Modified following business day convention

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A popular means of calculating interest periods and determining interest payment dates. Nearly as popular as the following business day convention.

How one adjusts the calculation period for a given interest period to account for the fact that it ends on a non-working day, and that therefore the interest payment can’t be made on schedule.

There are two things you might wish to adjust here: one is settlement date for the interest payment — that is, the day on which the interest payment is actually made, the other is the duration of the interest period — that is the day on which the interest period in question is deemed to end.

Unlike day count fractions, business day conventions are not applied in a standardised way across the industry: they are not tied to specific currencies or anything like that: it comes down to the basic preference of the institution calculating the interest rate.

That said, fixed rate products are a lot less bother than floating rate products, and tend to be unadjusted.

• Fixed rate products - yeah whatever: Folks tend to be fairly sanguine about interest payments for fixed rate interest products, since nothing really hangs on when a period begins or ends (you make it up over the life of the product: if this period is thirty one days, the next one will be twenty nine, and the present value of the difference between getting a payment now for 31 days and a payment in a month for 29 days, and just getting two payments for 30 days each. You can’t pay your interest payment on a non-work day, so just pay it on the next business day, but the calculation period runs to the originally scheduled day. You lose a day or two’s interest on the interest, but you’ll make that up next time.
• Floating rate products - hold on tiger: Floating rate products are a bit more nuanced because there is some path dependency here. The end of an interest calculation period determines not just the point at which you pay interest (and perhaps the number of days for which you pay it), but also the time at which you set the interest rate for the following period. Since interest rates are — or, at least, in the good old days were — volatile, the product is path dependent and a matter of a couple of days can make a difference to the overall amount of interest paid for the life of the product. Butterfly wings flapping in Amazon rainforests and all that.

Business day conventions for your reading pleasure

• No adjustment business day convention: The keep-calm-and-carry-on option: ignore non-work days of any kind. Cashflows due on non-workdays are assumed to be distributed on the actual date.
• Previous business day convention: Back to the day before: Cashflows falling on non-workdays are assumed to be distributed on the previous business day.
• Following business day convention: Cashflows falling on a non-workday are assumed to be distributed on the next business day.
• Modified previous business day convention: Cashflows falling on a non-workday are assumed to be distributed on the previous business day unless it would fall in a different month, in which case it’s the next business day.
• Modified following business day convention: Cashflows falling on a non-workday are assumed to be distributed on the next business day unless it would fall in a different month, in which case it’s the previous business day.

End of month - no adjustment business day convention: All cashflows are assumed to be distributed on the final day of the month (even if it is not a workday).

End of month - previous business day convention: All cashflows are assumed to be distributed on the final day of the month unless it is not a workday, in which case it’s the previous business day.

End of month - following business day convention: All cashflows are assumed to be distributed on the final day of the month unless it is not a workday, in which case it’s the next business day.