Consider an economy where

there are three possible states of the world at t = 1. A security with payoffs ~x(theta; 1) =

(5; 10; 15) in states 1, 2, and 3, respectively, has a price of 8 at t = 0. A risk-free security has

a gross return of 1.1 and a price of 1 at t = 0. A call option on the risky security has a strike

price of 12 and a price of 1 at t = 0. The probabilities of states 1, 2, and 3, repsectively, are

pi = (0:3; 0:4; 0:3).

1. Is the market complete?, If yes, what are the state prices?

2. Price a put option with a strike price of 8.