I am confused about the following question:
A trader holds a portfolio of short option positions. The trader limits the risk of these exposures by maintaining a delta hedging strategy. In evaluating the dynamic nature of this strategy, which of the following is correct about the interest cost of carrying the delta hedge? A. The cost will be highest when the options are deep out-of-the-money. B. The cost will be highest when the options are deep in-the-money. C. The cost will be highest when the options are at-the-money. D. The cost will be lowest when the options are at-the-money.
I believe the answer is C, because delta is most sensitive to changes in the underlying when the option is at the money. However, the solution claims the answer is B because the deeper the options are in-the-money, the larger their deltas and therefore the more expensive to delta hedge.
Can someone please explain this?