Amortizing Cap
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Amortizing Cap/Floor Valuation
Interest rate caps are financial contracts between two parties that provides an interest
rate ceiling or cap on the floating rate payments, whereas interest rate floors are similar
contracts where the buyer receives payments at the end of each period when the interest rate is below the strike.
| 1. Interest Rate Amortizing and Accreting Caps and Floors Introduction |
An amortizing cap is an interest rate cap whose notional principal amount declines during
the life of the contract whereas an accreting cap is an interest rate cap whose notional
principal amount increases during the life of the contract.
An amortizing cap is primarily used to hedge loans whose principal declines on a scheduled basis while an accreting
cap is primarily used to hedge construction loans whose principal increases on a scheduled basis to meet the expanding
working capital requirements. Amortizing caps are frequently purchased by issuers of
floating rate debt where the loan principal declines during the life. Similarly accreting
caps are frequently purchased by issuers of floating rate debt where the loan principal
increases during the life. The holders wish to protect themselves from the increased financing costs that would result
from a rise in interest rates.
An interest rate floor consists of a series of
European put options (floorlets) on interest rates. An amortizing floor is an
interest rate floor whose notional principal amount declines during the life of the contract
whereas an accreting floor is an interest rate floor whose notional principal amount increases
during the life of the contract.
An amortizing floor is primarily used to hedge loans whose principal declines on a scheduled basis while an
accreting floor is primarily used to hedge construction loans whose principal increases on a scheduled basis to meet
the expanding working capital requirements. Amortizing floors are frequently purchased by purchasers of
floating rate debt where the loan principal declines during the life. Similarly amortizing
floors are frequently purchased by purchasers of floating rate debt where the loan principal
increases during the life. The holders wish to protect themselves from the loss of income that would result from a
decrease in interest rates. This presentation gives an overview of interest rate amortizing or accreting floor
products and valuation model.
| 2. Interest Rate Amortizing and Accreting Caps and Floors Valuation |
An amortizing cap is an interest rate cap whose notional principal amount declines during
the life of the contract while an accreting cap is an interest rate cap whose notional
principal amount increases instead. The analytics are similar to a vanilla cap except the national amount used per
period may be different.
An amortizing floor is an interest rate floor whose notional principal amount declines
during the life of the contract while an accreting floor is an interest rate floor whose
notional principal amount increases instead. The analytics are similar to a vanilla floor except the national amount
used per period may be different.
The present value of an amortizing/accreting cap is given by
The present value of an amortizing/accreting floor can be expressed as
Practical Notes
- The pricing model for pricing caps/floors is the Black formula in the market.
- The forward rate is simply compounded.
- The first key is to generate the cash flows of a cap/floor. The cash flow generation is based on the start time, end time and payment frequency, plus calendar (holidays), business convention (e.g., modified following, following, etc.) and whether sticky month end.
- Then you need to construct yield curve by bootstrapping the most liquid interest rate instruments in the market. FinPricing provides useful tools to build various curves, such as swap curve, basis curve, OIS curve, bond curve, treasury curve, etc. Go to the list of the tools
- Another key for accurately pricing an outstanding cap/floor is to construct an arbitrage-free cap implied volatility surface. FinPricing is using SABR model to construct cap implied volatility surface. Go to the list of volatility construction tools
- The accrual period is calculated according to the start date and end date of a cash flow plus day count convention
- Any compounded yield curves data can be used to compute discount factor, of course the formulas will be slightly different. The most common used one is continuously compounded zero rates.
- The formula above doesn’t contain the last live reset cash flow whose reset date is less than valuation date
but payment date is greater than valuation date. The reset value is
PVreset = max( r – K, 0)NτD for cap
PVreset = max (k – r, 0)NτD for floor
that should be added into the above present value. - You need to determine notional principal amount for each cash flow when you generate it.
| 3. Related Topics |