Duration, Interest Rate Option price, option, because, instrument

ll11

Seems like that 3rd term is gamma, correct? If so, then I guess I would think of it as adjusting the delta for how deep in/out of the money the option is?

I'm pretty fried at this point, but that's what I'm going with.

cjs238

CFAI has this formula:

Duration, Int Rate Option = Delta, Option * Duration, U/L instrument * (p, U/L) / (p, option)

... which basically says, the option's duration is the

(1) duration of the underlying instrument (futures) times
(2) the option's delta, times
(3) the ratio of the underlying price to option price.

Here's my take:

(1) is very intuitive
(2) makes some sense (because option & futures prices wouldn't necessarily move in lock-step) (3) is puzzling? Why does duration move up with a higher ratio of the prices?

Book explanation is that (3) measures the leverage, and a higher price ratio means higher exposure to interest rate changes... if you think how an interest rate future's priced, it seems circular reasoning (higher interest rates means higher prices).

Anyway, any takers on explaining? LOS is 30f

infinitybenzo

On a semi related note i have a question...

The formua:

Option Duration = (Delta)(Duration of Underlying)(Price Underlying / Price Option)

The sign of the delta in this case would be dependent upon the type of the option correct?

(+) for calls
(-) for puts

is this right?

and if so, is it the opposite when you're the seller of the option

i.e.,

(-) for calls
(+) for puts?

wake2000

In my opinion, the last ratio shows how much more your option position will be sensitive to interest rate changes.. For example, if the underlying price is 200 and the option price is 20, option will be 10 times sensitive to interest rate changes than the underlying instrument because you will have to buy 10 options to make the dollar durations match..

I am not sure, though, that this intuition is correct..

I thought Gamma measures the relationship between option delta and underlying price..

mp3bu

I re-read the paragraph and it seems that CFAI assumes that Interest Rate Option on Futures are Options on Bond Futures...

They write: "If rates declines, the value of the interest rate call option will rise... (...)"

That would mean you have an option to go long on a T-Bond... And since rates declines, the T-Bond rises, hence your option position rises as well...


Please confirm...