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arXiv · 2309.04947

Dimension Reduction in Martingale Optimal Transport: Geometry and Robust Option Pricing

Joshua Zoen-Git Hiew·Tongseok Lim·Brendan Pass·Marcelo Cruz de Souza
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Abstract

This paper addresses the problem of robust option pricing within the framework of Vectorial Martingale Optimal Transport (VMOT). We investigate the geometry of VMOT solutions for $N$-period market models and demonstrate that, when the number of underlying assets is $d=2$ and the payoff is sub- or supermodular, the extremal model reduces to a single-factor structure in the first period. This structural result allows for a significant dimension reduction, transforming the problem into a more tractable format. We prove that this reduction is specific to the two-asset case and provide counterexamples showing it generally fails for $d \geq 3$. Finally, we exploit this monotonicity to develop a reduced-dimension Sinkhorn algorithm. Numerical experiments demonstrate that this structure-preserving approach reduces computational time by approximately 99\% compared to standard methods while improving accuracy.

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Joshua Zoen-Git Hiew, Tongseok Lim, Brendan Pass, Marcelo Cruz de Souza. 2023-09-10. Dimension Reduction in Martingale Optimal Transport: Geometry and Robust Option Pricing. https://arxiv.org/abs/2309.04947

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