= (delta of call option) × (duration of underlying) × (price of underlying) / (price of call option)
trying to make sure I understand this intuitively.
the 1st 2 segments make sense to me. You multiply a sensitivity factor (delta) to the underlying’s duration.
why do you then include the third component? Thanks.
Think of of this way…
delta = Dollar duration of options/ dollar duration of underlying
Here is the intuition behind the formula but it’s better just memorize the formula:
Bond Option Duration = - %delta_BOpt / delta_Y = - (delta_BOpt / BOpt) / delta_Y =
= (delta_BOpt / delta_B) * [-(delta_B / B) / delta_Y] * (B / BOpt) =
= BOpt_Delta * Bond_Duration * B / BOpt
B - bond price
BOpt - Bond option price
Y - interest rate