A European call option c with a strike price K of 50 is traded for 32. The current value of the underlying asset S0 is 31. The interest rate r is 10% pa, and the time-to-maturity T is equal to six months. The underlying asset pays no dividends. a) Which of the arbitrage bounds does the option value violate?

b) How would you profit from the violation of the arbitrage bound? Show the payoffs of your arbitrage

strategy assuming that the value of the underlying asset is either equal to 25 or equal to 55 at maturity. c) Show the payoff to the arbitrage strategy in a graph (with the payoff at maturity on the y-axis and the stock value at maturity on the x-axis). d) If the option were a put and not a call option, would its value still violate the equivalent arbitrage bound for put options?