What can we say about the gamma of the position?

The theta of a delta neutral options position is large and positive.

What can we say about the gamma of the position?
A . The gamma must be large and positive
B . The gamma must be large and negative
C . The gamma must be small and positive
D . The gamma must be small and negative

Answer: B

Explanation:

The relationship between the value of an option, and its delta, gamma and theta is given by rV = + rS + 0.5(S)2, where V is the value of the option, r the risk-free rate, S the spot price of the underlying, and , & are the respective Greeks.

For a delta neutral portfolio, = 0 and this equation reduces to rV = + 0.5(S)2. Now rV is generally a small number, which means that if is large and positive, must be large and negative to offset that. Therefore Choice ‘b’ is the correct answer.