Why Bond Accrued Interest Uses Linear Coupon Accrual

Summary

The document asks why accrued interest in bond pricing is commonly calculated by prorating the coupon according to the elapsed fraction of the coupon period. It contrasts this clean-price convention with the treatment of coupon and principal cash flows in dirty-price valuation, where future payments are discounted using yield to maturity.

The author wonders whether accrued interest should instead reflect the present value of the prorated coupon amount, since the full coupon is not paid until the next coupon date. The document contains no answer, derivation, or comparison of pricing conventions. It therefore raises a conceptual question about the relationship between accrued interest, clean and dirty prices, and time value rather than establishing a pricing method. The exact convention may depend on market practice and the bond’s day-count rules, neither of which is developed here.

Key ideas

• The document asks why accrued interest is usually prorated linearly over a coupon period.
• It distinguishes the clean price from the dirty price, which values future cash flows using yield to maturity.
• The author questions whether accrued interest should include discounting to the next coupon date.
• No answer or derivation is provided, so the document leaves the convention unexplained.

Tags

# Why is accrued interest prorated linearly?


# Why is accrued interest prorated linearly?












Cashflows from coupons and principal are discounted using the YTM to get PV of the bond in dirty price.

as shown here in this question Misunderstanding of 'day counts' and accrued interest

When backing out the clean price, the accrual is calculated as $coupon/freq*day/daycount$. But why do we linearly prorate the accrual?

Technically, shouldn't the accrued interest be the PV that is discounted by YTM of $coupon/freq*day/daycount$? The actual coupon amount will only be paid at the coupon date, so shouldn't the accrued interest take into account the time value between settlement date and coupon date?

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