a) Consider a compound option that is a call on a put. Does this compound option cost less than the put? Explain your answer. 

 b) You recently purchased and now hold an up-and-out put option. You now decide that you would rather have a plain vanilla put option that has the same exercise price and maturity. What additional exotic option should you purchase to achieve this? 

 c) Does an up-and-out call option have a positive or negative delta? How does its delta vary depending on how close the current stock price is to the barrier?