How Clean and Dirty Bond Prices Behave Between Coupon Dates
Summary
The document distinguishes a bond’s clean price from its dirty price. The dirty price includes coupon interest accrued since the previous payment, while the clean price excludes that accrued interest. As a result, the amount paid by a buyer between coupon dates can change with accrual even when the quoted clean price is stable.
For a bond priced at par under unchanged market conditions, the answer says the clean price should remain at par rather than steadily decline toward the coupon date. Changes in clean price instead reflect changes in relevant interest rates or the bond’s credit spread. The response also clarifies that a bond’s coupon is calculated from face value, and at maturity the investor receives face value plus the final coupon. This is a conceptual explanation based on an all-else-equal assumption; actual prices can also reflect other market factors and bond-specific terms.
Key ideas
- Dirty price includes accrued coupon interest, while clean price excludes it.
- A par bond’s clean price remains at par if market conditions and assumptions stay unchanged.
- Changes in interest rates or credit spreads can change the clean price.
- Coupons are calculated from face value, and maturity repayment includes face value plus the final coupon.
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Full text
# Clean price and dirty price in bonds # Clean price and dirty price in bonds I deconstructed a bond cash flow today (5%, trading at par). It seems very counterintuitive to me that the principle of a bond going up in "value" over time, the total cashflow going up in value over time, yet the clean price constantly decreases until the coupon payment date. Pricing bonds is based on the fact that money's value decreases over time, which leads to the definition of "bond discounting". Yet while they are practically going back to the original value, they are constantly susceptible to the time value of money. ## Answer by D Stanley (score 1) https://quant.stackexchange.com/a/85635 If you are "pricing the bond at par" then the "clean price" would always be 100, and not decrease. The "dirty price" is simply the clean price plus any coupon interest that accrues, since when you buy a bond on the market between coupon payments, you pay the accrued interest since the prior coupon was paid. > yet the clean price constantly decreases until the coupon payment date. This is not a natural phenomenon - I suspect that something is wrong with your modelling if the clean price always decreases. All else being equal, clean prices should stay the same. If they change, it's because either the underlying risk-free interest rates or the credit spread of this bond changes. If you are not changing these then the bond's clean price should be constant. > Assume you loan someone 100u, by the end of the term, the loan returns to you with 99.89u (due to time value) + 5% interest rate No - if you buy a bond, when the bond matures you get the face value (undiscounted) plus the final coupon. So if you "loan someone 100u" - meaning you buy a 100u bond at par - when the bond matures you get 105u (100 + 5%). The coupon is always calculated based on the par amount of the bond, not the amount that someone paid for it. > Pricing bonds is based on the fact that money's value decreases over time, which leads to the definition of "bond discounting" The coupon accounts for that discounting, plus or minus changes in the value of the bond at that coupon relative to other bonds of similar risk (i.e. as underlying interest rates change)
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