An Australian financial institution has a long position in 1,100 call options and written 1,500 call options and written 1,300 put options on the same currency. (Each option is to buy or sell 1 EUR.) The long call options have a delta of 0.6 and gamma of 1.0 while the written call options have a delta of 0.5 and gamma of 1.5. The written put options have a delta of -0.4 and gamma of 1.6.

i) Calculate the portfolios delta and gamma

ii) Show how the institution can use an exchange-traded call option on the EUR with a delta of 0.55 and gamma of 1.3 to make its portfolio delta and gamma neutral.