4) 20 points) An investor is analyzing an American call option and an American put option on a dividend-paying stock. Both options have a strike price of $40 and an expiration date in 6 months. The risk-free interest rate is 5% per year with continuous compounding), the current stock price is $38, and a $2 dividend is expected in two months. a) Find lower and upper bounds for the price of the American call option. b) Find lower and upper bounds for the price of the American put option. 5) 20 points The current price of a stock is 165.38 dollars per share (S(t) = 165.38). The interest rate is 3% per year with continuous com- pounding). The following table shows the prices of American put options for different strike prices. These options expire three months from today. Strike Option Price K Price PA 155 6.50 160 8.52 165 12.66 170 14.90 175 15.75 Find an arbitrage opportunity. To receive full credit, explain what you would do at time t = 0 and why the strategy that you propose is indeed an arbitrage oportunity