Problem. This question asks you to apply concepts from throughout the course. Imagine there is an investment manager looking for arbitrage opportunities. Any opportunities are found you must explain how to exploit them The investment manager now wants to look at the derivatives markets for arbitrage op- portunities. (a) A stock X goes up by a factor of 1.5 or down by a factor of 0.5 over the course of a year. Its initial stock price is $100. A call option with exercise price of $110 matures in 1 year. Is there an arbitrage opportunity if the call option sells for $22? b) Stock Y is currently worth S50. A year long call option with strike price $60 sells for $2. A year long put option with strike price $60 sells for $10. Is there an arbitrage opportunity? (c) The investor notices Stock Z, which has a current price of $100, is very volatile. How could he take advantage of this? Draw a payoff and profit graph