
An option that is atthemoney would have a delta of +50 if it's a call option, 50 for a put option.
Suppose you long a call option and it is currently atthemoney, so delta = +50. To hedge your delta, you short 0.5 stock to make overall delta = +50  (0.5*100) = 0.
For a long put option, you buy 0.5 stock to make overall delta = 50 +(0.5*100) = 0.
However, why question 2.40 from the book "Heard on Wall Street" suggests 1.5 stock? 




Read that answer again very carefully  it does not suggest "1.5 stock". 



Also, I'm not sure if the delta of an ATM option is exactly 0.5
It is often useful to fall back on put call parity: CP==FwdPVStrike. 




It can be a surprisingly deep question ...
I suppose the "delta ATM=0.5" is completely correct for a pure Normal diffusion, is roughly correct for BlackScholes for short expiries, and in the presence of skew, is model / skew dependent ( if you define delta as "how many units of the stock should I buy for a locally minimum variance hedge"). For example, a localvol model and a stochvol model are likely to give different deltas.
But then no reallife option remains ATM for long (pin risk)
I hadn't actually thought about this in a while but I'm sure it's discussed in various books (Rebonato, etc)



Baltazar


Total Posts: 1758 
Joined: Jul 2004 


And if asked in interview, maybe bring up the fact that ATM can mean different thing (ATM = delta 50? ATM means K=S ?, K=F?).
Indeed vols dynamics will impact your delta so maybe it is good to nuance BS deltas versus complete deltas. 
Qui fait le malin tombe dans le ravin 



Of course, I misread onehalf as 1.5. Silly me! 

