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Floating-Rate Note Duration and Sensitivity to the Next Reset

Article Quant Q&A · Author: wormeer
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Summary

The document addresses why a floating-rate note’s duration can correspond to the time until its next coupon payment or rate reset. The response considers the bond immediately after a coupon is fixed, when the next floating reference rate can still change. It expresses the price as the next coupon-bearing amount discounted at that rate and examines the price’s proportional sensitivity to a change in the rate.

The resulting sensitivity is associated with the six-month interval to the next payment in the example. This illustrates why a floater’s interest-rate exposure is often concentrated over the period before its coupon resets, rather than extending like that of a fixed-rate bond. The explanation is brief and tied to a particular coupon schedule and notation; it does not cover credit spreads, caps or floors, changing reset conventions, or a broader portfolio duration calculation.

Key ideas

  • A floating-rate note’s coupon is fixed for the period until its next reset.
  • The response measures price sensitivity to a change in the next floating reference rate.
  • In the example, that sensitivity corresponds to the six-month time until the next coupon payment.
  • The explanation is limited to a simplified pricing setup and does not address other sources of risk.

Tags

Fixed incomeDerivatives pricingRisk management
Full text
# Duration. Floating rate note


# Duration. Floating rate note












I don't understand why the duration of a floating rate note equal to the time to the next coupon payment? Please, look at my calculations.

Here: P - is price at moment 0.

## Answer by dm63 (score 1, accepted)

https://quant.stackexchange.com/a/46581

Let the first coupon be fixed at c, and consider the duration of the bond immediately thereafter. At this point $L_(0,6)$ can move. Now in your notation you should find that $$P=N(1+c/2)/(1+L_(0,6)/2)$$. Now if you calculate $(1/P)dP/dL$ you get $1/2* (1/(1+L/2))$ which is 1/2, discounted for 6 months, where $L=L_(0,6)$.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.