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An Introduction to the Bond Markets by Patrick J. Brown

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Appendix B

Mathematical Formulae

In order to make the formulae easier to understand, the following notation has been used throughout this section:

P dirty price of a bond
AI accrued interest to the settlement date
g annual coupon rate (%)
ND number of days accrued
CP clean price; hence P = CP + AI
C redemption value
n number of future cash flows until the assumed redemption date
CFi ith cash flow
L i time in years to the i th cash flow, allowing for the market conventions used in calculating any fraction of a year
v discounting factor, i.e. v = 1/(1 + y)
y redemption yield compounded annually (y = 0.06 for a yield of 6 %)

B.1 ACCRUED INTEREST

The accrued interest on a security varies according to the type of security and the market on which it is traded. The accrued interest (AI) is, although there are exceptions, generally defined as:

image

where:

AI accrued interest to the settlement date
g annual coupon rate (%)
ND number of days accrued from either the issue date or the last coupon date to the settlement date

It should be noted that there are several ways of calculating the number of days accrued up to the settlement date, and a further several ways of calculating the number of days in a year.

The accrued interest on a bond is almost always calculated from the issue date or, if there has been a subsequent coupon payment, the last coupon date up ...

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