# Best Way of Interpreting Black-Scholes Formula [duplicate]

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

• you have made the question and the answer: good job! Commented Jun 30, 2018 at 11:59
• No, they are both the probability of being in the money. See the related question about why N(d1) and N(d2) are different.
– dm63
Commented Jun 30, 2018 at 12:24
• Lars Tyge Nielsen: Understanding N(d1) and N(d2) ltnielsen.com/wp-content/uploads/Understanding.pdf Commented Jun 30, 2018 at 14:02