# Interest rate cap

Can someone help with this question? I thought buying a cap on interest rate is equivalent as buying put option on bond, so as interest rate go up, bond price go down and you are benefit from the put option on the bond

A cap on a floating rate note, from the bondholder’s perspective, is equivalent to: A) writing a series of puts on fixed income securities. B) owning a series of calls on fixed income securities. C) writing a series of interest rate puts. Your answer: C was incorrect. The correct answer was A) writing a series of puts on fixed income securities. For a bondholder, a cap, which puts a maximum on floating rate interest payments, is equivalent to writing a series of puts on fixed income securities. These would require the buyer to pay when rates rise and bond prices fall, negating interest rate increases above the cap rate. Writing a series of interest rate calls, not puts, would be an equivalent strategy. Calls on fixed income securities would pay when rates decrease, not when they increase.

Tricky one, I think this is the explanation.

Note that this is a floating rate security. As such the the coupon level is reset regularly so the price gets back to around par (100) at reset date. This happens if interest rates go up:

1. Price goes down until next reset date

2. At next reset date, the coupon is adjusted, so that the bond trades around par agian. E.g. if the interest rate has gone up, the new coupon will be higher.

3. If you have a cap on your floater, the coupon paid can maximum be at that level, so if interest rates are higher then your cap, your bond will get be capped and your cap and therefore trade below 100.

This is the same as having a uncapped floater + writing/selling puts on Bonds as a same level as your initial cap. E.g. when interest rate rise, the holders of the puts you sold will exercise their put options, and you will have to pay, this removes the “extra coupon” you got from your uncapped floater.

e.g. capped floater at X, interest rates are X+Y

you will not get the extra coupon of Y on your floater => trade below 100

uncapped floater, but wrote puts on bonds, corresponding to a interest rate level of X, when market interest is X+Y => your floater pays X+Y, but the Y will go to the holders of the bond puts you sold

does it makes sense?

There had been another thread on this, but I cannot find it.

A cap on a floater is an option owned by the issuer, not the bondholder. If the floating rate exceeds the threshold, the issuer exercises the option and receives (floating - cap rate); thus, his net interest payment is

floating – (floating – cap rate) = cap rate.

An option that pays (floating – fixed) is an interest rate call; thus, C cannot be correct.

We’re looking for an option that gains when interest rates rise (so floating – cap rate is positive). Call options on bonds gain when the bond prices rise, which happens when interest rates fall; so B is incorrect. Put options on bonds gain when bond prices fall, which happens when interest rates rise; thus, A is correct.

Ok, so I guess from a bondholder perspective, you are selling the cap on floater so you have to pay when interest rate is above strike price. Same as selling a put option on bond, if interest goes up, bond price down you have to make up the difference to the put option holder! U guys r genius!

You give us (well, me, at least) too much credit.

I got the C, u got the CFA, way ahead of me. Noticed I just failed ethics I was about to post this question even though I got the answer correct but my theory was different. Can I think this way, that is a cap is an option for the issuer which unfavorable for the bondholder. Call options have unlimited potential against the increase in price of an underlying asset where as put options value is limited. Here, the value is limited to the cap, hence it is equivalent to writing a series of put options on fixed income securities. Is it correct? Thanks in advance.

Yes.

Yes.

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Thank you very much, I learned it to think this way for these type of questions from you couple of days back.

Good to hear.