1. 12. Understanding Floating Rate and Derivative Securities
12.1 Variable Coupon Securities
Two types of variable components: (1) coupon payments and (2) interest rates.
Variable coupon securities are securities with coupons that change.
When the coupon is adjusted, the security is said to be repriced.
Used by institutions for speculative and hedging reasons.

2. 12.2 Types of Variable Coupon Securities
Floating Rate Notes (FRNs)
Variable Coupon Bonds
Perpetual Floaters
Variable Coupon Renewable Notes (VCRs)
Variable Annuities
Adjustable Rate Mortgages (ARMs)
They have periodic payments linked to an interest rate index, usually the LIBOR.
Floating rate notes, variable coupon bonds, and perpetual floaters differ only in maturity. (Intermediate, long term, and infinite maturities)
VCRs are FRNs with renewable options attached and interest rate bonuses to renew.
Variable Annuities vary principal not just interest. Payments are set higher than the interest rate unlike other variable securities because the annuity is set to amortize the principal over the maturity.

3. 12.3 Valuation of Variable Securities
Variable coupon securities reflect movement in interest rates, and the creditworthiness of the borrower.
The price P therefore consists of two parts:
P = V + A
V: price of a par floater with a given spread over the benchmark rate.
A: an adjustment due to a change in creditworthiness (credit spread). Evaluate the change in the credit spread as an annuity over the remaining maturity with a discount equal to the par discount of the variable security before any credit changes.
A is negative for an increase in the credit spread and positive for and decrease in the credit spread.

4. 12.3 Valuation of Variable Securities: An Example
What is the price of a floating rate note on March 1, 1999 if it was initially issued on March 1, 1997 with a maturity of 10 years and priced at 20 bp above the LIBOR. On March 1, 1999 the credit rating of the borrower has declined so that the price asked above the LIBOR is 50bp. Suppose that a eight year fixed rate security with similar credit risk has a discount rate of 6% on March 1, The face value of the floating rate note is $100.

5. 12.4 Perpetual Floaters
A perpetual floater is a variable-rate perpetuity. Payments fluctuate with a constant spread above an interest rate index but never return any principal.
For regulatory purposes the funds raised by selling perpetual floaters are considered to be qualifying capital.
Tax authorities consider the payments to be deductible interest payments.
Issuers, such as banks, thereby increase their regulatory capital while reducing taxes.
Since there is little interest rate risk, durations are quite short although the maturity is infinite.
The risk of a decline in credit quality is called basis risk. Since the spread on the payments is fixed, the basis risk must be reflected through a change in price. (ie. Changes in the coupon of a AAA firm only reflect changes in the interest not the fact it has dropped from a AAA to a BBB firm).

6. 12.5 Inverse Floaters
An inverse floater is another type of derivative security because its payoff is manufactured from other securities.
An inverse floater offers increasing payoffs when interest rates are falling and decreasing payoffs when they are increasing.
Floating rate portion is often combined with a interest rate cap to minimize exposure to the interest rate.

7. 12.6 Swaps Why do swaps exist?
A swap is a contract between two counterparties in which each agrees to pay the other’s stream of payments on their respective debt issues.
The principal amounts are generally equal and are referred to as notional principal. Principal is not exchanged, only cash flows.
Types include: interest rate swaps, currency swaps, commodity swaps, and mortgage swaps.
Why do swaps exist?
Interest rate risk does not dictate which type of asset an institution can purchase since the institution can unwind the interest rate risk using a swap later
Interest rate risk and exposure changes over time so swaps provide a means to alter interest rate risk
Low credit obligors usually find it cheaper to borrow at flexible rates and later swap for a fixed rates. Similarly, high credit obligors find it advantageous to borrow at fixed rates and swap for flexible rates.

