Valuation of a Floored Floater
A floater pays the market rate, and price stays at par. A capped floater limits the upside movement, leaving investors at some risk for receiving lower-than-market coupons. This causes capped floaters to trade at a discount.
What sort of limit do you think would cause a floater to always trade at a premium?
Not quite. That wouldn't be a floater. A set coupon is a fixed-rate coupon instead of a floater, and those can trade at a discount if market rates rise.
No. There's no way of telling the market to keep rates below some value written in a bond indenture.
Exactly!
If there's a minimum coupon rate offered to investors, then they'll like that. That's called a __floored floater__, and that floor will always have some value to cause the floored floater to trade at a premium.
Look at this interest rate tree for a three-year bond that may be familiar to you.
The coupon is set in arrears, just like for a capped floater. So the Time 2 rates tell you the Time 3 coupons. If the floor in a floored floater is 5.5%, then what's the highest coupon that's modeled to be paid in Time 3?
Yes!
The floor gives the minimum of 5.5%, but there's no maximum here. The interest rate tree has a top node of about 8.49%, so that's what is assumed in Time 3. That payment of 108.4936 will be discounted to par and so will the second node's coupon of 106.2922.
No. A higher rate could be paid in Time 3.
No. That's the minimum.
The bottom node is where the "boost" comes from to model a premium price. The Time 3 coupon of 4.6614 is too low, so the floor kicks in and mandates a coupon of 5.50 there. The coupon and face value of 105.50 is discounted at 4.6614% to give a bottom node value of
$$\displaystyle \frac{105.50}{1.046614} = 100.8013 $$.
Will there be any other binding floors when you perform backward induction?
Absolutely.
No. There will be.
Just look back at that tree. The 4.4336% rate in Time 1 won't work. Investors will get 5.5% coupons in both the down node and in the middle node average in Time 2. Similarly, in Time 1, the rate of 4.00% will be replaced by 5.50% in both the up and down nodes. That's a lot of flooring, and it will leave you with a current price of 102.12.
What do you think is the value of that floor?
No. The value isn't expressed as a rate.
You got it!
The value of the floor is any price difference above and beyond par, since the floater without the floor would trade at par. So the value of the floor is
$$\displaystyle 102.12 - 100 = 2.12 $$.
You never know how low rates can go. Sometimes it's nice to have a floor to know where you stand.
No. The price of 102.12 is already in the present.
To summarize:
[[summary]]
Some guaranteed minimum coupon rate
A limit on how high the market rate can be
Set the coupon at some fixed rate above the current market yield
5.50%
6.29%
8.49%
Yes
No
1.5%
2.12
The present value of 102.12
Continue
Continue
Continue
Continue
