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

  • Antonio Marini
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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 qx-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 qx-Bass martingales, we develop numerical methods for the discrete-time problems that do not require full marginal distributions at calibration maturities.

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Cite

BibTeXRIS
BibTeX
@misc{marini2026mimicking,
  title = {{Mimicking Volatilities under Marginal Constraints via $q_x$-Bass Martingales: A Parallel Computing Approach}},
  author = {Antonio Marini},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.31825},
  eprint = {2610.31825},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.31825},
}
RIS
TY  - UNPB
TI  - Mimicking Volatilities under Marginal Constraints via q_x-Bass Martingales: A Parallel Computing Approach
AU  - Antonio Marini
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2610.31825
UR  - https://arxiv.org/abs/2610.31825
AB  - 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.
ER  -