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Setting Coupon Dates for Bonds with Stub Periods

Article Quant Q&A · Author: HBoson
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Summary

The document addresses how to schedule coupon payments when a bond’s maturity does not align with its regular payment interval. Its practical rule is to count backward from maturity: place the final coupon at maturity, then step back by the stated coupon frequency. For an annual coupon bond maturing in two and a half years, this convention gives a short initial period if the bond is issued at the schedule’s start, while a bond purchased between regular coupon dates may simply have its next payment half a year away.

A second explanation describes stub periods, which are shorter or longer than the regular interval and can appear at the beginning or end of a schedule. The answers emphasize that several schedules are possible and that the exercise’s wording may not uniquely determine one. The reader should use any stated issue date, purchase date, or market convention; absent those details, the backward-counting rule is a reasonable default for a basic example. The discussion is an introductory convention, not a full treatment of bond day-count rules or market-specific coupon conventions.

Key ideas

  • For a regular coupon schedule, count backward from maturity in intervals matching the payment frequency.
  • A purchase between coupon dates can make the next payment fall sooner than one full coupon period away.
  • A stub is a shorter or longer coupon period used when maturity and payment frequency do not align.
  • The location of a stub can vary, so dates depend on the assumptions and conventions given.

Tags

Fixed income
Full text
# Time to maturity of a bond not divisible by payment period


# Time to maturity of a bond not divisible by payment period












I am relatively new to the topic of quantitative finance - at the classes I got an exercise about "2.5 year bond payed annually". Therefore I have a question about the time of payment of interest. The first payment will be payed after half a year or after a year? In other words, does the scedule of payment looks like 1/2, 1.5, 2.5 or rather like 1, 2, 2.5?

## Answer by nbbo2 (score 1)

https://quant.stackexchange.com/a/42741

As a general rule, unless told otherwise, start at the maturity date of the bond and work backwards: the last coupon payment will be at maturity, the one before will be 1 year earlier, then 1 year before that, and so on.

There are exceptions and special cases, but they would probably not occur in a simple example from a book. Most likely this is an ordinary yearly bond which has been purchased halfway between coupon payments, so the next coupon is 0.5 years away.

## Answer by Bram (score 0)

https://quant.stackexchange.com/a/42737

In general when payment frequency and tenor don't align, you can introduce a shorter period (called a stub) for one period. This can be at the beginning of the schedule or the end of the schedule. As far as I know, at the beginning is far more customary (because then you can 'forget' about weird periods earlier), but both do occur. Another alternative is to have a longer than normal period, but this happens less afaik.

So my best guess would be 0.5, 1.5 and 2.5, but there are a lot of variations possible.

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.