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# N(d2)

#### rickm123

##### Member
Do we need to know how to calculate this for the FRM 2?

In relation to the merton model please.

thanks

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Can't say if you need it, but I recommend d2 as the AIMs imply a want/need for d2 (i.e., distance to default in Merton), and GARP has quizzed it previously although not generously
More here http://www.bionicturtle.com/forum/threads/merton-model.5425/#post-15119 (and a search of Merton has many results on the forum)
Search of "Merton" on this forum will produce many related threads:
http://www.bionicturtle.com/forum/search/39297/?q=Merton&o=date

Intuition explained here @

you will be given any N(.) as that is beyond most calculators, thanks

Last edited:

Fantastic video

#### Turner737

##### Member
Hi David,

Question about the video. The 7.2% that was calculated as the PD. is this the equity option equivalent of saying their is a 7.2% chance that this will end up OUT of the money? Just making sure my intuition is correct. Great video, thanks.

Matt

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi Matt - yes, exactly the way to look at it, as an option-equivalent, this "option" starts today (T0) deeply ITM (S = 130, K=100) with an expectation of drift upward, such that the future (normal) distribution has future expected mean (and median) that are easily even more in-the-money and, where it would require -1.462 standard deviations for the future "stock" (asset value) to fall below the "strike" price (debt level). In option terms, then this model expect the option to be future ITM with probability = N(1.462) = 92.8% and future OTM with probablity = N(-1.462) = 7.2%. Thanks,

#### Turner737

##### Member
Perfect explanation. Thanks!

#### Turner737

##### Member
One last question.

In regards to your quote from above "you will be given any N(.) as that is beyond most calculators, thanks".

Unless my understanding of the conversion from d1 to N(d1) and d2 to N(d2) is incorrect wouldn't we just be able to use the z table that is given during the exam? As in, you are recommending that we do know d1/d2 but to me that seems like the more difficult part for the calculator and the conversion to N(d1/2) is just a lookup on the Z table plus some simple simple addition.

Thoughts?

Thanks as always.

Matt

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi Matt,

I agree that nobody needs to memorize N(.) beyond N(-2.33) and N(-1.645); although it's nice to know the other major quantiles; because, just as you suggest, as not all the calculators can find N(.), you will be given a means to retrieve N(Z) for a given Z.

But, the exam has tested the computation of distance to default (i.e., BSM d2 with riskfree rate replaced by asset drift), so to play it safe, I have always recommended understanding d2 and its computation (formula). Not really d1; despite its similarity, d1 has virtually null testability other than its concept as call option delta, so far that i can tell.

So, i'm just recommending understanding the formula of d2 ~= distance to default ~= a special case of a Z that is generated in BSM and Merton's use of BSM.
I do agree: don't worry about the calculation of N(d2) or N(Z).

I hope that makes sense? Thanks,

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
fwiw, on another thread, i was just reminded that P1.T4.Hull Chapter 18 (Greeks), among its AIMs, there is only one "calculate:" Compute delta for an option
... so i might be too cavalier w.r.t. N(d1), I'm not sure really

#### Success2014

##### Member
Hi all, which exam approved calculators can convert d1 or d2 to N(d1)or N(d2). Thanks.