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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?

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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.

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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.

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