Beatrice Acciaio (ETH Zurich)

Stretched Brownian Motion and Bass local-volatility model.

Abstract: The concept of stretched Brownian motion (SBM) has been introduced by Backhoff-Veraguas et al (2020) as the unique solution to a dynamic formulation of the martingale transport problem. The name originates from the characteristic of mimicking as closely as possible the movement of a Brownian particle, while fitting the prescribed marginals. Conze and Henry-Labordere (2021) suggested a fixed-point iteration scheme for the computation of the SBM. In this talk I will review fundamental results for the SMB and provide convergence results of the fixed-point  iteration. This constitutes the building block for the computation of the Bass local volatility model, which is a Markov model perfectly calibrated to vanilla options for finite maturities, and an approximation of the Dupire local volatility model.
[Based on a joint work with A. Marini and G. Pammer.]