Capped And Floored Floaters
What you'll learn
- LOS 25.mCalculate the value of a capped or floored floating rate bond.
A floating rate bond (“floater”) pays a coupon that adjusts every period based on an underlying reference rate. The coupon is typically paid in arrears, meaning the coupon rate is determined at the beginning of a period but is paid at the end of that period.
A capped floater effectively contains an issuer option that prevents the coupon rate from rising above a specified maximum rate known as the cap.
A related floating rate bond is the floored floater, which has a coupon rate that will not fall below a specified minimum rate known as the floor. In this instance, the embedded option belongs to the investor and offers protection from falling interest rates.
We can use the standard backward induction methodology in a binomial interest rate tree to value a capped or floored floater. As with the valuation of a bond with embedded options, we must adjust the value of the floater at each node to reflect the exercise of an in the money option (in this case, a cap or a floor).
Susane Albright works as a fixed income analyst with Zedone Banks, NA. She has been asked to value a $100 par, two year, floating rate note that pays MRR (set in arrears). The underlying bond has the same credit quality as reflected in the swap curve.
Albright has constructed the following two year binomial MRR tree:
How would we compute the following?
- The value of the floater, assuming that it is an option free bond.
- The value of the floater, assuming that it is capped at a rate of 6%. Also compute the value of the embedded cap.
- The value of the floater, assuming that it is floored at a rate of 5%. Also compute the value of the embedded floor.
Solution
- An option free bond with a coupon rate equal to the required rate of return will be worth par value. Hence, the straight value of the floater is $100.
- The value of the capped floater is $99.47, as shown here:
The upper node in Year 2 shows the exercise of the cap (the coupon is capped at $6.00 instead of rising to $7.18).
Note that when the option is not in the money, the floater is valued at par.
= ($100 + $6) / (1 + 0.071826) = $98.90
= (100 + 5.3210) / (1 + 0.05321) = $100
The Year 0 value is the average of the Year 1 values (including their adjusted coupons) discounted for one period. In this case, the Year 1 coupons require no adjustment, as the coupon rate is below the cap rate.
Thus the value of the embedded cap = $100 − $99.47 = 0.53.
- The value of the floored floater is $100.41, as shown here:
The nodes for Year 2 show the coupons for that period (none of the rates are below the floor, and hence the floor is not exercised). Strikethroughs for both nodes in Year 1 indicate that the floor was in the money; we replace the MRR = market reference rate. Having another rate after it is redundant coupon with a coupon based on the floor strike rate of 5%.
The Year 0 value is the average of the Year 1 values (including their adjusted coupons) discounted for one period:
Thus the value of the embedded floor = $100.41 − $100 = $0.41.