Answer the questions below, show your calculations step by step for all questions.

2b. We consider a stock with current price 3(0) 2 $62. The value at time t={] of several Eumpean and American Options with different strikes and maturity T : 2 years are given below: Strike Price 40 100 120 Eur0pean Call Price 24 6 3 Eur0pean Put Price 2 8 20 Strike Price 40 120 American Call Price 24 10 American Put Price 3 21 0 Question 1 (Spts): Assume no dividend payments and r = 0. Construct an arbitrage opportunity using the putcall parity relation for European options with strike price K = $100. Show that it indeed leads to an arbitrage. a Question 2 (Spts): Assume no dividend payments and r > 0. Prove that there is no value X leading to an arbitrage opportunity in a portfolio made of: long one call with strike price K : $40; short 4 calls with strike price K = $100; lend $3; and short X calls with strike price K = $120. a Question 3 (Tpts): Assume no dividend payments and r = 0. Compute the best lower bound available for the price of an American call option with strike price K = $55. a Question 4 (Tpts): Assume a dividend payment with present value D = 7 and r = 0. Compute a lower bound for a portfolio made of: along call with strike price K = $55 and a short put with strike price K = $55. 1. Suppose all the firms, in a competitive market, have the following cost-function C(y) = y2 + B, where B is some constant. a) What is the long-run competitive equilibrium price, p*? (Note, p* will be a function of B.)2. Suppose that x, follows an AR(1) process: Xt = Q1X-1 + Et, where & is a white noise process with mean zero and variance of and |a, |