Clean Bond Prices, Accrued Interest, and Market Conventions

Summary

The answer distinguishes a bond’s quoted clean price from the dirty price paid in a secondary-market transaction. The clean quote excludes accrued interest; the dirty proceeds include accrued interest through settlement and may also reflect adjustments for amortizing or payment-in-kind bonds. For many traditional fixed-coupon bonds, accrued interest is calculated as a fraction of the coupon period multiplied by outstanding principal, rather than by applying daily compounding to accrued amounts.

Accrual conventions vary by instrument and market. The period fraction may use actual calendar days or, in some cases, business days, while certain floating-rate instruments tied to daily observed indexes may compound daily. The answer characterizes linear accrual as conventional market practice, not as a universal mathematical pricing rule. It mentions a paper arguing that daily compounding can affect fair value, but gives no details or quantitative evidence, so the discussion does not establish when that adjustment is material.

Key ideas

• Clean bond quotes exclude accrued interest, while dirty transaction proceeds include it through settlement.
• Traditional fixed-coupon accrued interest is commonly computed from a period fraction and outstanding principal.
• Day-count conventions differ, and some instruments use daily compounding.
• Market convention explains linear accrual in many cases, but it does not imply a universal fair-value rule.

Tags

# Is this linear interpolation for clean bond price an approximation?


# Is this linear interpolation for clean bond price an approximation?












Consider the attached discussion from Berk and Demarzo's Corporate Finance.

I am confused about the calculation of a bond's "clean price". It seems that the procedure described above seems to tacitly "linearly discount" the accrued interest, rather than discounting cash flows with an appropriate factor. Put differently, why does the given graph suggest that Dirty Price grows linearly in between coupon payments, rather than according to some $(1+r)^t$ factor as would be expected based on (rigorous) discounting?

## Answer by Dimitri Vulis (score 1)

https://quant.stackexchange.com/a/77600

In most, but not all, markets, the convention is to quote a bond's clean price (ex accrued). When a bond is actually traded in a secondary market, the proceeds are the dirty price: cum accured until the settlement date, and also taking into account the factor for amortizing and PIK bonds.

Traditionally, the accrued interest is calculated as your book describes: a period fraction times the outstanding principal. The calculation of the period fraction may get quirky in practice - some bonds use actual days, but a few accrue only on business days, etc. Some floaters linked to an index observed daily do use daily compounding. I don't recall any examples of fixed-coupon bonds paying "interest on interest". This is just the traditional market practice. Here is a 2005 paper https://www.economics-finance.org/jefe/fin/Secrestpaper.pdf arguing that daily compounding affects a bond's fair price.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.