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This question already has an answer here:

I'm curious to know the best interpretation of the Black-Scholes formula for a European equity call option:

$$C(S,t)=S_tN(d_1)-Ke^{-r(T-t)}N(d_2),$$

where $d_1=\frac{1}{\sigma\sqrt{T-t}}\big[\ln(\frac{S}{K})+(r+\frac{\sigma^2}{2})(T-t)\big]$ and $d_2=d_1-\sqrt{T-t}$.

The way I look at it is that $N(d_1)$ is the probability of being in-the-money and $N(d_2)$ is the probability of being out-the-money and $S_t$ and the discounted value of our strike $K$ are the associated cash flows. Is this incorrect? I'd like the best interpretation.

Many thanks,

VN

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marked as duplicate by LocalVolatility, Alex C, Attack68, Helin, byouness Jul 1 '18 at 16:53

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    $\begingroup$ you have made the question and the answer: good job! $\endgroup$ – lehalle Jun 30 '18 at 11:59
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    $\begingroup$ No, they are both the probability of being in the money. See the related question about why N(d1) and N(d2) are different. $\endgroup$ – dm63 Jun 30 '18 at 12:24
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    $\begingroup$ Lars Tyge Nielsen: Understanding N(d1) and N(d2) ltnielsen.com/wp-content/uploads/Understanding.pdf $\endgroup$ – Alex C Jun 30 '18 at 14:02