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Clean and Dirty Prices for Risky Bonds

Article Quant Q&A · Author: Grzenio
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Summary

The note clarifies that clean and dirty prices are distinguished by whether accrued coupon interest is included, not by whether the bond is risky or by the method used to discount its cash flows. A dirty price includes interest accrued since the last coupon payment; a clean price removes that accrued amount. This convention applies to bonds with intermittent coupon payments, including defaultable or catastrophe-linked bonds.

Discounting remains a separate valuation step: the chosen discount rate is used to value cash flows whether the resulting quote is expressed as clean or dirty. To move between the quoted forms, the accrued interest is subtracted from the dirty price to obtain the clean price. The answers do not specify a day-count convention, coupon accrual formula, or special adjustments for default or catastrophe risk, so those details must come from the bond’s terms and market convention.

Key ideas

  • Dirty price includes coupon interest accrued since the previous coupon payment.
  • Clean price excludes accrued interest from the dirty price.
  • The clean-versus-dirty distinction is separate from the discount rate used to value cash flows.
  • The standard definitions apply to risky bonds as well as other coupon-paying bonds.
  • Accrued-interest calculations depend on bond terms and conventions not detailed in the note.

Tags

Fixed incomeRisk management
Full text
# What is the clean price and dirty price of a risky bond?


# What is the clean price and dirty price of a risky bond?












Following up on this question: Yield of a risky bond, what is the definition of clean and dirty prices for a risky (defaultable, catastrophe, etc.) bond?

I would think the dirty price should basically be the discounted cashflows. Then the clean price should be dirtyPrice-accruedAmount. What is the accruedAmount though? At what rate does it accrue?

## Answer by Matt Wolf (score 3, accepted)

https://quant.stackexchange.com/a/4947

Dirty bond price refers to the price of a bond that reflects the interest that has accrued since the issuance of the bond or last coupon payment. It has nothing to do with how you discount cash flows but just whether accrued interest is priced in or not. Thus, dirty and clean bond prices apply to all bonds that pay intermittent cash flows.

## Answer by SRKX (score 1)

https://quant.stackexchange.com/a/5973

The discount rate that you use to compute the price of the bond is a parameter that you use during the computation of both types of valuations (clean or dirty); it is the rate you use to discount the cash flows.

The only difference between clean and dirty price is that the clean price removes the accrued interest since the last coupon. Hence, the discount rate used for clean price computation should be the same you used as input for the dirty calculation.

## Answer by tagoma (score 0)

https://quant.stackexchange.com/a/4945

The standard definitions and formulas of clean price and dirty price apply for your "risky" bonds.

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.