Calibration of the Bass Local Volatility model

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.