Duration of a call option

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.
 
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.
 
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.
 
cpk123 wrote:call option duration = delta of option * (price of underlying / call price) * Duration of Underlying
Click to expand...
So,
option duration = option delta × (underlying price/option price) × underlying duration
= Δoption price/Δunderlying price × (1/option price) × (underlying price × underlying duration)
= Δoption price/option price × (1/Δunderlying price) × (Δunderlying price/ΔYTM(%))
= %Δoption price × (1/ΔYTM(%))
= %Δoption price/%ΔYTM
For a parallel shift in the yield curve, %ΔYTM = %Δrf, so,
option duration = %Δoption price/%Δrf
Wow!
I got a question right for once.
 
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 …. :)
3 points for 1 mins work.
 
cpk123 wrote:
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 …. :)
3 points for 1 mins work.
Click to expand...
2012 AM Q7 D.
Using fixed income’s quata.
 
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