6. Bounds on option prices on a stock. a. Suppose an American call option is worth less than its intrinsic value (the payoff if the option were to be exercised now). Show that there is an arbitrage opportunity. Suppose there are a finite number of states of the world where each state has nonzero probability. Definition: A weak arbitrage opportunity is a portfolio with a positive cash flow today and nonnegative cash flows (cash flows of zero or higher) in all possible states. b. Prove that a European call option is worth no more than the stock price. That is, if a European call option is worth more than the stock price, prove that there is a weak arbitrage opportunity. 7. Three American call options with the same strike price are written on the same underlying stock: Call A expires in one month, Call B expires in two months, and Call C expires in three months. a. List the call options from highest to lowest price. Explain. b. How would your answer change if the options were European