The current stock price of BHP is $40. The Greeks for European options on BHP are as follows

Delta Gamma Vega

Call 0.50 0.08 0.08

Put -0.09 0.04 0.03

The Greeks in this table are for a long position in one call or put option. Assume that one call option

gives you the right to buy one share and one put option gives you to right to sell one share.

(a) You have sold (shorted) 2000 call options on BHP. What positions in the underlying and/or

in the put option should you take to create portfolio that is both delta neutral and gamma

neutral? Clearly indicate whether the positions are long or short positions.

[10 marks]

(b) By how much does the value of the delta- and gamma-hedged portfolio in question 3(a)

change when the volatility of the BHP stock price goes down by 1%? [10 marks]