Example 8 Reading 19

CFA Level III Economics
#1

Example 8 Reading 19, Solution has me confused:

Solution to 2:

A is correct. The surprise rate hike should cause the NZD to appreciate against most currencies. This appreciation would mean a depreciation of the NZD/AUD rate, which a put option can profit from. _ A 5-delta option is deep-OTM, but the price reaction on the option premiums will be more extreme than a higher-delta option. That is to say, the percentage change in the premiums for a 5-delta option for a given percentage change in the spot exchange rate will be higher than the percentage change in premiums for a 25-delta option. In a sense, a very low delta option is like a highly leveraged lottery ticket on the event occurring. _

I kinda get it, but kinda don’t get it.

If the option is deep OTM, I get that the premium is very low (extreme case a few cents) and if our predictions are correct, the price movement is much stronger (say from $0.01 to $0.02 mean it doubled in value) whereas for a 25 delta Option that is closer to being ITM (say the premium is $1.25) the change in price while larger in absolute terms (say from $1.25 to $1.50) is smaller in relative terms.

Is that what the answer implies here??

But aren’t we supposed to assume that if we want to maximize price impact to go with the larger delta??

And isn’t delta relative measure, that is delta of 5 would mean for a 1 unit move in the underlying produces a 5% change in the premium.

#2

Or is this case different because the solution talks about a given percentage change in the underlying and not a given absolute change, as in the definition of delta?

#3

Yes, the option’s delta is the rate of change of the price of the option with respect to its underlying price

for short put option, the delta is from 0 to 1. The deep OTM put option delta is 0.05 in this case, it is very cheap to buy deep OTM put option, so if underlying price does move in favorable direction, the price impact will be bigger on 0.05 delta put option, than on 0.25 delta put option.

#4

Got it, makes sense. Thank you!!