Problem
A British financial institution has written 1,300 call options and written 2,600 put options and holds (long) 1000 put options on the euro (EUR). (Each option is to buy or sell 1 EUR.) The written call options have a delta of 0.6 and gamma of 1.5, while the written put options have a delta of -0.4 and gamma of 1.1. The long put options have a delta of -0.6 and gamma of 1.0.
a. Calculate the portfolio's delta and gamma.
b. Show how the institution can take a position in the currency and use an exchange-traded call option on the EUR with a delta of 0.5 and gamma of 1.3 to make its portfolio delta and gamma neutral.