Question

If you sell an overpriced option and hedge your delta exposure, what is the Gamma of your portfolio?

Answer 1

Solution

It has important implications in analyzing option strategies. It measures the rate of change of Delta, which is how much an option price changes given a one-point movement in the underlying asset. Delta increases or decreases along with the underlying asset price, whereas Gamma is a constant that measures the rate of change of Delta. Gamma is one of the more obscure Greeks.

IN other word delta in get effects with underlying price of assets but Gamma remain same for delta .

For more explain please see below table.

Stock Price	Option Price	Delta	Gamma
$21.00	$2.00	0.55	0.04
$22.00	$2.00	0.50	0.04
$19.00	$1.00	0.45	0.04

Suppose that two options have the same Delta value, but one option has a high Gamma and one has a low Gamma. The option with the higher Gamma will have a higher risk since an unfavorable move in the underlying stock will have an oversized impact. High Gamma values mean that the option tends to experience volatile swings, which is a not good thing for most traders looking for predictable.

Since, In the given problem delta value is hedged then any change in overpriced option does not effect the value of delta and hence there was no any effect in Gamma.