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


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,


  • 2
    $\begingroup$ you have made the question and the answer: good job! $\endgroup$
    – lehalle
    Jun 30, 2018 at 11:59
  • 3
    $\begingroup$ 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, 2018 at 12:24
  • 1
    $\begingroup$ Lars Tyge Nielsen: Understanding N(d1) and N(d2) ltnielsen.com/wp-content/uploads/Understanding.pdf $\endgroup$
    – Alex C
    Jun 30, 2018 at 14:02