Floating-Rate Bond Valuation Between Coupon Dates
Summary
The note explains why a floating-rate bond is generally valued near its face value when issued and immediately after a coupon resets. For the first accrual period, the forward coupon rate is already known and matches the discount rate used for that period, so discounting the coupon plus principal gives par in the example. This first-period reasoning does not imply that the bond is callable.
For later periods, valuation uses forward rates inferred from the relevant interest-rate curve and discounts the cash flows consistently with that curve. The full bond value can also be expressed as the present value of all expected coupons plus principal at maturity. The explanation is a simplified curve-based account; it does not address credit risk, liquidity, differing reference and discount curves, or embedded features that could move the bond away from par.
Key ideas
- A floating-rate bond’s first coupon is based on a rate known at the start of its accrual period.
- When the coupon and discount rates match for that period, the coupon plus principal discounts to face value.
- Valuing later cash flows requires forward rates and discount factors from the interest-rate curve.
- The par-value argument does not require a call feature.
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Full text
# Valuing a floating-rate bond
# Valuing a floating-rate bond
Suppose we have a floating-rate bond with arbitrary face value.
I am given to understand that the value of such a bond is the face value, at the time it is issued and also after each coupon payment.
As an example, let the face value be 100, and let the interest rate at the time of issuance be 5%, so the coupon payment at the end of the first period is 5. Hence, the value of the bond is: $ \frac{(100 +5)}{1.05}=100$
A couple of things: 1. Why do we only consider the first period? Does this assume the bond is callable? 2. Do we assume the discount rate is the same as the floating rate?
## Answer by simzoor (score 0)
https://quant.stackexchange.com/a/54534
A floating rate bond is typically referencing to some interest rate curve (3m LIBOR, 6m EURIBOR etc.)
- You can also consider other periods, you just need to know the forward rate for that period, which is first derived from the interest rate curve and second discounted by that interest rate curve. This doesn't assume any embedded options.
- Only for the first period, since the first period forward rate is equal to the discount rate (after each coupon payment, you already know the next e.g. 3m LIBOR rate, which will be payed after 3 months).
HINT: the sum of the PV coupon payments over the entire life of the bond and the PV of the face value at maturity is equal to the face value today.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.