(5 marks) You are the lead on a team dedicated to finding arbitrage opportunities at a hedge fund. You have recently observed the following prices in the market. Option Type Price Strike Standard put 8 30 Standard put 18 37 Standard put 22 Also, the annual effective interest rate is 3%. a. (0.5 marks) Check whether or not the third proposition comparing option prices to strike prices is satisfied. b. (1 mark) Explain the steps you would take to exploit the misprice (You can only buy and sell integer amounts of options). c. (3.5 marks) Draw the payoff and profit graphs of your position in b) and show that profit is always non-negative. Also, write out the profit function as a piecewise function and identify the peak profit amount. (5 marks) You are the lead on a team dedicated to finding arbitrage opportunities at a hedge fund. You have recently observed the following prices in the market. Option Type Price Strike Standard put 8 30 Standard put 18 37 Standard put 22 Also, the annual effective interest rate is 3%. a. (0.5 marks) Check whether or not the third proposition comparing option prices to strike prices is satisfied. b. (1 mark) Explain the steps you would take to exploit the misprice (You can only buy and sell integer amounts of options). c. (3.5 marks) Draw the payoff and profit graphs of your position in b) and show that profit is always non-negative. Also, write out the profit function as a piecewise function and identify the peak profit amount