Duration of a call option

CFA Level III Derivatives
#1

How do you explain a duration of a call option?

#2

I don’t recall seeing this in the Level III curriculum; where’d you see it?

If I had to hazard a guess, I’d say that it’s the percentage change in the call option’s price for a 1% change in the risk-free rate.

#3

There was a formula in Schweser for call option delta=(call price *call duration) / (price of underlying*Duration of underlying) which does not make much sense to me.

You can take out the call duration from here.

#4

it is in the middle of the Fixed Income 2nd reading - in the white text.

call option duration = delta of option * (price of underlying / call price) * Duration of Underlying.

when option is out of the money - delta of option is low, call price is low. (price of underlying / call price) will be high.

when option is in the money - delta is high, call price is high. (price of underlying / call price) will be low.

In essence there is a push up / pull down effect on the first two factors.

1 Like
#5

so bascially depens on Duration of Underlying.

#6

So,

option\ duration = option\ Δ × \frac{underlying\ price}{option\ price} × underlying\ duration
= \frac{Δoption\ price}{Δunderlying\ price} × \frac{1}{option\ price} × \left(underlying\ price × underlying\ duration\right)
= \frac{Δoption\ price}{option\ price} × \frac{1}{Δunderlying\ price} × \left(underlying\ price × \frac{Δunderlying\ price}{underlying\ price × \%ΔYTM}\right)
= \%Δoption\ price × \frac{1}{\%ΔYTM}
= \frac{\%Δoption\ price}{\%ΔYTM}

For a parallel shift in the yield curve, \%ΔYTM = \%Δr_f, so,

option\ duration = \frac{\%Δoption\ price}{\%Δr_f}

Wow!

I got a question right for once.

1 Like
#7

I do remember in the 2013 exam they had provided the 4 other things and asked to calculate the duration of the call option - direct formula application … :slight_smile:

3 points for 1 mins work.

#8

Awesome!

#9

2012 AM Q7 D.

Using fixed income’s quata.

#10

Anybody know if this has been removed (duration of call option)? Was in the 2012 AM Mock but can’t remember seeing it in text. Thanks.

#11

it is in the middle of the Fixed Income 2nd reading - in the white text.

call option duration = delta of option * (price of underlying / call price) * Duration of Underlying.

look IN THE WHITE TEXT…

Check section 5.3.6.1 …

#12

got it, thanks CPK

#13

How do you get the most recent material?

#14

the reading has not changed in forever !

so the section numbers on the reading do not change either…

it is the same in the books I used – and I asked you to look it up in yours - and it was the same!

no magic there!

#15

This derivation looks so complicated