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Option pricing models without probability: a rough paths approach

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  • John Armstrong
  • Claudio Bellani
  • Damiano Brigo
  • Thomas Cass

Abstract

We describe the pricing and hedging of financial options without the use of probability using rough paths. By encoding the volatility of assets in an enhancement of the price trajectory, we give a pathwise presentation of the replication of European options. The continuity properties of rough‐paths allow us to generalize the so‐called fundamental theorem of derivative trading, showing that a small misspecification of the model will yield only a small excess profit or loss of the replication strategy. Our hedging strategy is an enhanced version of classical delta hedging where we use volatility swaps to hedge the second‐order terms arising in rough‐path integrals, resulting in improved robustness.

Suggested Citation

  • John Armstrong & Claudio Bellani & Damiano Brigo & Thomas Cass, 2021. "Option pricing models without probability: a rough paths approach," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1494-1521, October.
    • Handle: RePEc:bla:mathfi:v:31:y:2021:i:4:p:1494-1521
    DOI: 10.1111/mafi.12308
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    References listed on IDEAS

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    Cited by:

    1. Halidias Nikolaos, 2024. "A novel portfolio optimization method and its application to the hedging problem," Monte Carlo Methods and Applications, De Gruyter, vol. 30(3), pages 249-267.
    2. John Armstrong & Andrei Ionescu, 2023. "Gamma Hedging and Rough Paths," Papers 2309.05054, arXiv.org, revised Mar 2024.

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