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Determination of N(d1) and N(d2)

Uolless

New Member
Hi everyone! I have a question related to the BSM model.
When we calculate N(d1) and N(d2), we’re using cumulative normal table(Z-table).
but in this example it states that d1 = 0.1783 -> N(d1) = 0.5708 and d2 = 0.03688 -> N(d2) = 0.5147. Can someone explain why the results are different from the table? Thanks!
 

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David Harper CFA FRM

David Harper CFA FRM
Staff member
Subscriber
Hi @Uolless Those are correct and easily verified with Excel: NORM.S.DIST(.1783, true) = 0.5708. GARP's 2021 Practice only shows z < 0, so you definitely need to be facile with symmetrical normal's implication that N(z) = 1 - N(-z); in this case N(0.1783) = 1 - N(-0.1783) = 1 - 0.4293 = 0.5708.

See 5th bullet in my WIFE at https://www.bionicturtle.com/forum/threads/week-in-financial-education-2021-03-29.23750/ with link to https://www.bionicturtle.com/forum/...deviate-in-spectral-measure.23708/#post-87714 i.e.,
Hi @julienfrancaoui Yea this is a basic skill that is already much-discussed in the forum; e.g., see https://www.bionicturtle.com/forum/threads/probability-function.23487/post-83885

See below. The Z-lookup table gives you the relationship between N(z) = p; for example (see red below) N(-2.33) = 0.0099 ≅1.0%. We need to be able to use this lookup table "interactively" by which I mean we need to be able to invert to get z = N^-1(p) as in -2.33 = N^-1(1.0%). Further, we need to be facile with the fact that all of these values are one-tailed CDFs, by definition. If we want a two-sided 99.0% confidence interval, then we want 2.58 at 99.0% (because if we want 1.0% to be shared between each tail, then it's the same as the one-tailed quantile at 0.50%, see purple below). VaR is always one-sided, but CIs are typically two-sided. Okay, I've now re-explained this for literally the one hundreth time on the forum! I hope it's helpful and feel free to use search in the future because it saves us all a lot of time when you look to see if a question has been previously asked/answered....

 
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