The Bass Local Volatility Model: Properties, Convergence Of The Fixed-Point Iteration, and Connections with Martingale Optimal Transport

This thesis centers on martingale optimal transport applications to finance, specifically examining the 1-dimensional Bass Local Volatility model. Its calibration is attained through the resolution of a fixed-point equation introduced by Conze and Henri-Labordère in 2021. This work establishes the convergence of the fixed-point scheme and explores the geometric properties of the associated integral operator in the semidiscrete setting. It also introduces practical methods for model calibration and identifies properties to simplify computational cost.