Martingale Optimal Transport in Financial Modeling
Summary
Martingale optimal transport (MOT) has emerged as a unifying framework for model-independent pricing and hedging of financial derivatives. By combining the classical theory of optimal mass transport with the martingale constraint dictated by absence of arbitrage, MOT characterises the extremal couplings between marginal distributions of asset prices that are consistent with market data. This approach yields sharp bounds on option prices without reliance on a specific stochastic model, and naturally gives rise to dual formulations in terms of superhedging strategies. In continuous time, MOT connects with robust superreplication via pathwise methods, embedding techniques and dynamic programming principles, while in discrete time it underlies nested distance metrics that respect the temporal information structure. Across these developments, the interplay between geometry of transport plans, duality theory and financial applications has led to new insights into stability of hedges, sensitivity to model misspecification and the design of trading strategies that perform uniformly well across a range of possible price evolutions.
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Martingale Optimal Transport in Financial Modeling publication trend
The graph below shows the total number of articles in martingale optimal transport in financial modeling across all publications each year (not limited to Nature Index journals).
Technical terms
Martingale optimal transport: The problem of finding transport plans between given marginal distributions that satisfy the martingale property, minimising or maximising a cost functional without assuming a specific price process model.
Optimal transport: A mathematical theory concerned with moving one probability measure to another at minimal cost, traditionally without additional constraints.
Superhedging: The construction of a trading strategy whose terminal value dominates a contingent claim in every admissible scenario, yielding a model-independent price bound.
Adapted Wasserstein distance: A variant of the Wasserstein metric on path space that respects the temporal information structure of stochastic processes, ensuring continuity of dynamic strategies.
Skorokhod embedding: A method for representing a target distribution as the distribution of Brownian motion at a stopping time, often used to derive model-independent pricing bounds.
References
- A model‐free approach to continuous‐time finance. Mathematical Finance (2023).
- Adapted Wasserstein distances and stability in mathematical finance. Finance and Stochastics (2020).
- The geometry of multi-marginal Skorokhod Embedding. Probability Theory and Related Fields (2019).
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