fully flexible SABR/LMM implementation for global banks"]