State pricing theory and no-arbitrage pricing theory.
(1) ψ1 and ψ2 are prices. What do they price?
(2) What is the required condition that ψ1 and ψ2 must satisfy to prevent arbitrage opportunities between the securities in a state pricing representation?
(3) The current traded price of an underlier is $10, and it may be either $5 or $15 at the end of the period. Riskless borrowing and lending for the period is 10% p.a. A European vanilla Put option on the underlier with strike price of $9 is trading in the market. What is the no-arbitrage value of the European vanilla Put option?
(4) What is the risk neutral probability for state 1?
(5) When valuing a risky derivative with no-arbitrage methods, why can we discount its expected end-of-period payoff at the riskless rate?