Robust Pricing and Hedging of Options on Multiple Assets and Its Numerics

DOI10.1137/19M1286256zbMATH Open1467.91212arXiv1909.03870OpenAlexW3132842644MaRDI QIDQ4987713

Stephan Eckstein, Tongseok Lim, Gaoyue Guo, Jan Obłój

Publication date: 4 May 2021

Published in: SIAM Journal on Financial Mathematics (Search for Journal in Brave)

Abstract: We consider robust pricing and hedging for options written on multiple assets given market option prices for the individual assets. The resulting problem is called the multi-marginal martingale optimal transport problem. We propose two numerical methods to solve such problems: using discretisation and linear programming applied to the primal side and using penalisation and deep neural networks optimisation applied to the dual side. We prove convergence for our methods and compare their numerical performance. We show how adding further information about call option prices at additional maturities can be incorporated and narrows down the no-arbitrage pricing bounds. Finally, we obtain structural results for the case of the payoff given by a weighted sum of covariances between the assets.

Full work available at URL: https://arxiv.org/abs/1909.03870

zbMATH Keywords

linear programmingnumerical methodsmachine learningoptimal transportmartingale optimal transportrobust pricing and hedgingdeep neural networksmulti-marginal transportrobust copula

Mathematics Subject Classification ID

Numerical methods (including Monte Carlo methods) (91G60) Martingales with discrete parameter (60G42) Numerical methods involving duality (49M29) Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.) (90C08) Derivative securities (option pricing, hedging, etc.) (91G20) Discrete approximations in optimal control (49M25)

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Related Items (12)

Robust deep hedging ⋮ Geometry of vectorial martingale optimal transportations and duality ⋮ Bounds on Choquet risk measures in finite product spaces with ambiguous marginals ⋮ On intermediate marginals in martingale optimal transportation ⋮ Duality Formulas for Robust Pricing and Hedging in Discrete Time ⋮ Robust pricing and hedging of double no-touch options ⋮ Neural networks can detect model-free static arbitrage strategies ⋮ Pricing, no-arbitrage bounds and robust hedging of instalment options ⋮ Detecting data-driven robust statistical arbitrage strategies with deep neural networks ⋮ A multi-marginal c-convex duality theorem for martingale optimal transport ⋮ Improved robust price bounds for multi-asset derivatives under market-implied dependence information ⋮ Robust statistical arbitrage strategies

Uses Software

• Wasserstein GAN

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