Merton formulas: equity and debt N(d) vs. N(d1) and N(d2)

[[email protected]]

I can't seem to find this answer in the forum.

I've seen two different iterations used when calculating merton's equity and debt. Results are not the same, so can you advise which we should use (N (d) or N (d1 and d2) and how necessary it is to memorize the formulas?

Merton value of equity:

V N(d1) - Fe^-rt N(d2).

V N(d) - Fe^-rt N(d - sigma T^.5).

Thanks!

T

 

[David Harper CFA FRM]

Hi Tplbch,

They are the same: d = d1, and d-sigma*sqrt(t) = d2.
My long note might be helpful: https://forum.bionicturtle.com/threads/merton-model-a-summary-of-the-issues.5646/
I generally recommend memorizing the outer BSM; i.e., the formula you show
and i prefer d2 because it is so similar to Merton credit risk DD, see link
and d1 is optional (IM). thanks,