Bond Clean and Dirty Prices: Accrued Interest Is a Quoting Convention
Summary
The question compares the conventional linear accrued-interest adjustment used to derive a dirty bond price from its clean quote with a compounding-based price approximation. It asks whether the difference between these calculations could create arbitrage, particularly for bonds with large face values. The accepted answer explains that the market values the bond on an all-in basis; clean price is a quoting convention designed to keep quoted prices from jumping at coupon dates.
Accrued interest is then applied to express the all-in value as a clean quote, rather than used to determine a separate economic value that market participants might misprice. Because the adjustment is conventional, the answer argues that using a simpler linear accrual formula does not itself create an arbitrage opportunity. The document offers a conceptual explanation, not a quantitative comparison or analysis of transaction costs, market frictions, or deviations from fair value.
Key ideas
- The dirty price represents the bond’s all-in value, including accrued interest.
- The clean price convention helps smooth quoted prices around coupon dates.
- The linear accrued-interest adjustment is a quoting convention rather than an independent valuation method.
- The difference from a compounding formula does not by itself imply an arbitrage opportunity.
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Full text
# Do price approximations lead to arbitrage opportunities?
# Do price approximations lead to arbitrage opportunities?
Do price approximations lead to arbitrage opportunities against a price computed using the exact formula?
For instance, dirty bond price uses a linear approximation to compute the accrual interest: $$P_{d}=P_{c}+\alpha t$$ Whereas the exact formula gives a slightly higher value for $0<t<1$ (with time unit the time between payments), for both continuous or discrete compounding (assuming par): $$P(t)=ce^{i(t-1)}+e^{i(t-1)}P(0)$$ $$P(t)=\frac{c}{(1+i)^{t-1}}+\frac{P(0)}{(1+i)^{t-1}}$$ Giving the high nominal of some bonds, does the difference is ever high enough to produce arbitrage opportunities?
## Answer by Chris Taylor (score 8, accepted)
https://quant.stackexchange.com/a/35744
No. The dirty price is the market's estimate of fair value for the bond. The clean price is just a quoting convention (so that the price doesn't jump when you pass over a coupon date).
The market doesn't try to estimate the clean price and then get the all-in (dirty) price wrong. The market estimates the all-in price, and then applies the accrued interest adjustment when it comes to submitting a quote.
The adjustment is just a convention that everyone agrees on to make the price series nicer. Since the adjustment has no economic impact whatsoever, it doesn't matter what adjustment is used, and you might as well use the simpler, linear adjustment for days accrued, rather than a more complex adjustment that takes compounding into account.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.