The formula for duration of interest rate option is given as Duration of underlying *Delta* Pirce of underlying/price of option Why does price ratio. Isnt delta & duration of underlying adequate enoguh
Delta of an option is akin to duration of a bond, Gamma is roughly the same as convexity. Not sure exactly what you are asking.
Bigwilly Aplogoies for the typo formula for duration of interest rate option is given as Duration of underlying *Delta* Prrce of underlying/price of option I am talking about “option” here How does the price of underlying/price of option affect the duration of the interest rate option. Could you please clarify that.
rammusubbu Wrote: ------------------------------------------------------- > Bigwilly > Aplogoies for the typo > formula for duration of interest rate option is > given as > Duration of underlying *Delta* Prrce of > underlying/price of option > I am talking about “option” here > How does the price of underlying/price of option > affect the duration of the interest rate option. > Could you please clarify that. Actually your formula is incorrect. The correct formula is Option Duration = Duration of Underlying * (Price of Underlying/Price of Option) Delta is not a factor here. The ratio of the two prices adjust the duration up or down according to the leverage used. If the option is out-the-money, the leverage will increase and this will give you a higher duration contribution from the option.
what is a duration of a bond? A change in bond price give a 1% change in interest rates so how much wil underlier change if interest rate change? duration * underlying price / 100 How much will the option price change? (duration * underlying price / 100) * delta Now to find duration of an option we need to divide this by price of an option ((duration * underlying price / 100) * delta ) / price of an option given that duration expressed as decimal, we can remove 100, so duration * delta * underlying price/price of an option = option duration
mo34, please see my comments, i think they make sense
comp_sci_kid Wrote: ------------------------------------------------------- > mo34, please see my comments, i think they make > sense CSK, I just reviewed my notes and double-checked with the CFAI notes, delta is not a factor in this case. I agree that the duration of the option will be related to delat, but that’s already taken care of by adjusting for the leverage ratio. The higher the leverage the lower the delta ( further out of the money) and vice versa, that’s probably why they don’t include delta in this equation.
mo34 can you please point to page# in schweser or CFAI? Thanks i can see your point as ofcourse as price of option increases delta increases and vice versa, so these effects will offset each other. Just wanted to make sure this formula is correct
Volume 4 page 22 CFAI text. The formula never made it to Schweser.
also, this formula is given with an error in the CFAI Volume 4, but errata is posted on it
mo34 Wrote: ------------------------------------------------------- > Volume 4 page 22 CFAI text. The formula never made > it to Schweser. Is there any LOS for this? - sticky
mo34 Wrote: ------------------------------------------------------- > rammusubbu Wrote: > -------------------------------------------------- > ----- > > Bigwilly > > Aplogoies for the typo > > formula for duration of interest rate option is > > given as > > Duration of underlying *Delta* Prrce of > > underlying/price of option > > I am talking about “option” here > > How does the price of underlying/price of > option > > affect the duration of the interest rate > option. > > Could you please clarify that. > > > Actually your formula is incorrect. > > The correct formula is > > Option Duration = Duration of Underlying * (Price > of Underlying/Price of Option) > > Delta is not a factor here. > > The ratio of the two prices adjust the duration up > or down according to the leverage used. If the > option is out-the-money, the leverage will > increase and this will give you a higher duration > contribution from the option. mo34, it’s Option Duration = Duration of the underlying instrument * (Change in price of option/change in price of underlying) = Duration of underlying * Delta This is according to Stalla.
so did we conclude that?: Option Duration = Duration of the underlying instrument * (Change in price of option/change in price of underlying) or Duration of underlying * Delta
ok let me clarify my calculations O - price of option U - price of underlying duration of underlying = dU/dI delta = dO/dU Where S is price change duration of option = dO/dI dO/dI = dO/dU * dU/dI so duration of option = duration of underlying * delta.
One way o think about all these probems is just think that (locally) an option is just a fractional underlier. Thus an option with delta = 0.3 is 0.3 shares. Then “the duration of an option” (which is a term I hate, incidentally) becomes pretty clear.
or just create partial differention equation and solve it 
That ain’t no partial differential equation - that’s the chain rule. Anyway, I suck at solving partial differential equations because to be any good at it you have to have a bag of stupid tricks. That means you have to do it enough to collect the bag of stupid tricks. However, I seem to get by ok on “That equation is not hard to solve numerically”.
Thanks guys. I think-the correct formula should be that given by comp sci. It makes lot of sense & the formula in cfai text seens to be wrong. Now to find duration of an option we need to divide this by price of an option ((duration * underlying price / 100) * delta ) / price of an option given that duration expressed as decimal, we can remove 100, so duration * delta * underlying price/price of an option = option duration
rammu, did you read the whole thread? or no?
Yes i read the whole thread.