唉，英文太差了！

1.a St小于45:$45 call not exercised，$55 call not exercised. net payoff =0
St大于45，小于55，$45 call exercised, payoff=St-45, $55 call not exercised. Net payoff = St -45
St大于55：$45 and $55 all exercised, payoff for $45 call=St-45 ,payoff for $55 call=55-St Net payoff=55-St+St-45=$10
conclusion: 这个组合保证最后的payoff minimum是0，maximum是10

2b i：lower bound of European call option：max(0, S0-pv(dividend)-e^(-rT)X
c=max(0, 55-e(-0.089*0.25)*50)=max(0,6.1002), c=6.1002

initial: buy option @$4, Borrow $4 from bank@8.9%p.a, sell a future contract.
Final: repay $4.09=4*e(0.25*0.089)
if St小于50，do not exercise option, buy a share from market at St, deliver it to future buyer @56.24=50*e^(0.25*0.089), gain on future=56.24-St, total gain=56.24-St-4.09=52.15-St.Because St小于50，至少2.15 profit.
if St 大于50, Exercise option, purchase share@$50, Sell for future @56.24. Net gain=56.24-50-4.09=2.15 如果st大于50，保证2.15profit
conclusion：至少$2.15 profit，如果St小于50能赚更多

dingle................