  In the spirit of Arrow-Debreu, we introduce a family of financial derivatives
that act as primitive securities in that exotic derivatives can be approximated
by their linear combinations. We call these financial derivatives signature
payoffs. We show that signature payoffs can be used to nonparametrically price
and hedge exotic derivatives in the scenario where one has access to price data
for other exotic payoffs. The methodology leads to a computationally tractable
and accurate algorithm for pricing and hedging using market prices of a basket
of exotic derivatives that has been tested on real and simulated market prices,
obtaining good results.
