An Arrow-Debreu security is a theoretical financial instrument that pays exactly 1 unit of currency in one specific state of the world and 0 in all other states. The state price vector is the collection of the current prices of all such Arrow-Debreu securities for the finite set of states in the market model.
Conditions: The market model has a finite set of states.; Payoffs are normalized to 1 in one state and 0 elsewhere.; The model is a one-period setting.
An Arrow-Debreu security is a theoretical financial instrument that pays exactly 1 unit of currency in one specific state of the world and 0 in all other states. The state price vector is the collection of the current prices of all such Arrow-Debreu securities for the finite set of states in the market model.
Conditions: The market model has a finite set of states.; Payoffs are normalized to 1 in one state and 0 elsewhere.; The model is a one-period setting.
To derive the linear pricing equations, you impose the no-arbitrage condition that the current price of each traded asset must equal the sum of its state-contingent payoffs weighted by the corresponding state prices. This produces one linear equation per traded asset, with the state prices acting as the unknowns.
Conditions: One-period model with a finite set of states.; Prices of all traded assets are known today.; State-contingent payoffs for each asset are known.; The unknowns are the state prices (Arrow-Debreu security prices).
To derive the linear pricing equations, you impose the no-arbitrage condition that the current price of each traded asset must equal the sum of its state-contingent payoffs weighted by the corresponding state prices. This produces one linear equation per traded asset, with the state prices acting as the unknowns.
Conditions: One-period model with a finite set of states.; Prices of all traded assets are known today.; State-contingent payoffs for each asset are known.; The unknowns are the state prices (Arrow-Debreu security prices).