Interest rate caps - when do the underlying options expire?

CFA Level II
#1

From what I understand, an interest rate cap gives the holder the right to exercise the underlying options and borrow at a specific rate at multiple dates in the future. The rate is fixed i.e. capped.

This is can be viewed as a portfolio of call options on interest rates.

My questions is:

Say we have a cap with 4 underlying options (caplets). Say there are 4 payment periods.

So does this mean at the beginning we have in our portfolio:

Call option 1 - expires at time 1

Call option 2 - expires at time 2

Call option 3 - expires at time 3

Call option 4 - expires at time 4

Basically I want to know whether at the outset we have a portfolio of call options each of which expire at different dates in the future (in this case at 4 different dates)

Any help is much appreciated.

Thanks

#2

We can use interest rate options to replicate a fixed income instrument with floating rate payment and caps/floors. Here’s an example of how we can replicate a capped floating rate note:

As an example, let’s assume we own the following instrument:

  • a capped floating rate note with a face value of $1M that pays LIBOR, has a cap of 4.00%, matures in 1 year, and has quarterly payments.

We can replicate this instrument by:

  • buying a floating rate note (with no caps) with a face value of $1M that pays LIBOR and has the same maturity and payment frequency
  • selling 4 European interest rate call options, each with a strike rate of 4.0% (i.e., the cap rate) and a notional of $1M, and which expire on each of the four coupon payment dates of the floating rate note
#3

Thanks very much