2. For the situation considered in Problem 12.12 , what is the value of a six-month European put option with a strike price of $51 ? Verify that the European call and European put prices satisfy put-call parity. If the put option were American, would it ever be optimal to exercise it early at any of the nodes on the tree? 2. For the situation considered in Problem 12.12 , what is the value of a six-month European put option with a strike price of $51 ? Verify that the European call and European put prices satisfy put-call parity. If the put option were American, would it ever be optimal to exercise it early at any of the nodes on the tree