Calibration of the Bass Local Volatility model

TL;DR

This paper proves the existence, uniqueness, and convergence of a fixed-point scheme for calibrating the Bass local volatility model, which approximates the Dupire model and is perfectly calibrated to vanilla options.

Contribution

It establishes mathematical guarantees for the calibration process of the Bass local volatility model, including existence, uniqueness, and convergence of the fixed-point solution.

Findings

Existence and uniqueness of the fixed-point solution.

Linear convergence rate of the fixed-point iteration.

The model effectively approximates the Dupire local volatility model.

Abstract

The Bass local volatility model introduced by Backhoff-Veraguas, Beiglb\"ock, Huesmann, and K\"allblad is a Markov model perfectly calibrated to vanilla options at finitely many maturities, that approximates the Dupire local volatility model. Conze and Henry-Labord\`ere 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.