Arrow-Debreu model
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The Arrow-Debreu-McKenzie model (ADM model) is the central model in the General (Economic) Equilibrium Theory and often used as a general reference for other microeconomic models. It is named after Kenneth Arrow, Gerard Debreu and Lionel W. McKenzie.
The model suggests that, should the assumptions made about the conditions under which it works hold (ie. Convexity, Perfect Competition and Demand Independence), then there will be a set of prices such that aggregate supplies will equal aggregate demands for every commodity in the economy, and that there will be price for every commodity and such a market for every time period and forward prices for every commodity at all time periods. This is the idea of maximally complete markets.
The ADM model is one of the most general models of competitive economy and is a crucial part of general equilibrium theory, as it can be used to prove the existence of general equilibrium (or Walrasian equilibrium) of an economy. Once we can prove the existence of such an equilibrium, it is possible to show that it is unique.
Applications to finance theory
In financial economics the term Arrow-Debreu is most commonly used with reference to an Arrow-Debreu security. A canonical Arrow Debreu security is a security that pays one unit of numeraire if a particular state of the world is reached and zero otherwise. As such, any derivatives contract whose settlement value is a function on an underlying whose value is uncertain at contract date can be decomposed as linear combination of Arrow-Debreu securities.
The concept of Arrow-Debreu security is a good pedagogical tool to understand pricing and hedging issues in derivatives analysis. Its practical use however in financial engineering has turned out to be very limited, especially in the multi-period or continuous markets.
The Black Scholes analysis and its extensions, despite their strong questionable assumptions have proven more successful in practice and has led to explosion of the derivatives industry.
An emerging concept has now appeared, called BICS, extending and generalizing arrow-debreu security as well as synthesizing the Black Scholes analysis in a multi-period markets while being practically very tractable. A Basis Instrument Contract or BIC is a representative derivative contract that is an element of a set of classes of equivalence of contracts. Together, these contracts uniquely enable the static replication of any derivatives contract in a multi-period trading market without any model assumption.
External links
- ADM model [link]
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