Jiew Kwang
Member
Hi,
Can anyone help me connect the idea that N(d1) is also delta? Thanks a bunch!
jk
Can anyone help me connect the idea that N(d1) is also delta? Thanks a bunch!
jk
N(d1) & delta
- Thread starter Jiew Kwang
- Start date
Hi jk,
delta is first partial derivative, the change in call price with respect to a change in the stock price (dc/dS).
The derivation is a bit involved but I like to ("mnemonically") cheat by letting N(d1) = A, then
c = S*exp(-qT)*N(d1) - exp(-rT)*K*N(d2), becomes
c = S*exp(-qT)*A - exp(-rT)*K*N(d2)
Now, you know that if c = aS, then dc/dS = a, and if we just *pretend* that exp(-rT)*K*N(d2) is a constant, we can imagine
if c = S*exp(-qT)*A - k, such that
dc/dS = exp(-qT)*a = exp(-qT)*N(d1) or,
if q = 0, dc/dS = N(d1)
This is NOT the correct derivation of the first partial derivative (as the N(d2) contains the S), which is more complex, HOWEVER it simplifies to this anyway! ... so it works for me as a way to recall that delta is just a first partial derivative (with respect to stock price). I hope that helps.
David
delta is first partial derivative, the change in call price with respect to a change in the stock price (dc/dS).
The derivation is a bit involved but I like to ("mnemonically") cheat by letting N(d1) = A, then
c = S*exp(-qT)*N(d1) - exp(-rT)*K*N(d2), becomes
c = S*exp(-qT)*A - exp(-rT)*K*N(d2)
Now, you know that if c = aS, then dc/dS = a, and if we just *pretend* that exp(-rT)*K*N(d2) is a constant, we can imagine
if c = S*exp(-qT)*A - k, such that
dc/dS = exp(-qT)*a = exp(-qT)*N(d1) or,
if q = 0, dc/dS = N(d1)
This is NOT the correct derivation of the first partial derivative (as the N(d2) contains the S), which is more complex, HOWEVER it simplifies to this anyway! ... so it works for me as a way to recall that delta is just a first partial derivative (with respect to stock price). I hope that helps.
David
Jiew Kwang
Member
Hi david,
I was thinking about what you said yesterday in the webinar but i still have some doubt regarding my understanding of the BSM.
I tried to draw out what i visualized on excel and I do not understand esp what N(-d1) signify. Initially i thought it was the delta of a put. But then i recalled that it is actually N(d1)-1 and that its negative.. So, the N(-d1) thing is still bugging me.. did i do anything wrong in the attached?
thanks for hearing.
regards,
jk
I was thinking about what you said yesterday in the webinar but i still have some doubt regarding my understanding of the BSM.
I tried to draw out what i visualized on excel and I do not understand esp what N(-d1) signify. Initially i thought it was the delta of a put. But then i recalled that it is actually N(d1)-1 and that its negative.. So, the N(-d1) thing is still bugging me.. did i do anything wrong in the attached?
thanks for hearing.
regards,
jk
Similar threads
