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Revisiting semidefinite programming approaches to options pricing: complexity and computational perspectives

Didier Henrion(henrion***at***laas.fr)
Felix Kirschner(f.c.kirschner***at***tilburguniversity.edu)
Etienne de Klerk(e.deklerk***at***tilburguniversity.edu)
Milan Korda(korda***at***laas.fr)
Jean Bernard Lasserre(lasserre***at***laas.fr)
Victor Magron(magron***at***laas.fr)

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 (SOS) hierarchy of Lasserre to obtain bounds on the range of the possible prices. A complementary approach (also due to 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.

Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Category 2: Applications -- OR and Management Sciences (Finance and Economics )


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Entry Submitted: 11/15/2021
Entry Accepted: 11/15/2021
Entry Last Modified: 11/15/2021

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