Two call options have the same delta but option A has a higher gamma than option B. When the price of the underlying asset increases, the number of option A calls necessary to hedge the price risk in 100 shares of stock, compared to the number of option B calls, is a: A - larger (negative) number. B - larger positive number. C - smaller positive number. D - smaller (negative) number.
A. Gamma is the rate of change in the Delta, if the stock increases the Delta of Stock"A" will increase more then the delta on stock B there for there will be a greater negative number of calls needed to hedge the stock.
You would need to short a lesser amount of calls. So I guess that is D
A’s delta will increase more than B’s because of the higher gamma. Say option A’s delta increases from .5 to .7 while option B’s gamma increases from .5 to .6. If you have 100 shares of stock, the amount of calls you must write is equal to #shares/delta. For A you originally needed 100/.5 =200 but now you need 100/.7 = 143 For B you originally needed 100/.5 = 200 but now you need 100/.6 = 167 Both are negative numbers because you are writing the calls and as you can see you have a smaller negative number with A. D is the answer.
Delta will increase at a faster rate with option A. Since the hedge ratio is #Shares/Option Delta, if the denominator is larger, you need fewer options to hedge. You need to short call options to hedge against a long equity position.
Your answer: B was incorrect. The correct answer was D) smaller (negative) number. For call options larger gamma means that as the asset price increases, the delta of option A increases more than the delta of option B. Since the hedge ratio for calls is – 1/delta, the number of calls necessary for the hedge is a smaller (negative) number for option A than for option B. - I missed the part about holding the assets, but I guess it was written into the question.
Ooooooo I thought they were refering the the actual change in the number of options Like in Niblita75’s explination Option A: 143 - 200 = -57 Option B: 167 - 200 = -33 Option A has a larger (Negative) amount of options needed to hedge