A deep learning approach to data-driven model-free pricing and to martingale optimal transport
This provides a tractable solution for financial practitioners needing fast pricing and hedging in high-dimensional scenarios, though it is incremental as it builds on existing deep learning methods.
The paper tackles the problem of computing model-free price bounds and optimal hedging strategies for financial derivatives using a neural network approach, demonstrating its accuracy with real market data and extending it to solve martingale optimal transport problems.
We introduce a novel and highly tractable supervised learning approach based on neural networks that can be applied for the computation of model-free price bounds of, potentially high-dimensional, financial derivatives and for the determination of optimal hedging strategies attaining these bounds. In particular, our methodology allows to train a single neural network offline and then to use it online for the fast determination of model-free price bounds of a whole class of financial derivatives with current market data. We show the applicability of this approach and highlight its accuracy in several examples involving real market data. Further, we show how a neural network can be trained to solve martingale optimal transport problems involving fixed marginal distributions instead of financial market data.