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Option pricing models without probability: a rough paths approach

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Title: Option pricing models without probability: a rough paths approach
Authors: Armstrong, J
Bellani, C
Brigo, D
Cass, T
Item Type: Journal Article
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.
Issue Date: 5-May-2021
Date of Acceptance: 15-Mar-2021
URI: http://hdl.handle.net/10044/1/88634
DOI: 10.1111/mafi.12308
ISSN: 0960-1627
Publisher: Wiley
Journal / Book Title: Mathematical Finance
Copyright Statement: © 2021 The Authors. Mathematical Finance published by Wiley Periodicals LLC This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Sponsor/Funder: Engineering & Physical Science Research Council (E
Funder's Grant Number: BKR01300
Keywords: Finance
0102 Applied Mathematics
1502 Banking, Finance and Investment
Publication Status: Published online
Online Publication Date: 2021-05-05
Appears in Collections:Financial Mathematics
Faculty of Natural Sciences

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