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

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  • Antonio Marini

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.

Suggested Citation

  • Antonio Marini, 2026. "Mimicking Volatilities under Marginal Constraints via $q_x$-Bass Martingales: A Parallel Computing Approach," Papers 2610.31825, arXiv.org.
    • Handle: RePEc:arx:papers:2610.31825
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    File URL: https://arxiv.org/pdf/2610.31825
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