Clean and Dirty Pricing of Inflation-Linked Bonds
Summary
The response explains how to relate clean and dirty prices for an inflation-linked bond. In the example, the quoted clean price and ordinary accrued coupon are combined first; that amount is then multiplied by the index ratio to obtain the indexed dirty price. Thus the inflation adjustment applies to both the clean notional and accrued interest in the settlement value.
The answer illustrates the calculation using terms for a German inflation-linked federal bond, including an index base, a lagged daily index ratio, and accrued interest. It breaks the resulting value into clean notional, accrued coupon, inflation adjustment to notional, and inflation adjustment to accrued coupon. The example suggests a way to interpret accrued inflation in this quotation convention, but does not establish that every government or corporate linker uses the same conventions. Bond terms and market quotation practices should be checked for each instrument.
Key ideas
- The example derives indexed dirty price by multiplying clean price plus accrued interest by the index ratio.
- The inflation adjustment therefore applies to both the notional price and accrued coupon in the example.
- The calculation separates clean notional, accrued interest, and their respective indexation amounts.
- Quotation conventions may vary, so instrument-specific terms should be consulted.
Tags
Full text
# Inflation Bond accrued inflation
# Inflation Bond accrued inflation
Let's say an inflation bond has inflation adjusted coupons and nominal. With respect to dirty and clean price, is the accrued inflation of the nominal usually included in the clean quote? For example, this inflation indexed bond
Germany 0.10% inflation-linked Federal bond 2021 (2033), ISIN DE0001030583
https://www.deutsche-finanzagentur.de/en/federal-securities/factsheet/isin/DE0001030583
is quoted without the nominal accrued inflation.
And could it be that there is a difference in quotation of government issued inflation bonds and corporate inflation bonds?
Thanks
## Answer by Attack68 (score 5)
https://quant.stackexchange.com/a/77895
Your URL provides the majority of the terms for these German linkers. I too had not come across them before but they seem identical to Canadian style (and now UK style) linkers with daily index interpolation and 3 month lag.
The link page gives (or implies) the following properties:
```
Clean price on 3rd Jan (settle 5th): 100.32 ytm: 0.07%
Indexed Dirty price for settle 5th: 119.23
Base index: 104.474748
Index Ratio for 5th Jan: 1.18764
```
Pricing this then results in applying the usual the usual bond formula to the un-indexed bond:
```
# PYTHON
from rateslib import *
ibnd = IndexFixedRateBond(
effective=dt(2021, 2, 11),
front_stub=dt(2022, 4, 15),
termination=dt(2033, 4, 15),
frequency="A",
fixed_rate=0.1,
convention="ActActICMA",
modifier="none",
calendar="tgt",
payment_lag=0,
index_base=104.474748,
index_lag=3,
index_method="daily",
calc_mode="ukg",
)
ibnd.ytm(price=100.32, settlement=dt(2024, 1, 5)) # 0.06538
ibnd.accrued(settlement=dt(2024, 1, 5)) # 0.07240
```
You can use this data to derive the indexed dirty price on the page of 119.23:
$$ Index \; dirty \; price = (Clean \; price + Accrued) \times Index \; ratio \\ 119.23 = (100.32 + 0.07240) \times 1.18764 $$
If you like you can consider this as 4 components:
```
Clean notional: 100.32
Clean accrued: 0.07240
Indexed notional: 18.82404 /* = 100.32*0.18764 */
Indexed accrued: 0.01359 /* = 0.07240*0.18764 */
Total: 119.230
```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.