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Option pricing models without probability: a rough paths approach
Author(s) -
Armstrong John,
Bellani Claudio,
Brigo Damiano,
Cass Thomas
Publication year - 2021
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12308
Subject(s) - hedge , econometrics , valuation of options , volatility (finance) , implied volatility , volatility risk , financial market , economics , stochastic volatility , mathematics , mathematical economics , computer science , volatility swap , finance , ecology , biology
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.