Editing Arrow–Debreu model (section)

=== Accounting for time, space, and uncertainty ===
{{see|Financial economics#State prices|State prices#Application to financial assets|Contingent claim analysis}}
The commodities in the Arrow–Debreu model are entirely abstract. Thus, although it is typically represented as a static market, it can be used to model time, space, and uncertainty by splitting one commodity into several, each contingent on a certain time, place, and state of the world. For example, "apples" can be divided into "apples in New York in September if oranges are available" and "apples in Chicago in June if oranges are not available".

Given some base commodities, the Arrow–Debreu complete market is a market where there is a separate commodity for every future time, for every place of delivery, for every state of the world under consideration, for every base commodity.

In [[financial economics]] the term "Arrow–Debreu" most commonly refers 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 (the price of such a security being a so-called "[[State prices|state price]]"). 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.

Since the work of [[Douglas Breeden|Breeden]] and [[Robert Litzenberger|Lizenberger]] in 1978,<ref>{{cite journal |title=Prices of State-Contingent Claims Implicit in Option Prices |first1=Douglas T. |last1=Breeden |first2=Robert H. |last2=Litzenberger |journal=[[Journal of Business]] |volume=51 |issue=4 |year=1978 |pages=621–651 |jstor=2352653 |doi=10.1086/296025|s2cid=153841737 }}</ref> a large number of researchers have used options to extract Arrow–Debreu prices for a variety of applications in [[financial economics]].<ref>{{cite journal |last1=Almeida |first1=Caio |last2=Vicente |first2=José |year=2008 |title=Are interest rate options important for the assessment of interest risk? |journal=Working Papers Series N. 179, Central Bank of Brazil |url=http://www.bcb.gov.br/pec/wps/ingl/wps179.pdf }}</ref>