Option pricing models without probability: a rough paths approach

We describe the pricing and hedging of financial options without use probability using rough paths. By encoding volatility assets in an enhancement price trajectory, we give a pathwise presentation replication European options. The continuity properties rough-paths allow us to generalize so-called fundamental theorem derivative trading, showing that small misspecification model will yield only excess profit or loss strategy. Our strategy is enhanced version classical delta where swaps hedge second-order terms arising rough-path integrals, resulting improved robustness.