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

Didier Henrion (), Felix Kirschner (), Etienne De Klerk (), Milan Korda (), Jean-Bernard Lasserre () and Victor Magron ()
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Didier Henrion: Faculty of Electrical Engineering, Czech Technical University, 166 36 Prague 6, Czechia; Laboratory for Analysis and Architecture of Systems, French National Center for Scientific Research, 31400 Toulouse, France
Felix Kirschner: Tilburg University, 5037 AB Tilburg, Netherlands
Etienne De Klerk: Tilburg University, 5037 AB Tilburg, Netherlands
Milan Korda: Faculty of Electrical Engineering, Czech Technical University, 166 36 Prague 6, Czechia; Laboratory for Analysis and Architecture of Systems, French National Center for Scientific Research, 31400 Toulouse, France
Jean-Bernard Lasserre: Laboratory for Analysis and Architecture of Systems, French National Center for Scientific Research, 31400 Toulouse, France
Victor Magron: Laboratory for Analysis and Architecture of Systems, French National Center for Scientific Research, 31400 Toulouse, France

INFORMS Journal on Computing, 2023, vol. 35, issue 2, 335-349

Abstract: In this paper, we consider the problem of finding bounds on the prices of options depending on multiple assets without assuming any underlying model on the price dynamics but only the absence of arbitrage opportunities. We formulate this as a generalized moment problem and utilize the well-known moment-sum-of-squares hierarchy of Lasserre to obtain bounds on the range of the possible prices. A complementary approach (also from Lasserre) is employed for comparison. We present several numerical examples to demonstrate the viability of our approach. The framework we consider makes it possible to incorporate different kinds of observable data, such as moment information, as well as observable prices of options on the assets of interest.

Keywords: semidefinite programming; options pricing; moment-SOS hierarchy (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:orijoc:v:35:y:2023:i:2:p:335-349

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