Mimicking Volatilities under Marginal Constraints via $q_x$-Bass Martingales: A Parallel Computing Approach

Source abstract

We study the calibration of continuous-time martingale models to observed derivative prices via a dynamic martingale optimal transport problem that penalizes deviations from the volatility of a prescribed reference model. Using $q_x$-Bass martingales, we approximate this problem through a sequence of discrete-time problems and prove that the continuous-time interpolations of their optimizers are asymptotically optimal. Building on the theory of $q_x$-Bass martingales, we develop numerical methods for the discrete-time problems that do not require full marginal distributions at calibration maturities.