interest rate caps and flors

[ludi.dejo]

schweser book 5,pg 251, concept checkers,14. An interest rate floor on a floating-rate note(from the issuers perspective) is equivalent to a series of:
a long interest rate puts
b short interest rate puts
c short interest rate calls
correct answer is b,but i am a lottle confused,is the issuer of the note is a buyer of the floor(right?) shouldnt he have the long position if he is buying the put option?

 

[Cinderella]

The issuer buys the cap and sells the floor.

 

[S2000magician]

If you draw a picture - I always advocate that my students draw pictures: timelines for cash flows, payoffs for options, and so on - with market interest rate on the horizontal axis and interest rate received on the vertical axis, then you’ll see that with a floating-rate note without a cap or floor, the line slopes down to the right at a 45° angle, like this: \. (Remember, we’re looking at this from the issuer’s point of view, so he pays interest, or receives negative interest.) If you draw a picture of a floating-rate note with a floor, then the upper (left) portion of that diagonal line becomes horizontal (to the left) at the (negative of the) floor rate, like this: ¯\. The question is: what shape payoff do you have to add to the original (without a floor, diagonal down-to-the-right: \) line to get the new (with a floor, kinked: ¯\) graph? You have to add a graph that is zero where the new graph still slopes down (so you don’t change it), and slopes up where the new graph is horizontal (to counter the original, downward-sloping graph): /¯. Look at that graph and tell me whether it’s a payoff for:
a) a long put
b) a short put
c) a short call.
If you don’t know immediately that that’s a short put payoff, go study the graphs, and draw lots of pictures.

 

[tgile512]

Hi s2000magician,
If we were dealing with a floating-rate note with a cap, would it be safe to assume that it would include a long call for the issuer?
My thought process is that if a floating-rate note without a cap or floor is downward sloping ( \ ) then adding a cap would change the shape to ( \_ ). Wouldn’t this be achieved by incorporating a long call ( _/ ) ?

 

[S2000magician]

tgile512 wrote:Hi S2000magician …

Howdy.

tgile512 wrote:If we were dealing with a floating-rate note with a cap, would it be safe to assume that it would include a long call for the issuer?

It would include a long interest rate call, but you don’t have to assume it …

tgile512 wrote:My thought process is that if a floating-rate note without a cap or floor is downward sloping ( \ ) then adding a cap would change the shape to ( \_ ). Wouldn’t this be achieved by incorporating a long call ( _/ )?

… you just proved it. Good job!