Improved model-free bounds for multi-asset options using option-implied information and deep learning
Evangelia Dragazi, Shuaiqiang Liu, Antonis Papapantoleon
TL;DR
The paper addresses model-free bounds for $d$-asset options under dependence uncertainty with additional market information, formalized by $\mathcal{Q}=\{ \mu: \mu_j=\nu_j, \int \phi_i \,d\mu=p_i \}$. It establishes a fundamental theorem of asset pricing (no uniform strong arbitrage iff $\mathcal{Q}\neq\emptyset$) and a superhedging duality $\Phi(f)=\max_{\mu\in\mathcal{Q}}\int f\,d\mu$, enabling a dual formulation over trading strategies. A penalized neural-network scheme is proposed to solve the dual problem, with convergence $\Phi^m_{\theta,\gamma}(f) \to \Phi(f)$ as $m,\gamma\to\infty$, and computation scales linearly with the number of assets. Numerical experiments on artificial data show that additional option-implied information sharpens bounds, especially when information is of the same payoff structure as the target and thus most relevant for accuracy versus efficiency. The approach supports fast, scalable pricing and hedging under dependence uncertainty and data-driven market information, guiding practitioners to prioritize relevant information in high-dimensional settings.
Abstract
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.