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

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2021

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Guo, Gaoyue
Lim, Tongseok
Obłój, Jan

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SIAM Journal on Financial Mathematics. SIAM. 2021, 12(1), pp. 158-188. eISSN 1945-497X. Available under: doi: 10.1137/19M1286256

Zusammenfassung

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 multimarginal martingale optimal transport problem. We propose two numerical methods to solve such problems: using discretization and linear programming applied to the primal side and using penalization and deep neural networks optimization 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.

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510 Mathematik

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ISO 690ECKSTEIN, Stephan, Gaoyue GUO, Tongseok LIM, Jan OBŁÓJ, 2021. Robust Pricing and Hedging of Options on Multiple Assets and Its Numerics. In: SIAM Journal on Financial Mathematics. SIAM. 2021, 12(1), pp. 158-188. eISSN 1945-497X. Available under: doi: 10.1137/19M1286256
BibTex
@article{Eckstein2021Robus-53511,
  year={2021},
  doi={10.1137/19M1286256},
  title={Robust Pricing and Hedging of Options on Multiple Assets and Its Numerics},
  number={1},
  volume={12},
  journal={SIAM Journal on Financial Mathematics},
  pages={158--188},
  author={Eckstein, Stephan and Guo, Gaoyue and Lim, Tongseok and Obłój, Jan}
}
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