Non-parametric models describe a class of asset pricing models which are used to value exotic options written on the price path of one asset in terms of an entire initial term and strike structure of standard option prices. In this survey, we restrict attention to non-parametric models for which the state is entirely described by the time and the stock price, whose risk-neutral dynamics are Markovian. Examples include the deterministic local volatility model of Dupire\cite{d94}, sticky strike models, and sticky delta models. We provide an integrated framework for these models and show how each of these models imposes additional structure in order to uniquely infer the risk-neutral dynamics of the stock price from the initial data.
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