Question: answer all the questions please thankyou! Question 3 [14 points) Consider an economy with two dates (t=0,1) and at t=1 there are three states. The

answer all the questions please thankyou!

Question 3 [14 points) Consider an economy with two dates (t=0,1) and at t=1 there are three states. The following three stocks are traded: X1=(10,0,30) X2=(0,20,40) X3=(20,20,0) The t=0 prices of these stocks are given as follows (P1, P2, P3)=(12, 14, 8). (a) Is there an arbitrage? [2p] Suppose an investment firm sells options. (b) What is the t=0 price (premium) of a call option on stock 2 with exercise price E=10? [3p] (c) What is the t=0 price (premium) of a put option on stock 1 with exercise price E=20? [3p] Suppose a start-up company wants to go public. The firm has total costs of $100,000 at date t=1 and sales of $120,000 in state 1, $130,000 in state 2, and $240,000 in state 3. The firm wants to issue 1,000 IPO shares. (A share is endowed with a cash flow right of 0.1% of the total profits of the firm.) (d) The underwriter suggests an IPO price of $62 per share. Will this IPO be successful, i.e. will there be a positive demand for the shares? [6p]

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