Difference between N(d1) and N(d2)

CFA Level II Derivatives
#1

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 (N(d1)) 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 !

#2

N(d1) 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.

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#3

This is how I have understood it:

N(d2) represents the risk‐neutral probability of No default on a company’s debt, or probability (AT>= K) N(d1) represents the risk‐neutral probability of default on debt, or probability (AT < K)

Where

AT represent value of a company’s Assets at Time T

K represents the face value of the only Liability of the Company, a Zero coupon bond maturing in Time T

#4

N(d2) = P(ST>X) Risk neutral probability

N(-d2) = 1 - N(d2) = P(ST<=X)

#5

I think Mosey gave the correct explanation