Calculation of the N(d1) and N(d2)

[sneakyplacebo]

Hi, I am looking through the very first set of study notes ( allen) for the valuation and risk models. As an exercise for myself I was trying to replicate the figures for the black scholes calculation on page 30, but was wondering firstly what value you are translating in the Z table to convert the d1 to the N(d1) and also if there is rounding in the calculation as from my example I'm coming up with 6.96 as the initial price of this. Could someone possibly run through the worked example for me?

Thanks.

 

[David Harper CFA FRM]

Hi @sneakyplacebo Thanks for running the calcs (I love that ). It's rounding. I attached the calculations in an XLS in case you can open it. I notice that if I use N(d1) = 0.6100 and N(d2) = 0.4900, then indeed the BSM call price = $6.96; an $0.08 difference that is wider than I would have expected! The exhibit is using Excel's =NORM.S.DIST(Z, cumulative=TRUE) function such that the actual numbers (before their rounded appearance via formatting) are:

d1 = 0.283333
N(d1) = 0.611539
d2 = (0.016667)
N(d2) = 0.493351
Call price = $6.8766

Alternatively, if we round d1 and d2:
d1 = 0.283333
N(d1) = 0.610000
d2 = (0.016667)
N(d2) = 0.490000
Call Price $6.9607

I hope that explains, thanks!