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Option Pricing without Price Dynamics: A Probabilistic Approach

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  • Dimitris Bertsimas
  • Natasha Bushueva

Abstract

Employing probabilistic techniques we compute best possible upper and lower bounds on the price of an option on one or two assets with continuous piecewise linear payoff function based on prices of simple call options of possibly distinct maturities and the no-arbitrage condition, but without any assumption on the price dynamics of underlying assets. We show that the problem reduces to solving linear optimization problems that we explicitly characterize. We report numerical results that illustrate the effectiveness of the algorithms we develop.

Suggested Citation

  • Dimitris Bertsimas & Natasha Bushueva, 2006. "Option Pricing without Price Dynamics: A Probabilistic Approach," Papers math/0612075, arXiv.org.
    • Handle: RePEc:arx:papers:math/0612075
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    References listed on IDEAS

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    1. Stephen A. Ross, 1976. "Options and Efficiency," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 90(1), pages 75-89.
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    Cited by:

    1. Ariel Neufeld & Antonis Papapantoleon & Qikun Xiang, 2023. "Model-Free Bounds for Multi-Asset Options Using Option-Implied Information and Their Exact Computation," Management Science, INFORMS, vol. 69(4), pages 2051-2068, April.

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