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Price dispersion and vanilla options in a financial market game

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  • Toraubally, Waseem A.

Abstract

We construct a game-theoretic model characterised by perfect information, no transaction costs, in which agents can borrow at the risk-free interest rate and engage in short selling. Traders can freely and instantaneously eliminate any unexploited profit opportunities through pure arbitrage just as the efficient market hypothesis postulates they should. Yet, in this work, we put forth, in a frictionless framework, a counterexample in which the Law of One Price fails in the underlying asset markets at equilibrium. At a theoretical level, this leads both the Binomial Option Pricing Model (BOPM) and in the limit, the Black–Scholes–Merton Model (BSMM), to misprice the vanilla options written on these assets. This compelling result is pregnant with far-reaching ramifications: (i) theoretically, it establishes that no-arbitrage, while necessary, is not sufficient for any of the BOPM and BSMM to yield consistent results; (ii) practically, it crystallises the need for practitioners to rely on additional, more data-adaptive, methods of option pricing.

Suggested Citation

  • Toraubally, Waseem A., 2022. "Price dispersion and vanilla options in a financial market game," Finance Research Letters, Elsevier, vol. 50(C).
    • Handle: RePEc:eee:finlet:v:50:y:2022:i:c:s1544612322004883
    DOI: 10.1016/j.frl.2022.103305
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    References listed on IDEAS

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    1. Baldwin, Kenneth & Alhalboni, Maryam, 2020. "The impact of profit-sharing investment accounts on shareholders’ wealth," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 69(C).
    2. Toraubally, Waseem A., 2022. "Strategic trading and Ricardian comparative advantage," Journal of Economic Behavior & Organization, Elsevier, vol. 195(C), pages 428-447.
    3. Koutsougeras, L., 1999. "A Remark on the Number of Trading Posts in Strategic Market Games," Discussion Paper 1999-04, Tilburg University, Center for Economic Research.
    4. Peck, James & Shell, Karl, 1990. "Liquid markets and competition," Games and Economic Behavior, Elsevier, vol. 2(4), pages 362-377, December.
    5. Owen A. Lamont & Richard H. Thaler, 2003. "Anomalies: The Law of One Price in Financial Markets," Journal of Economic Perspectives, American Economic Association, vol. 17(4), pages 191-202, Fall.
    6. Koutsougeras, L., 1999. "A Remark on the Number of Trading Posts in Strategic Market Games," Other publications TiSEM eac59545-f91e-41f1-8067-1, Tilburg University, School of Economics and Management.
    7. Toraubally, Waseem A., 2018. "Large market games, the law of one price, and market structure," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 13-26.
    8. KOUTSOUGERAS, Leonidas C., 1999. "A remark on the number of trading posts in strategic market games," LIDAM Discussion Papers CORE 1999005, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
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    Cited by:

    1. Baldwin, Kenneth & Alhalboni, Maryam, 2023. "A value-based measure of market power for the participatory deposits of Islamic banks," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 87(C).

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    More about this item

    Keywords

    Shapley–Shubik market games; Law of one price; Vanilla options; Short sales; Binomial option pricing; Oligopoly;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General

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