You look up the prices of European calls today on a particular stock and discover the following prices for call options: Strike Price Price 195 47.80 200 C 200 205 44.20 (a) (2 pts) Can the price C200 of the European call option with strike price K = 200 be C200 46.80? (Hint: use the fact that the price of European call is convex on strike K.) (b) (8 pts) Now suppose that the real price is C200 45.60. A friend has confidence that the stock price will rise in the future, and offers to bet any amount of money Q (a constant that you two decide today) that the stock will be worth at least 200 in 1 year. The risk-free annual compounding interest rate r = 0.05. Can you make an arbitrage by betting with this friend and trading spread? If yes, give the value of Q and your corresponding strategies. (Hint: Which spread will you choose? Bull, bear or butterfly?) You look up the prices of European calls today on a particular stock and discover the following prices for call options: Strike Price Price 195 47.80 200 C 200 205 44.20 (a) (2 pts) Can the price C200 of the European call option with strike price K = 200 be C200 46.80? (Hint: use the fact that the price of European call is convex on strike K.) (b) (8 pts) Now suppose that the real price is C200 45.60. A friend has confidence that the stock price will rise in the future, and offers to bet any amount of money Q (a constant that you two decide today) that the stock will be worth at least 200 in 1 year. The risk-free annual compounding interest rate r = 0.05. Can you make an arbitrage by betting with this friend and trading spread? If yes, give the value of Q and your corresponding strategies. (Hint: Which spread will you choose? Bull, bear or butterfly?)