The Bass local volatility model introduced by Backhoff-Veraguas–Beiglböck–Huesmann–Källblad is a Markov model perfectly calibrated to vanilla options at finitely many maturities, that approximates the Dupire local volatility model. Recently Conze and Henry-Labordère showed that its calibration can be achieved by solving a fixed-point equation. In this talk I will present our results of existence and uniqueness of the solution to this equation, and of convergence of the fixed-point iteration scheme. This talk is based on joint work with A. Marini and G. Pammer.