Why Bond Duration Uses Dirty Price Rather Than Clean Price

Summary

The document addresses which bond price belongs in a duration calculation. It defines modified duration using the derivative of price with respect to yield divided by price, and identifies that price as the dirty price, which includes accrued coupon interest. Clean price remains the usual market quotation in many bond markets, but quoted price and valuation input need not be the same.

The answers state that yield, DV01, and duration analytics generally use dirty price, which represents the bond’s full market value. One response observes that accrued coupon does not depend on yield, while still noting dirty-price convention. The discussion is brief and does not derive how clean- and dirty-price sensitivities relate across coupon dates or address market-specific conventions beyond noting that quoting practices vary.

Key ideas

• Modified duration is defined using the dirty bond price in the denominator.
• Clean price is a common quoting convention, while dirty price includes accrued coupon and represents full market value.
• Yield, DV01, and duration analytics are generally computed using dirty price.
• Market quoting conventions can vary, and accrued interest affects the relationship between quoted and valuation prices.

Tags

# Clean vs. Dirty Price and its impact on duration


# Clean vs. Dirty Price and its impact on duration












When calculating duration would you use the clean price or the dirty price? why for either?

## Answer by Helin (score 6)

https://quant.stackexchange.com/a/42661

By definition, modified duration is $$ D_\text{mod} = \frac{1}{P} \frac{dP}{dy} $$ where $P$ is the dirty price of a bond.

Clean price is the standard quoting convention for the vast majority of bond markets (though not all), but nearly all analytics, be it yield to maturity, DV01, or duration, are all computed using dirty price.

## Answer by Ezy (score 1)

https://quant.stackexchange.com/a/42660

Accrued coupon does not depend on yield so it does not really matter but the convention is to use dirty price which is the market value of the bond

EDIT: i initially incorrectly stated that the clean bond price was used by convention. Helin was correct to point out the opposite is true. For instance here is a documentation from FTSE where you can see that the market value of bonds is used for calculation (market value being dirty price that is clean price plus accrued coupons)

https://www.ftse.com/products/downloads/FTSE_Fixed_Income_Index_Guide_to_Calculation_new.pdf

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.