Amortizing Bond


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Amortizing Bond Valuation


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


1. Amortizing Bond and Accreting Bond Introduction

An amortizing bond is a fixed rate bond whose principal (face value) decreases due to repaying part of the principal along with the coupon payments. Each payment to the amortizing bond holder consists of a portion of interest and a portion of principal. While an accreting bond is a fixed rate bond whose principal increases during the life of the deal. Each payment to the accreting bond holder is just a part of interest. The other part of coupon is added to the principal of the bond.

Amortizing bonds are used specifically for tax purposes as the amortized principals are treated as part of a company’s interest expense. Accreting bonds are used to improve the profit of the existing bonds and make them more marketable. Pension funds and insurance companies are major investors in accreting bonds. This presentation gives an overview of amortizing bonds and accreting bonds.


2. Amortizing Bond and Accreting Bond Valuation

An amortizing bond is a bond whose principal 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

Valuing amortizing bond in FinPricing

Practical Notes

  • The present value of a bond computed by any pricing models is the bond dirty price of the bond. 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 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.  View market data analytics 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 zero rate 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.
  • You need to determine notional principal amount for each cash flow when you generate it.

3. Related Topics
3.1. Floating Rate Note (FRN) or Floating Rate Bond

A floating rate note has variable coupons, depending on a money market reference rate, such as LIBOR rate, 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 have 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 present value of a floating rate note is given by

float rate bond or float rate note valuation in FinPricing

Practical notes

  • All practical notes for pricing amortizing and accreting bonds are applicable to floating rate bonds.
  • 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.

You can find more details at Floating Rate Notes

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

Zero coupon bond valuation in FinPricing

You can find more details at Zero Coupon Bonds

3.3. 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

Fixed rate bond valuation in FinPricing

References