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The Measure Preserving Martingale Sinkhorn Algorithm

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  • Benjamin Joseph
  • Gregoire Loeper
  • Jan Obloj

Abstract

We contribute to the recent studies of the so-called Bass martingale. Backhoff-Veraguas et al. (2020) showed it is the solution to the martingale Benamou-Brenier (mBB) problem, i.e., among all martingales with prescribed initial and terminal distributions it is the one closest to Brownian motion. We link it with the semimartingale optimal transport and deduce an alternative way to arrive at the dual formulation recently obtained in Backhoff-Beraguas et al. (2023). We then consider computational methods to compute the Bass martingale. We propose an approach analogous to the famous Sinkhorn algorithm used to solve the entropic optimal transport problem. Our algorithm, dubbed the measure preserving martingale Sinkhorn (MPMS), is equivalent to the fixed-point method of Conze and Henry-Labordere (2021) and performs very well on a range of examples, including a market data case study.

Suggested Citation

  • Benjamin Joseph & Gregoire Loeper & Jan Obloj, 2023. "The Measure Preserving Martingale Sinkhorn Algorithm," Papers 2310.13797, arXiv.org, revised Dec 2023.
    • Handle: RePEc:arx:papers:2310.13797
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    References listed on IDEAS

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    1. Bruno Bouchard & G. Loeper & Y. Zou, 2017. "Hedging of covered options with linear market impact and gamma constraint," Post-Print hal-01611790, HAL.
    2. Bruno Bouchard & G Loeper & Y Zou, 2016. "Almost-sure hedging with permanent price impact," Post-Print hal-01133223, HAL.
    3. Bruno Bouchard & G Loeper & Y Zou, 2017. "Hedging of covered options with linear market impact and gamma constraint," Post-Print hal-01247523, HAL.
    4. Ivan Guo & Grégoire Loeper & Shiyi Wang, 2022. "Calibration of local‐stochastic volatility models by optimal transport," Mathematical Finance, Wiley Blackwell, vol. 32(1), pages 46-77, January.
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    Cited by:

    1. Beatrice Acciaio & Antonio Marini & Gudmund Pammer, 2023. "Calibration of the Bass Local Volatility model," Papers 2311.14567, arXiv.org.

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