Option pricing models without probability: a rough paths approach

TY - JOUR

T1 - Option pricing models without probability: a rough paths approach

AU - Armstrong, John

AU - Brigo, Damiano

AU - Cass, Thomas

AU - Bellani, Claudio

PY - 2021/5/5

Y1 - 2021/5/5

N2 - 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 generalise 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.

AB - 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 generalise 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.

M3 - Article

SN - 0960-1627

JO - MATHEMATICAL FINANCE

JF - MATHEMATICAL FINANCE

ER -