Constructing the Short End of an Inflation Swap Curve

Summary

The document discusses how to build the sub-one-year portion of an inflation curve from zero-coupon inflation swaps. It describes three possible inputs: broker monthly fixings, published CPI values with seasonal factors and the one-year market quote, or published values combined with economic forecasts and those same curve anchors. Given a known or forecast index value, the author shows how to derive a breakeven rate consistent with the index growth from the curve base, then use it to shape the front of the curve.

The practical concern is instability as published CPI observations roll forward or a new release arrives. The author asks how to reduce that volatility while preserving market consistency. The document does not provide a solution, describe an interpolation framework, or show evidence comparing the alternatives. It is useful for framing the inputs and source of short-end jumps, but the appropriate smoothing approach remains unanswered and would depend on market conventions and the intended curve use.

Key ideas

• The short end can be built from broker fixings, published CPI, or CPI combined with forecasts.
• Seasonal factors and the one-year quote help connect near-term index information to the market curve.
• Known or forecast index levels can be converted into breakeven rates consistent with index growth.
• Rolling CPI observations and new releases can create volatility in the front of the curve.
• The document raises, but does not answer, how to smooth the curve while retaining market consistency.

Tags

# Inflation (index) curve construction


# Inflation (index) curve construction












We have constructed an inflation curve which is based on liquid ZCIS. All in all it fits well with other providers (including the seasonal factors).

I am looking for alternative references on how to construct the inner most part of the curve (sub 1Y). As far as I can see from books, technical documents and other online resources then there are three options:

- Monthly fixings (up to 1Y) from brokers.

- Using the known index values (published CPI), the seasonal factors, the known 1Y quote (and interpolate between these.

- Using the known index values (published CPI), economic forecasts, the seasonal factors, the known 1Y quote (and interpolate between these.

Note, that when we have a known published CPI value or an inflation forecast, then we can back out a "breakeven" value consistent with the following equality and use this "breakeven" for the beginning of the breakeven curve:

$Index_t=Index_0*(1+b(0,T_s,T_e))^t$

where we know $Index_t$ (known CPI or forecasted CPI), $Index_0$ (base of the curve - known CPI) and $t$ (maturity).

Point 2 and to a certain extent 3. above give a lot of volatility in first part of the curve (when switching to a new month as we go from 3 known CPI values to 2, and then again later mid-month when a new CPI value is published).

What options, if any, are available to reduce this volatility, while still maintaining a market consistent curve?

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.