Revisiting Semidefinite Programming Approaches to Options Pricing: Complexity and Computational Perspectives

In this paper, we consider the problem of finding bounds on prices options depending multiple assets without assuming any underlying model price dynamics but only absence arbitrage opportunities. We formulate as a generalized moment and utilize well-known moment-sum-of-squares hierarchy Lasserre to obtain range possible prices. A complementary approach (also from Lasserre) is employed for comparison. present several numerical examples demonstrate viability our approach. The framework makes it incorporate different kinds observable data, such information, well interest. History: Accepted by Antonio Frangioni, area editor Design & Analysis Algorithms–Continuous. Funding: This work was supported European Union’s Horizon 2020 research innovation program under Marie Skłodowska-Curie grant agreement [Grant 813211 (POEMA)]. Supplemental Material: software that supports findings study available within paper its Supplementary Information [ https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.1220 ] or IJOC GitHub repository ( https://github.com/INFORMSJoC ) at http://dx.doi.org/10.5281/zenodo.6602361 ].