Although the fundamental process of pricing a bond results in a single price, there are two types of bond prices to be aware of and to be clear on the distinction between the dirty price and the clean price, the yield to maturity formula discounts all cash flows of a bond with the same discount rates.

This gives the current value of the bond or the dirty price, and is the price paid by investors when buying the bond.

However, there's also the clean price, which is calculated from the dirty price by subtracting something called accrued interest.

So what is accrued interest? Accrued interest is the interest that has accumulated on the bond since the last coupon payments up to the purchase date of the bond.

Since coupon payments are made at regular intervals, EG semi-annually or annually or annually, a bond holder earns interest over time, even though they only receive payments at the set intervals.

If the bond is sold in between these payment dates, the seller is still entitled to the interest that accrued during their ownership, even though they sell it before the actual interest payments.

This amount is the accrued interest, and it's important that it's included in bond pricing.

But which price is quoted in the markets? The dirty price, the actual amount to be paid or the clean price? Well, in most markets it is the clean price that is quoted.

This is the bond price, excluding the accrued interest, which feels a bit strange.

However, once a trade is agreed upon, based on the clean price, accrued interest is then added to the clean price to determine the dirty price, which is the actual amount the buyer must pay.

So this raises the question, why don't we quote bond prices using the dirty price directly? The answer is to have less variables included in the price.

The clean price reflects the market's perception of the bond's value, considering factors like credit risk, interest rate, risk, and timed maturity.

Accrued interest, on the other hand, is simply a function of time and the the bond's coupon rates, the dirty price changes daily as interest accrues.

And this causes price fluctuations that don't necessarily reflect changes in the bond's market value or the bond's risk, or its return profile.

So by using clean prices, the market can focus on those bond fundamentals without the noise of daily variations caused by accrued interest.