Question

Question
A trader’s portfolio is delta neutral and has a gamma of -4,250. The delta and gamma of
a particular traded call option are 0.62 and 1.52, respectively. The trader wants to make
the portfolio gamma neutral as well as delta neutral.

1.1 What position should the trader take.

1.2 Explain to the trader what protection delta and gamma neutrality can provide to his
portfolio.

Answer 1

1.
Let x be the number of options bought, y be the number of shares bought

For gamma neutrality:
1.52x-4250=0
=>x=4250/1.52
=>x=2796.05

For delta neutrality:
0.62x+y=0
=>y=-0.62x=-0.62*2796.05=-1733.55

Buy 2796 options and sell 1734 shares of the stock/underlying

2.
This protects risk of changes in underlying asset & in delta itself. Traders hedge delta to limit risk of small movements in price of the underlying security, & hedge gamma to protect remaining exposure created through use of delta hedge. Overall it protects from movement in the option's delta.