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# Clean and Dirty Price

Definition:

## What is a Clean and Dirty Price?

The clean price of a coupon bond is the price before any interest payments have been made. On financial news sites, the clean price is frequently quoted. This price does not include any interest accumulated between the bond’s scheduled coupon instalments. The dirty price is the polar opposite of a clean price. A dirty price is when a bond price includes interest accrued since the latest coupon payment.

## Example of Clean and Dirty Price:

The dirty price is the price the bond seller must pay to give up ownership. It includes the present value of the bond plus the accrued interest. The clean price is the dirty price less accrued interest:

clean price = dirty price – accrued interest

To calculate both prices, we would also need the formula for the accrued interest:

$Accrued Interest = F*\frac{C}{M}*\frac{D}{T}$

Where:
F = Face value
C = Total annual coupon rate
M = number of coupon payments per year
D = Days since last payment date
T = Accrual period (number of days between payments)

Consider a \$100 par value bond that pays a 3% coupon semiannually. This means a coupon of \$1.50 is paid every six months. If the bond is sold (and settles) 41 days after the last coupon, the buyer will need to pay the seller \$1.50 × 41 182 = \$0.3379 for every \\$100 purchased. When calculating the discount factor, the amount of the accrued interest needs to be added to both the bid and asked for a quote before calculating the midpoint.

Owais Siddiqui