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A new elementary geometric approach to option pricing bounds in discrete time models

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  • Braouezec, Yann
  • Grunspan, Cyril

Abstract

The aim of this paper is to provide a new straightforward measure-free methodology based on convex hulls to determine the no-arbitrage pricing bounds of an option (European or American). The pedagogical interest of our methodology is also briefly discussed. The central result, which is elementary, is presented for a one period model and is subsequently used for multiperiod models. It shows that a certain point, called the forward point, must lie inside a convex polygon. Multiperiod models are then considered and the pricing bounds of a put option (European and American) are explicitly computed. We then show that the barycentric coordinates of the forward point can be interpreted as a martingale pricing measure. An application is provided for the trinomial model where the pricing measure has a simple geometric interpretation in terms of areas of triangles. Finally, we consider the case of entropic barycentric coordinates in a multi asset framework.

Suggested Citation

  • Braouezec, Yann & Grunspan, Cyril, 2016. "A new elementary geometric approach to option pricing bounds in discrete time models," European Journal of Operational Research, Elsevier, vol. 249(1), pages 270-280.
    • Handle: RePEc:eee:ejores:v:249:y:2016:i:1:p:270-280
    DOI: 10.1016/j.ejor.2015.08.024
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    References listed on IDEAS

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    Cited by:

    1. Alexander Chigodaev, 2016. "Recursive Method for Guaranteed Valuation of Options in Deterministic Game Theoretic Approach," HSE Working papers WP BRP 53/FE/2016, National Research University Higher School of Economics.
    2. Braouezec, Yann & Joliet, Robert, 2019. "Valuing an investment project using no-arbitrage and the alpha-maxmin criteria: From Knightian uncertainty to risk," Economics Letters, Elsevier, vol. 178(C), pages 111-115.
    3. Braouezec, Yann, 2017. "How fundamental is the one-period trinomial model to European option pricing bounds. A new methodological approach," Finance Research Letters, Elsevier, vol. 21(C), pages 92-99.

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