An Australian financial institution has a long position in 1,000 euros (EUR) and written 1,500 call options and written 1,700 put options on the same currency. (Each option is to buy or sell 1 EUR.) The call options have a delta of 0.55 and gamma of 1.6, while the put options have a delta of -0.45 and gamma of 1.9.

i) Calculate the portfolios delta and gamma

ii) Show how the institution can use an exchange-traded put option on the EUR with a delta of -0.65 and gamma of 1.25 to make its portfolio delta and gamma neutral.