Paper: arXiv 2304.13402

Authors: David García-Lorite, Raul Merino

Abstract

In this paper, we develop a novel method based on Malliavin calculus to find an approximation for the convexity adjustment for various classical interest rate products. Malliavin calculus provides a simple way to get a template for the convexity adjustment. We find the approximation for Futures, OIS Futures, FRAs, and CMSs under a general family of the one-factor Cheyette model. We have also seen the excellent quality of the numerical accuracy of the formulas obtained.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper demonstrates strong mathematical rigor by leveraging Malliavin calculus to derive analytic templates for convexity adjustments in interest rate derivatives under the Cheyette framework. However, it leans primarily theoretical, relying on synthetic numerical validation rather than extensive empirical backtesting with real market data.

Research Flowchart

  flowchart TD
    A["Research Goal: Approximate Convexity<br>Adjustments for Interest Rate Products"] --> B["Framework: One-Factor Cheyette Model"]
    B --> C["Methodology: Malliavin Calculus<br>Derivation Template"]
    C --> D["Apply to Products:<br>Futures, OIS Futures, FRAs, CMSs"]
    D --> E["Derive Analytical Approximation Formulas"]
    E --> F["Numerical Validation & Accuracy Testing"]
    F --> G["Outcome: Simple, Highly Accurate<br>Convexity Adjustment Formulas"]