# Revision booklet 6 question 3

Discussion in 'CM2' started by NS206, Sep 11, 2019.

1. ### NS206Member

Hi,

I'm not quite following the following part of the answer, please can someone point me in the right direction?

Sept 2008 Qu9 part (ii)

The answers in the revision booklet give a formula for the pdf of d1 over the pdf of d2. I'm not sure I understand this.

Thanks!

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3. ### Anna BishopActEd TutorStaff Member

Hello

The derivation of the Greeks from the BS option pricing formulae used to be a syllabus objective. It is no longer, so I would say it is highly unlikely to come up. However, not impossible, if the examiners feel they want to ask a difficult application question and test your differentiation.

I attach some tutorial notes that I produced several years ago that show where the φ(d1)/φ(d2) result comes from and then take you step by step through the differentiation of the call option formula to derive the Greeks.

I wouldn't spend ages on this. It is more important that you can quote the formulae for delta for a call and delta for a put in relation to the BS option pricing formulae, ie:

Delta(call) = exp{-q(T-t)}Φ(d1)
Delta(put) = -exp{-q(T-t)}Φ(-d1)

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In case it's useful for helping to understand some of the differentiation:

Big Φ(x) is the CDF of the N(0,1) distribution.
Little φ(x) is the PDF of the N(0,1) distribution.

dΦ(d1)/dSt
= [dΦ(d1)/dd1] * [dd1/dSt] by the chain rule
= φ(d1) * [dd1/dSt] as when we differentiate the CDF we get the PDF.

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Anna

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