Dirty_price

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.^{[citation needed]} 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^{[citation needed]}. 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:

$Accrued\; Interest\; +\; \backslash sum\_\{i=1\}^\{n\}\; \backslash frac\{\backslash frac\{C\_i\}\{m\}\}\{\backslash left(1+\backslash frac\{YTM\}\{m\}\backslash right)^i\}\; +\backslash frac\{F\}\{\backslash left(1+\backslash frac\{YTM\}\{m\}\backslash right)^n\}$

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.
• 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

See also

• Clean price
• Accrued interest

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