Before revision: We make use of a family of primitive securities, in the spirit of Arrow-Debreu, to price and hedge in a model-free way path-dependent exotic derivatives in discrete time. These primitive securities are called signature payoffs. First, we show that cash flows of exotic derivatives in discrete time can be approximated arbitrarily well by these primitive securities, and we then conclude that signature payoffs can be used to price path-dependent exotic derivatives.
After revision: We make use of a family of primitive securities, in the spirit of Arrow-Debreu, to price and hedge in a model-free setting when the trader has access to market prices of a rich enough class of exotic and vanilla options. This is achieved by estimating an unobservable quantity called "implied expected signature" from such market prices, which are used to price path-dependent exotic derivatives.