Dirty price

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The dirty price of a bond is the sum of a bond's clean price and the accrued interest since the previous coupon date. The clean price is simply the present value of a bond's future cash flows. The dirty price is also called the "full price."

The clean price is, in effect, the price of the bond on the first day of the coupon period. The dirty price of a bond is its price including accrued interest[1]. Bond prices are usually quoted "clean" (without accrued interest), and then settled "dirty" (with accrued interest). In other words, the dirty price contains an additional cost that was not included in the quoted price.

When a bond is sold in the secondary market at some time between interest payment dates, the bond seller is entitled to payment of the accrued interest since the last payment date[2]. This compensates the bondholder for the amount of interest that has accumulated between the previous coupon date and the settlement date.

The dirty price is calculated as follows:

Accrued Interest + \sum_{i=1}^{n} \frac{\frac{C_i}{m}}{\left(1+\frac{YTM}{m}\right)^i} +\frac{F}{\left(1+\frac{YTM}{m}\right)^n}

where:

  • Ci = coupon payment in period i
  • F = face value or redemption value at maturity
  • YTM = yield to maturity or redemption yield, for example YTM = 6% per year = 0.06 per year
  • m = number of coupon periods in one period over which YTM is measured. For example, if YTM is given as 6% per year, and coupon payments are six-monthly, then m is 2. The convention is that, for example, the six-monthly YTM is calculated to be 3%, and is reported as 6% per year, instead of the accurate yearly yield of 1.03^2 - 1 = 6.09%
  • n = total number of coupon periods. For example, if the bond has 8.5 years to maturity and coupons are paid six-monthly, then n = 17

[edit] Footnotes

  1. ^ see Clean and Dirty Prices.
  2. ^ see Trade Interest Bought/Sold.

[edit] References

[edit] See also

v • d • e
Bond market
Types of bonds by issuer
Types of bonds by payout
Derivatives
Pricing
Yield analysis
Credit and spread analysis
Interest rate models