2. (20 marks) Consider a one-period model with 2 states and 3 assets: a bank account and two stocks. Assume that

the bond sells for $1 at t = 0 and paid $(1 + r) at t = 1. For stock 1, the initial stock price is $10.4 and it has two

possible prices $12 and $8 at t = 1; for stock 2, the initial stock price is $10 and it has two possible prices $s and $2.5

at t = 1. A call option on stock 1 with a strike price of $9 has the price of $1.8.

(1). Verify that this model is arbitrage free and complete.

(2). Find the unique state price vector and the risk-neutral probability measure.

(3). Find the value of r.

(4). Find the value of s.

(5). If the price of a call option on stock 2 is $2.4, what is the strike price of this call option?