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. Second, signature payoffs are used to derive a numerically feasible methodology to dynamically hedging exotic derivatives. It turns out that the only information one needs about the market to dynamically hedge exotic derivatives is the prices of these signature payoffs. These two aspects lead to a model-free approach to numerically price and hedge exotic derivatives from market data - more specifically, from market prices of other exotic derivatives. We demonstrate the feasibility of our approach in several numerical experiments.
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