We describe the pricing and hedging practices refraining from the use of probability . We encode volatility in an enhancement of the price trajectory and we give pathwise presentations of the fundamental equations of Mathematical Finance. In particular this allows us to assess model misspecification, generalising the so-called fundamental theorem of derivative trading (see Ellersgaard et al. 2017). Our pathwise integrals and equations exhibit the role of Greeks beyond the leading-order Delta, and makes explicit the role of Gamma sensitivities .
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 .
R
practices refraining from
of financial options without
R
. We encode volatility
using rough paths. By encoding the volatility of assets
R
and we give pathwise presentations of the fundamental equations of Mathematical Finance. In particular this allows us to assess model misspecification, generalising
, we give a pathwise presentation of the replication of European options. The continuity properties of rough-paths allow us to generalise
R
(see Ellersgaard et al. 2017). Our pathwise integrals and equations exhibit the role of Greeks beyond the leading-order Delta, and makes explicit the role of Gamma sensitivities
, 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