Introduction to Fixed Income Analytics: Relative Value Analysis, Risk Measures, and Valuation, Second Edition

CHAPTER 3

Day Count Conventions and Accrued Interest

When we computed present values in previous chapters, we assumed that the next cash flow was one full period away (i.e., the exponent on the first discount factor was one). When we value coupon-paying bonds that deliver cash flows semiannually in the next chapter, we will see that the next coupon payment is one full period away on only two days a year—the coupon payment dates. This is true for the traditional coupon bond because the compounding frequency and payment frequency are the same (i.e., semiannual). On all other dates, the next cash flow is less than one full period away (i.e., the exponent on the first discount factor is less than one).

Two complications arise when we try to value a bond between coupon payment dates. The first complication is the procedure used in the bond market for calculating the number of days between two dates (e.g., the number of days between the settlement date and the next coupon payment). These procedures are called day count conventions. Second, when the settlement date falls between coupon payment dates, a bond will have accrued interest . Simply put, accrued interest is that portion of the bond’s next coupon payment that the buyer owes the seller on the settlement date when a bond changes hands between coupon payment dates. These two complications are the subject of this chapter.

DAY COUNT CONVENTIONS

The day count basis specifies the convention used to determine the number of days in ...