Différence N(d1) and N(d2)

[archived_user]

I think this post could answer many questions as it is a very asked question…
What is the difference between N(d2) and N(d1) ?
for a call :
N(d2) = probability of S to be above K
N(d1) = delta of the call
I really thought that the delta (Nd1) was the probability of the option to be exercised ( so S to be above K) and so if the option is at the money, there 50% chance that S goes above are below with delta = 0.50
Could you explain it with simple words ?
Thanks !

 

[archived_user]

(Nd1) and N(-d1) are the deltas of call and put. The delta shows the change of the option value for a unit ($1) of change in the stock value.
You calculate delta by how much the option value changes if the value of S changes 1 unit.
And the N(d2) and N(-d2) are the probabilities that the options expire in the money (i.e. S is above or below X) as you describe.
This is how I interpreted.