 # Duration of Interest Rate Call Option

Hi, please help me with this problem concerning Interest Call Options: The following info doesn’t make sense to me: (a) When interest rates decline, the value of an interest rate call option will rise. (i.e. positive duration, CFAI, Vol.4, p.122) (b) An interest rate call option allows the holder to pay fixed/strike and receive floating. Now, if the floating rate declines, I’d would assume that the value of the interest rate call decreases (i.e. negative duration). Thus, I don’t get CFAIs statement. Any help appreciated! Carsten

Good catch… For an int rate call, you’re in-the-money if the reference rate’s above the strike rate at expiration… because you’re borrowing. So, a higher rate’s good for you. p. 122 of the reading says the delta of int rate call option’s greater than 0 … which makes sense, because if the underlying rate goes up then your option price goes up. But, if this is true then a downward change in rates should mean a downward movement in the option price. Others? p.s. your statement (b), isn’t that describing an interest rate swap? not an option

I am confused by those statements on P.122 too.

you know that really confuses me, i’ve check the errata’s and its not there and i can’t find it in schweser. I’m guessing its something just to skip! although the formula at the start may be useful (but then its not in schweser either)

Even though this issue is not in LOS, I think it’s better for us to know it. Because in CFA exam history, some questions out of the scope of LOS appeared on the exam. Anyone can clarify ?

This also confused me and seems to be contrary to the formulas found in volume 5, p 433. The only thing I can think of is that when they say ‘value’ in the context of the passage on page 122, they are referring to the value of duration. Otherwise, this makes no sense. best, TheChad

TheChad Wrote: ------------------------------------------------------- > This also confused me and seems to be contrary to > the formulas found in volume 5, p 433. > > The only thing I can think of is that when they > say ‘value’ in the context of the passage on page > 122, they are referring to the value of duration. > p 122 talks about options on an instrument based interest rate, like futures or bonds. This is the kind of options traded on the CME exchange. I believe it is discussed on page 121, so when the interest rate is down, the bond or futures is up thus also the call value. v5 talks about an OTC option customized according to your individual needs (to match a loan, CF) and is based on interest rate (strike is interest rate based), so call has positive value when interest rate INCREASES. It is obvious then that two options move in opposite direction.

elcfa, Can I say : Long a I/R call = Long a bond put ? Then, bond value increase if I/R decrease and bond value decrease if I/R increase. Thus, the call value increase if I/R decrease and the call value decrease if I/R increase. Correct me if I am wrong !

AMC Wrote: ------------------------------------------------------- > elcfa, > > Can I say : Long a I/R call = Long a bond put ? > Then, bond value increase if I/R decrease and bond > value decrease if I/R increase. > Thus, the call value increase if I/R decrease and > the call value decrease if I/R increase. > > Correct me if I am wrong ! Just want to be clear. There are TWO kinds of options, both called interest rate options (in the CFAI book in any case) Type 1: Options on bonds or bond futures are called interest rate options (per def on pg 121) Type 2: options based interest rate are also called interest rate options (per def on v5) Conceptually: type 1 call = type 2 put and vice versa, (very broadly speaking)

elcfa Wrote: ------------------------------------------------------- >> Type 1: Options on bonds or bond futures are called interest rate options (per def on pg 121) > > Type 2: options based interest rate are also called interest rate options (per def on v5) > > Conceptually: type 1 call = type 2 put and vice versa, (very broadly speaking) So, am I right or wrong ?

Long a I/R (type 2 above) call = Long a bond (type 1 above) put > Then, bond value increase if I/R decrease and bond > value decrease if I/R increase. > Thus, the call value increase if I/R decrease and > the call value decrease if I/R increase. Yes Long a bond put is also called Long an I/R PUT (as per pg 121) so you have to be clear what you mean by an I/R call.

elcfa, OK, now I get it. TKVM !

Gotcha…this concept also tripped me up in the previous levels…thanks for the clarification elcfa

Thanks elcfa, now I get it 