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The Interval Market Model in Mathematical Finance pp 17–26Cite as

Birkhäuser

Option Pricing: Classic Results

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Part of the book series: Static & Dynamic Game Theory: Foundations & Applications ((SDGTFA))

Abstract

We recall here the basics of the most classic result of option pricing, perhaps the most famous result in mathematical finance: the Black–Scholes theory for the pricing of “European options” in a perfect market, infinitely divisible and liquid, with no “friction” such as transaction costs or information lag. However, in keeping with the spirit of this volume, we derive it via a game-theoretic approach, devoid of any probabilities.

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Notes

  1. 1.

    We could have, without loss of generality, taken D = 1 and then considered D such options. We resisted this simplification to avoid losing the dimensionality: like \(\mathcal{K}\), D is an amount in some currency.

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Authors and Affiliations

  1. INRIA Sophia Antipolis-Méditerranée, Sophia Antipolis, France

    Pierre Bernhard

  2. CentER, Department of Econometrics and Operations Research Tilburg School of Economics and Management, Tilburg University, Tilburg, The Netherlands

    Jacob C. Engwerda & J. M. Schumacher

  3. Department of Industrial Engineering and Business Information Systems School of Management and Governance, University of Twente, Enschede, The Netherlands

    Berend Roorda

  4. Department of Statistics, University of Warwick, Coventry, UK

    Vassili Kolokoltsov

  5. Université Paris Dauphine, Paris, France

    Patrick Saint-Pierre

  6. VIMADES (Viability, Markets, Automatics, Decisions), Paris, France

    Jean-Pierre Aubin

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  1. Pierre Bernhard
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Bernhard, P. et al. (2013). Option Pricing: Classic Results. In: The Interval Market Model in Mathematical Finance. Static & Dynamic Game Theory: Foundations & Applications. Birkhäuser, New York, NY. https://doi.org/10.1007/978-0-8176-8388-7_2

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