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GARP.FRM.PQ.P1 GARP P1 Question 37 - dynamic delta hedge

liyi1989

New Member
I have a question about this GARP question:

Question 37. In evaluating the dynamic delta hedging of a portfolio of short option positions, which of the following is correct?

A. The interest cost of carrying the delta hedge will be highest when the options are deep out-of-the-money.
B. The interest cost of carrying the delta hedge will be highest when the options are deep in-the-money.
C. The interest cost of carrying the delta hedge will be highest when the options are at-the-money.
D. The interest cost of carrying the delta hedge will be lowest when the options are at-the-money.

Correct Answer: B. The deeper the options are in-the-money, the larger their deltas and therefore the more expensive to delta hedge.

I understand that the delta of a, say call, option is logistic type, which has largest value when deep-in-the-money (AND changes FASTEST at-the-money, i.e. largest gamma).

My question is why the dynamic hedge has the largest cost when delta is large? I sort of agree that with larger delta, we need to buy more underlying. BUT, this is the "initial static" part of the dynamic hedging.

I think the reason for the cost of dynamic hedge is large is because the delta constantly changes, so that a trader has to rebalance all the time, which corresponds to the largest gamma situation, i.e. at-the-money.

Did I miss Anything? or it is somehow related to the "interest cost of carry" (not the overall cost) so that we need to borrow money to buy (a lot of) underlying (so that the larger delta, the larger interest cost of carry)?

Thanks!
 

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Nicole Seaman

Director of FRM Operations
Staff member
Subscriber
I have a question about this GARP question:

Question 37. In evaluating the dynamic delta hedging of a portfolio of short option positions, which of the following is correct?

A. The interest cost of carrying the delta hedge will be highest when the options are deep out-of-the-money.
B. The interest cost of carrying the delta hedge will be highest when the options are deep in-the-money.
C. The interest cost of carrying the delta hedge will be highest when the options are at-the-money.
D. The interest cost of carrying the delta hedge will be lowest when the options are at-the-money.

Correct Answer: B. The deeper the options are in-the-money, the larger their deltas and therefore the more expensive to delta hedge.

I understand that the delta of a, say call, option is logistic type, which has largest value when deep-in-the-money (AND changes FASTEST at-the-money, i.e. largest gamma).

My question is why the dynamic hedge has the largest cost when delta is large? I sort of agree that with larger delta, we need to buy more underlying. BUT, this is the "initial static" part of the dynamic hedging.

I think the reason for the cost of dynamic hedge is large is because the delta constantly changes, so that a trader has to rebalance all the time, which corresponds to the largest gamma situation, i.e. at-the-money.

Did I miss Anything? or it is somehow related to the "interest cost of carry" (not the overall cost) so that we need to borrow money to buy (a lot of) underlying (so that the larger delta, the larger interest cost of carry)?

Thanks!
@liyi1989 Please note that I edited your post to include the full question and answer. The forum's search function does not recognize words within images, so we ask that in the future you copy/paste the full question and answer. I've also tagged the post with the tag garp21-p1-37 (garp 2021 practice exam, part 1, question 37). This allows us to quickly see if this question has already been asked and answered in the forum. For our paid members, there is a very good explanation about this practice question from David here: https://www.bionicturtle.com/forum/threads/2014-practice-exam-question-21.9527/.
 
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