Improved model-free bounds for multi-asset options using option-implied information and deep learning
This work addresses the challenge of pricing multi-asset options in financial markets where dependence structures are uncertain, offering a computationally efficient method that prioritizes relevant derivative information for improved accuracy.
The paper tackles the problem of computing model-free bounds for multi-asset options under dependence uncertainty by incorporating partial market information, such as known prices for multi-asset options, and develops a method using a penalization approach combined with deep learning to solve the optimization efficiently, with computational time scaling linearly with the number of assets.
We consider the computation of model-free bounds for multi-asset options in a setting that combines dependence uncertainty with additional information on the dependence structure. More specifically, we consider the setting where the marginal distributions are known and partial information, in the form of known prices for multi-asset options, is also available in the market. We provide a fundamental theorem of asset pricing in this setting, as well as a superhedging duality that allows to transform the maximization problem over probability measures in a more tractable minimization problem over trading strategies. The latter is solved using a penalization approach combined with a deep learning approximation using artificial neural networks. The numerical method is fast and the computational time scales linearly with respect to the number of traded assets. We finally examine the significance of various pieces of additional information. Empirical evidence suggests that "relevant" information, i.e. prices of derivatives with the same payoff structure as the target payoff, are more useful that other information, and should be prioritized in view of the trade-off between accuracy and computational efficiency.