Delta of an option with dividend given N(d1)

[hsuwang]

Hello David,

I'm wondering if this is a fair question to ask:

You are given the following information about a call option:
Time to maturity: 2 years
Continuous risk-free rate: 4%
Continuous dividend yield: 1%
N(d1) = .64

Calculate the delta of this option.

The answer is N(d1)exp-q(t), however, did we touch on this concept in the curriculum?

Thanks!

 

[David Harper CFA FRM]

Hi Jack,

Yes, that sort of question could be asked (is indeed "fair game")
While i reviewed delta, I did not review delta with dividend (but I wish I had, and will make a note; next version I will).
I think i decided to show delta of forward/futures, instead ....but this should be covered, too...

Thanks, David

 

[enjofaes]

of a put this is e(-qt)*N(-d1) or (N(d1) - 1)*e(-qt)?

 

[David Harper CFA FRM]

dividend-adjusted delta = delta*exp(-qT) such that call delta = N(d1)*exp(-qT) and put delta = [N(d1)-1]*exp(-qT)

 

[enjofaes]

dividend-adjusted delta = delta*exp(-qT) such that call delta = N(d1)*exp(-qT) and put delta = [N(d1)-1]*exp(-qT)

Top equivalent to the 2 approaches I mentioned. Thanks David for the quick feedback

 

[David Harper CFA FRM]

@enjofaes Oh, I see. Given N(z) - 1 = -N(-z), I think [N(d1)-1]*exp(-qT) = -N(-z)*exp(-qT) is the equivalent expression for the put's delta; e.g.,

• if z = 1, then N(z) = 84.1% and N(z) - 1 = -15.9%;
• N(-z) = N(-1) = 15.9% but -N(-1) = -15.9%. Same as your just with a negative in front, thanks for finding a second way to put delta!