## FRN

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**Data API**.**Excel Add-ins**.**Model Analytic API**.**GUI APP.**

**Data API**.**Excel Add-ins**.**Model Analytic API**.**GUI APP.**

*FinPricing provides probably the most comprehensive valuation models for financial products, including computation of:*

- Bond Accrued Interest Calculator
- Bond Coupon Rate Calculator
- Bond Price Calculator
- Bond Yield Calculator
- Bond Duration Convexity Calculator
- Bond Spread Calculator
- Check FinPricing valuation models

1. Floating Rate Note Introduction |

A bond is a debt instrument in which an investor loans money to the issuer for a defined period
of time.

A floating rate note has variable coupons, depending on a money market reference rate, such as LIBOR, plus a floating spread.
When interest rate raises, the coupons of a FRN increases in line with the increase of the forward rates, which means its price
remains relatively constant. Therefore, FRNs bear small interest rate risk. On the other hand, FRNs carry lower yields than
fixed rate bonds of the same maturity. They also have unpredictable coupon payments.

The price of a FRN has very low sensitivity to changes in interest rates because the floating coupon increases
but the discounting also increases as interest rate rises. An investor who wants conservative
investments may choose floating rate bonds. FRNs become more popular when interest rates are expected to increase.
A FRN carry lower yield than fixed rate bonds of the same maturity and has unpredictable
coupon payments. This presentation gives an overview of FRNs valuation. Click the links below for details.

2. Floating Rate Note Valuation |

The present value of a floating rate note is given by

**Practical notes**

- The present value of a bond computed by any pricing models is the bond dirty price. To purchase a bond, the buyer pays the bond dirty price.
- Although investors pay bond dirty prices, bonds are typically
quoted in terms of bond clean prices.

Bond Dirty Price = Bond Clean Price + Accrued Interest - Intuitively, can be regarded as a credit risk adjusted discount factor.
- First, one should generate cash flows based on the start time, end time and payment frequency of the bond, plus calendar (holidays), business convention e.g., modified following, following, etc.) and whether sticky month end.
- Second, one needs to construct yield curve by bootstrapping the most liquid i nterest 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
- Then calibrate the model price to the market quoted price by solving the credit spread. Comparing to yield curve construction or calibration for exotic products, the solving here is very simple.
- After making the model price equal to the market price, one can calculate sensitivities by shocking yield curve and credit spread.
- We use LIBOR curve plus credit spread rather than bond specific curves for discounting because bond specific curves rarely exist in the market, especially issued by small entities. Using LIBOR curve plus credit spread not only accounts for credit risk but also solve the missing data issue.
- Usually the forecasting curve is different from the discounting curve. For instance, the forecasting curve is the treasury curve but the discounting curve is the LIBOR curve plus credit spread.

3. Related Topics |

3.1. Fixed Rate Bond |

A fixed rate bond pays coupons at a fixed rate over the bond life. An investor who wants to earn a guaranteed interest rate for a specified term can choose fixed rate bonds. Due to the fixed coupon, the market value of a fixed rate bond is susceptible to fluctuation in interest rate and therefore has a significant interest rate risk.

**The present value of a fixed rate bond can be expressed as**

**You can find more details at Bond Valuation**

3.2. Zero Coupon Bond |

A zero coupon bond is a bond that doesn’t pay interest/coupon and instead pays one lump sum face value at maturity. Investors buy zero coupon bonds at a deep discount from their face value. Zero coupon bonds are probably the simplest bond type in the market.

**The present value of a zero coupon bond is given by**

**You can find more details at Zero Coupon Bonds**

3.3. Amortizing Bond or Accreting Bond |

An amortizing bond is a bond whose principal (face value) decreases due to repaying part of the principal along with the coupon payments, while an accreting bond is a bond whose principal increases during the life of the deal. The analytics are similar to a fixed rate bond except the principal amount used for each period may be different.

**The present value of an amortizing bond or
accreting bond is given by**

**Practical notes**

- All practical notes for pricing floating rate notes are applicable to amortizing bond or accreting bonds.
- You need to determine notional principal amount for each cash flow when you generate it.

**You can find more details at Amortizing Bond or Accreting Bonds**

References |