8. A B A B 12.6.1 Interest Rate Swaps
Interest rate swaps are arrangements whereby parties “swap” interest payments on their debt issues.
Coupon Swap
Example. Fixed rate note is 10%/year on 100 mil and the floating rate is LIBOR plus a 50 bp credit spread on 100 mil. The LIBOR is currently 8%.
Basis Swap
Who pays if LIBOR < Treasury Bill +100bp?
Who pays if LIBOR > Treasury Bill +100bp?
Fixed Rate A B
Floating Rate
LIBOR + 100bp A B
Tbill +200 bp

9. Currency Swaps
A currency swap is a pair of simultaneous spot and forward transactions in which the forward transaction unwinds the spot transaction.
TODAY
FUTURE
British Pound A B
US$
US$ A B
British Pound

10. 12.7 Swaptions 12.8 Bond Warrants
A holder of a swaption has the right, but not the obligation, to enter into a new swap or cancel or extend participation in an existing swap.
Receiving Fixed Rate Payments and paying floating rate is the underlying security.
Call swaption: Holder has the right to receive fixed rate and pay floating.
Put swaption: Holder has the right to receive floating and pay fixed rate.
12.8 Bond Warrants
Bond warrants give the purchaser the right, but not the obligation, to purchase or sell a bond at specific price at some future date.
Unlike Swaptions, exercising a warrant requires owning the bond or the underlying security before you can sell it.
The decision to exercise a warrant is based on the return on capital of the company whereas for swaps the decision to exercise is based on general interest rates

11. 12.9 Interest Rate Caps and Floors
Caps are private contracts between two parties in which one party protects the other against interest rate movements above a pre-specified level.
The investor pays a fee; in return, the cap’s originator offers monetary compensation whenever interest rates rise above the cap or strike level.
The payments made on caps and floors depends on three components: (1) the size of the contract (2) the length of time rates remain positive and (3) the difference between interest rates and the cap.
What is the payment if interest rates are currently 12% on a 10% cap with monthly readjustments on $100 million?

12. 12.24 10.2 8.5 8.5 7.08 5.9 12.10 Valuation of Interest Rate Caps
Interest rate caps can be viewed as a package of single-payment caps whose maturity dates range from the earliest cap to the last cap.
Caps can be valued as a combination of interest rate options, or by using the interest rate lattice approach.
Example. What is the value of an interest rate cap of 8% if interest rates can progress along one of four paths in the next 2 years with equal probabilities. The underlying (or notional) principal of the cap is $100,000.
12.24
10.2
8.5
8.5
7.08
5.9

13. Cap Price as % of Notional Amount
Price Sensitivity of Caps to Interest Rates: By Maturity
Caps are highly convex instruments with very large negative durations.
The price of a cap is higher for a longer maturity.
Cap Price as % of Notional Amount
7 years
5 years
3 years
Interest Rates

14. Cap Price as % of Notional Amount
Price Sensitivity of Caps to Interest Rates: By Cap level
Caps are highly convex instruments with very large negative durations.
The price of a cap is higher for a lower cap level.
Cap Price as % of Notional Amount
8% Cap
10% Cap
12% Cap
Interest Rates

15. Cap Price as % of Notional Amount
Price Sensitivity of Caps to Interest Rates: By Volatility
Caps are highly convex instruments with very large negative durations.
The price of a cap is higher for a higher volatility.
QUESTION: What is the relation of maturity, volatility and a floor price?
Cap Price as % of Notional Amount
28%
20%
16%
Maturity

16. Floor = Cap + Swap (Pay Floating, Receive Fixed)
Relationship to Interest Rate Swaps and Floors
Interest rate floors provide protection against falling interest rates.
Floors and caps can be synthesized with the aid of swaps:
Floor = Cap + Swap (Pay Floating, Receive Fixed)
Cap = Floor + Swap (Receive Floating, Pay Fixed)
Example. Combine a Cap of 10% on the 3 month LIBOR with a swap where you receive a fixed rate of 10% on a bond and pay a floating rate equal to the 3 month LIBOR.
Cap payments: Receive 3 mo LIBOR -10% whenever 3 mo LIBOR>10%
Swap payments: Receive 10% - 3 mo LIBOR
Cap + Swap: Receive 10% - 3 mo LIBOR whenever 3 mo LIBOR<10%

17. Summary
The instruments considered in this chapter include variable rate instruments, derivative securities, and complex contracts which have developed in response to the needs of investors to hedge or protect their asset portfolios.
Valuation of these instruments was achieved via standard discounted cash flow methods or by construction of synthetic counterparts.