Option pricing models without probability: a rough paths approach

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...

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Veröffentlicht in:Mathematical finance 2021-10, Vol.31 (4), p.1494-1521
Hauptverfasser: Armstrong, John, Bellani, Claudio, Brigo, Damiano, Cass, Thomas
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:0960-1627
1467-9965
DOI:10.1111/mafi.12308