Calculating Deltas for a put

[[email protected]]

Hi,

For put deltas:

e^(-qt)x(N(d1) - 1)

Do we first derive the N(d1) value from the Z table, and then subtract that value by 1?

I know how to calculate the deltas for a call, and the N(d1) derivation is straightfoward, however, I am a bit thrown off the put delta, and wanted to make sure.

I know that you can double check you put's value by the put call parity so long as you've calculated your call value correctly -- however, on the exam, I'd like to be as efficient with my time as possible.

Thanks!

 

[David Harper CFA FRM]

Hi shi,

Your formula is good. Unlike the BSM option value for a put, which contains a N(-d1), the put delta is more simply:

[N(d1) - 1]*exp(-qT); i.e.,
[call option delta -1]*discounted by dividend

The exam is likely to just give you N(d1) … since you would need a lookup table unless it happens to be:

N(1.645) = 95%, or
N(2.33) = 99%
(per our typical normal VaRs, right?)

And just mentally keep in mind, or I prefer to visualize the two delta graphs:
Call option delta = N(d1) = must be 0 to 1.0 with ATM near the middle
Put option delta = N(d1) - 1 = -1 must be -1.0 to 0.0 with ATM near the middle
(I assume non-dividend asset here)

Good luck on the exam!!
Please report back ….

Thanks, David