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Estimating Real Rates from OIS and Inflation Swap Rates

Article Quant Q&A · Author: An old man in the sea.
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Summary

The document explains how market rates can be used to form measures of inflation expectations and expected real interest rates. It identifies inflation swap rates as the likely source of the cited medium-term inflation expectation measure, including the five-year rate beginning five years ahead. Such a swap rate reflects market pricing of inflation over that future period; it is a market-implied measure, not a direct survey forecast.

For the real-rate path shown in the referenced figure, the response describes subtracting an inflation swap rate from a nominal OIS rate to construct an approximate real rate. The approach is a simple market-based estimate and should be read as approximate: the document provides no detailed calculation conventions, adjustments, or discussion of risk premia that can affect swap-implied inflation measures.

Key ideas

  • Inflation swap rates provide a market-based measure of expected inflation over a specified horizon.
  • A five-year rate beginning five years ahead measures inflation pricing for a future five-year period.
  • An approximate real rate can be constructed by subtracting an inflation swap rate from a nominal OIS rate.
  • The document gives a high-level explanation without detailing adjustments, conventions, or the influence of risk premia.

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Fixed incomeDerivatives pricingStatistics
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# Measuring Medium-term Inflation expectations and real interest rate from OIS and Inflation Swaps


# Measuring Medium-term Inflation expectations and real interest rate from OIS and Inflation Swaps












In this speech by Mario Draghi, in section '2:Responding to high unemployment', and subsection 'Boosting aggregate demand', Mario states «Over the month of August financial markets have indicated that inflation expectations exhibited significant declines at all horizons. The 5year/5year swap rate declined by 15 basis points to just below 2% - this is the metric that we usually use for defining medium term inflation. »

How does the ECB get the markets inflation forecast with the 5y/5y swap rate?

Also in the same subsection of the text, there's 'Figure 7: Expected real interest rate path in the euro area and the US'. In this figure, the forecast is obtained from OIS-Inflation swap, according to the subtitle on the vertical axis. How do they obtain this? What's the rationale for it?

Any help would be appreciated.

## Answer by Mats Lind (score 1)

https://quant.stackexchange.com/a/29629

The section two remark likely refers to inflation swaps. In figure 7: OIS is a nominal rate index, subtracting from this the inflation rate on the inflation swaps gives a constructed real rate as written in the header. Real rate = (approx) nominal rate - imflation rate.

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.