Multi-Dimensional Martingales from Mutual Information
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911325841522688 |
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| author | Kay, Michael M. |
| author_facet | Kay, Michael M. |
| contents | In the context of Risk Neutral Pricing theory, we consider the classic problem of calibrating a martingale over $\mathbb{R}^n$ to a finite number of marginals thereof, or more practically, to prices of an arbitrary finite set of (joint) European contingent claims. For $n=1$, one can rely on the work of Dupire, while for $n\geq 2$ an analogous natural unique construction seems to be lacking. We provide such a unique candidate as the result of pure Martingale Entropic Optimal Transport. As a byproduct, the latter allows us to obtain a constructive proof of a classic result of Strassen. Finally, and in contrast to the proposed approach, we prove a result that demonstrates how a certain class of local correlation models fails in general to calibrate to basket option prices, particularly in the foreign exchange market. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16544 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multi-Dimensional Martingales from Mutual Information Kay, Michael M. Probability In the context of Risk Neutral Pricing theory, we consider the classic problem of calibrating a martingale over $\mathbb{R}^n$ to a finite number of marginals thereof, or more practically, to prices of an arbitrary finite set of (joint) European contingent claims. For $n=1$, one can rely on the work of Dupire, while for $n\geq 2$ an analogous natural unique construction seems to be lacking. We provide such a unique candidate as the result of pure Martingale Entropic Optimal Transport. As a byproduct, the latter allows us to obtain a constructive proof of a classic result of Strassen. Finally, and in contrast to the proposed approach, we prove a result that demonstrates how a certain class of local correlation models fails in general to calibrate to basket option prices, particularly in the foreign exchange market. |
| title | Multi-Dimensional Martingales from Mutual Information |
| topic | Probability |
| url | https://arxiv.org/abs/2512.16544 |