Problem 1. Consider the following option strategy a Long one call with 3100 strike price, bought for $11 I Long one call with $90 strike price7 bought for $20 I Short one call with $105 strike price, sold for 58 I Short one call with $95 strike price, sold for $16 (a) Draw a picture of the payoff of the option strategy at expiration as a function of the stock price . (b) Draw a picture of the investor's profitas a function of the stock price . Problem 2. A stock sells for $50 today. The riskless rate over the period is 10%. Assume that next period (one year) the stock will either I. go up by 30% (to $65), I or go down by 20% (to $40). (If you want, you can assume that these happen equally likely7 although you do not need to know this.) Suppose you own an out of the money European call option on the stock , which expires in one year from now. The stock will pay no dividends until then. The strike price equals the futures price _ (a) Show that the futures price on the stock : $55, assuming no costs or benets to own ership . (b) What is replicating portfolio for the call 27 (c) What is the cell's current price (that is, what is the value of the replicating portfolio )1? (d) What are the "riskineutral probabilities" of the up and down moves? (7r and 1 7r, respectively ) (c) Find again the price of the call option , this time using the risk wneutral probabilities