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Pricing theory for derivative securities is a highly technical topic in finance. Its foundations rely on trading practices and its theory relies on advanced methods from stochastic calculus and numerical analysis. Financial assets are subdivided into several classes, some being quite basic while others are structured as complex contracts referring to more other assets. Examples of elementary asset classes include stocks, which are ownership rights to a corporate entity, bonds which are promises by one party to make cash payments to another in the future, commodities which are assets, such as wheat, metals, and oil that can be consumed and real estate assets,
which have a convenience yield deriving from their use.
A trading strategy consists of a set of rules indicating what positions to take in response to changing market conditions. For instance, a rule could say that one has to adjust the position in a given stock or bond on a daily basis to a level given by evaluating a certain function. The implementation of a trading strategy results in pay-offs that are typically random. Most traded derivatives are structured in such a way that it is possible to implement
trading strategies in the underlying assets that generate streams of pay-offs that replicate the pay-offs of the derivative claim. In this sense, trading strategies are substitutes for derivative claims. One of the driving forces behind derivatives markets is that some market participants, such as market makers, have a competitive advantage in implementing replication strategies, while their clients are interested in taking certain complex risk exposures synthetically by entering into a single contract.