© 2020, © 2020 Informa UK Limited, trading as Taylor & Francis Group. We estimate prices of exotic options in a discrete-time 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 other exotic derivatives. The implied expected signature is an object that characterizes the market dynamics.