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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Didier Henrion & Felix Kirschner & Etienne De Klerk & Milan Korda & Jean-Bernard Lasserre & Victor Magron, 2023. "Revisiting Semidefinite Programming Approaches to Options Pricing: Complexity and Computational Perspectives," INFORMS Journal on Computing, INFORMS, vol. 35(2), pages 335-349, March.
    • Handle: RePEc:inm:orijoc:v:35:y:2023:i:2:p:335-349
    DOI: 10.1287/ijoc.2022.1220
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    References listed on IDEAS

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    1. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Flemming Holtorf & Paul I. Barton, 2024. "Tighter Bounds on Transient Moments of Stochastic Chemical Systems," Journal of Optimization Theory and Applications, Springer, vol. 200(1), pages 104-149, January.

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