Larger Game --> larger price for call–> larger shares needed to hedge ?? I dont get it. PLEASE HELP!
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 positive number. B) larger (negative) number. C) smaller (negative) number.
Your answer: A was incorrect. The correct answer was C) 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 number of calls to hedge is (– 1/delta)x(number of shares), the number of calls necessary for the hedge is a smaller (negative) number for option A than for option B.
let’s break this down into what you need to understand
If both these call options have a delta of 0.33, then you need to sell (go short) 3 of these calls for every 1 share you are long. You are delta neutral (-3 * 0.333 deltas from your call + 1 delta from you underlying = 0 delta). You are delta hedged by taking a short position in your calls.
Given the above, if the delta of the calls increased for some reason (say from 0.333 to 0.5), then you would need less calls in your portfolio to be delta neutral (-2 * 0.5 + 1 = 0).
Gamma is the change in Delta with respect to a change in underlying. It’s measure how much the delta of the call option will change when the underlying changes. So if you have a larger gamma, it will take less of a move in your underlying to change the delta of the option from say 0.333 to 0.5. Option A in this question has the larger gamma.
So going back to the question, the option with larger gamma (option A) will see it’s delta increase more for the underlying price move (option A delta will move from 0.333 to 0.5, while option B might only go from 0.333 to 0.4). Given this, you can see that it will take less calls of Option A to be delta neutral (-2 * 0.5 + 1 = 0 for option A, vs -2.5 * 0.4 + 1 = 0 for option B). In this case, you need less calls of Option A to hedge your underlying position than you would if you had hedged with Option B.
