Paper: arXiv 2311.14567

Authors: Beatrice Acciaio, Antonio Marini, Gudmund Pammer

Abstract

The Bass local volatility model introduced by Backhoff-Veraguas, Beiglböck, Huesmann, and Källblad is a Markov model perfectly calibrated to vanilla options at finitely many maturities, that approximates the Dupire local volatility model. Conze and Henry-Labordère show that its calibration can be achieved by solving a fixed-point equation. In this paper we complement the analysis and show existence and uniqueness of the solution to this equation, and that the fixed-point iteration scheme converges at a linear rate.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: This paper presents a strong theoretical contribution by proving the existence, uniqueness, and linear convergence rate for the Bass local volatility model’s calibration scheme. However, it is primarily a theoretical mathematical finance paper with limited empirical backtesting or real-market data application.

Research Flowchart

  flowchart TD
    A[Research Goal: Prove existence, uniqueness, and convergence of Bass Local Volatility Model calibration] --> B[Input Data: Vanilla Option Prices at Finitely Many Maturities]
    B --> C[Formulate Calibration as a Fixed-Point Equation]
    C --> D[Apply Fixed-Point Iteration Scheme]
    D --> E[Theoretical Analysis: Prove Contraction Mapping Properties]
    E --> F[Outcome 1: Guaranteed Existence & Uniqueness of Solution]
    E --> G[Outcome 2: Proof of Linear Convergence Rate]