Exxon stock sells for $80/share. The annual interest rate is 2%, and the annual standard deviation on Exxon stock is 30%. The time to expiration of all options is 6 months. You are short 150 put options on Citi with a strike price of 82. To hedge you position, you can buy or sell Exxon stock, or call options on Exxon with a strike price of 82.

Given this,

Derive the position you will take if you want to delta-gamma hedge your position.