Option pricing models without probability: a rough paths approach
File(s)
Published online version
Author(s)
Armstrong, John
Bellani, claudio
Brigo, Damiano
Cass, thomas
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.
Date Issued
2021-05-05
Date Acceptance
2021-03-15
Citation
Mathematical Finance, 2021
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.
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.
License URL
Sponsor
Engineering & Physical Science Research Council (E
Grant Number
BKR01300
Subjects
Finance
0102 Applied Mathematics
1502 Banking, Finance and Investment
Publication Status
Published online
Date Publish Online
2021-05-05