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).
The state prices ψj represent the prices of Arrow-Debreu securities, which are monetary values and do not necessarily sum to 1. The transformed vector qj represents risk-neutral probabilities, obtained by multiplying each state price by the gross risk-free factor (1+i).
Conditions: The market is a one-period finite-state model.; ψj are the solved state prices (Arrow-Debreu security prices).; i is the per-period risk-free interest rate.; qj is defined as qj=(1+i)ψj.
The state prices ψj represent the prices of Arrow-Debreu securities, which are monetary values and do not necessarily sum to 1. The transformed vector qj represents risk-neutral probabilities, obtained by multiplying each state price by the gross risk-free factor (1+i).
Conditions: The market is a one-period finite-state model.; ψj are the solved state prices (Arrow-Debreu security prices).; i is the per-period risk-free interest rate.; qj is defined as qj=(1+i)ψj.