A U.S. financial institution has a short position in 2,000 Australian dollars (AUD) and written 1,500 call options and written 1,800 put options on the same currency.(Each option is to buy or sell 1 AUD.)The call options have a delta of 0.4 and gamma of 1.6, while the put options have a delta of -0.6 and gamma of 1.2.

i)Calculate the portfolio's delta and gamma

ii)Show how the institution can use an exchange-traded put option on the AUD with a delta of -0.3 and gamma of 1.4 to make its portfolio delta and gamma neutral.