## Inflation Swap Curve

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FinPricing offers the following curves for various currencies via API. All the interest rate curves have data points up to 50 years.

- OIS curves
- RFR (risk free rate) curves
- SOFR, €STR (ESTR, ESTER), SONIA, TONA, CORRA, AONIA, SARON curves
- IBORs (LIBOR, EURIBOR, TIBOR, CDOR, EONIA, etc.) fallback rate curves
- Swap rate curves
- Basis curves
- Spot rate or zero rate curves
- Forward rate curves
- Discount curves
- Inflation Swap rate (CPI, RPI, HICP) curves
- Nordic electricity futures curve
- VIX futures curve
- S&P 500 futures curve

**1. Inflation Swap Introduction**

Inflation linked securities, such as inflation swaps, have cash flows with a calculation rule contingent on an inflation index, either Consumer Prices Index (CPI) or Retail Prices Index (RPI). To calculate the mark-to-market price and market risk of inflation linked contingent securities we need to construct a forward curve for the CPI or RPI index.

Inflation markets exhibit strong seasonal patterns and, thus, forward index curve should capture this behavior. Since coupon calculation rule for inflation linked securities typically specifies a lag of some months between the RPI observation and payment, the forward curve implied from market traded securities implicitly includes some convexity adjustment. In this report, pricing is examined only on ZC inflation swap and, thus, convexity adjustment is not considered in pricing.

Inflation curve is calibrated to inflation swaps and includes an adjustment factor to account for the observed seasonal fluctuations in CPI or RPI. In the UK, the inflation indices are calculated and published by the Office for National Statistics (ONS). A time series of RPI data has a clear and significant annual cycle of monthly seasonal fluctuations imposed on the generally observed trend of increasing RPI. Inflation swaps can be used to forecast the trend of forward RPI. However, these instruments do not provide any information about monthly fluctuations.

Historical RPI data is used to calculate seasonal deviations from the trend in RPI and use this as the best estimate for future seasonal fluctuations. The seasonal adjustment factors are calculated using a standard statistical procedure

A zero coupon inflation swap is a contract to exchange the realized performance of inflation index (inflation floating) for fixed rate. Whereas an inflation linked asset swap is a security in which a stream of inflation linked cash flows, that match the payments of an inflation linked bond, are swapped for a stream of cash flows that pay LIBOR/SOFR plus a spread, or a fixed rate.

FinPricing provides the most liquid inflation swap rate data. An inflation swap rate curve is shown below:

Currency | CurveName | Instrument | ValuationDate | Tenor | Value |
---|---|---|---|---|---|

USD | USD.CPI | InflationSwapRate.1YR | 2023-01-05 | 1YR | 2.182 |

USD | USD.CPI | InflationSwapRate.10YR | 2023-01-06 | 10YR | 2.462 |

USD | USD.CPI | InflationSwapRate.12YR | 2023-01-07 | 12YR | 2.451 |

USD | USD.CPI | InflationSwapRate.15YR | 2023-01-08 | 15YR | 2.431 |

USD | USD.CPI | InflationSwapRate.2YR | 2023-01-09 | 2YR | 2.292 |

USD | USD.CPI | InflationSwapRate.20YR | 2023-01-10 | 20YR | 2.403 |

USD | USD.CPI | InflationSwapRate.25YR | 2023-01-11 | 25YR | 2.385 |

USD | USD.CPI | InflationSwapRate.3YR | 2023-01-12 | 3YR | 2.321 |

USD | USD.CPI | InflationSwapRate.30YR | 2023-01-13 | 30YR | 2.405 |

USD | USD.CPI | InflationSwapRate.4YR | 2023-01-14 | 4YR | 2.355 |

USD | USD.CPI | InflationSwapRate.5YR | 2023-01-15 | 5YR | 2.395 |

USD | USD.CPI | InflationSwapRate.6YR | 2023-01-16 | 6YR | 2.418 |

USD | USD.CPI | InflationSwapRate.7YR | 2023-01-17 | 7YR | 2.431 |

USD | USD.CPI | InflationSwapRate.8YR | 2023-01-18 | 8YR | 2.442 |

USD | USD.CPI | InflationSwapRate.9YR | 2023-01-19 | 9YR | 2.456 |

**2. Inflation Curve Introduction**

Inflation curve or inflation forward curve is also called Consumer Price Index (CPI) curve that is the term structures of CPI rates is defined as the relationship between CPI and different terms. The popular indices are Euro HICP (HICPxT), UK RPI, and US CPI.

Inflation curves are used to price inflation securities and inflation derivatives, such as inflation linked bonds, inflation swaps and inflation caps/floors.

Inflation products are used to hedge inflation risk. For example, real estate companies may want to shed their exposure to inflation risk, while pension funds may want to cover their natural liabilities which are exposed to inflation.

Both investors illustrated above care about real income rather than nominal income, preferring to invest in securities guaranteeing them a real return as opposed to nominal one. The real yield on bond can be decomposed into a nominal yield and breakeven inflation yield component. The breakeven inflation gives the inflation rate that makes an investor indifferent between nominal and inflation-linked investments.

Inflation indexed bonds, also called inflation linked bonds or real return bonds, are bonds where the principal is indexed to inflation or deflation on a daily basis in terms of a reference index, such as Consumer Price Index (CPI)

Inflation swaps are bilateral contracts that enable an investor or hedger to secure an inflation-protected return with respect to an inflation index. The inflation buyer (also called the inflation receiver) pays a predetermined fixed or floating rate (usually minus a spread). In return, the inflation buyer receives from the inflation seller (also called the inflation payer) inflation-linked payment(s).

The zero-coupon inflation swap has become the standard inflation derivative. For many, it is the basic building block of the inflation derivatives market. Its appeal is its simplicity and the fact that it offers investors and hedgers a wide range of possibilities that did not previously exist in the cash market. Other inflation swaps are typically portfolios of zero-coupon swaps in one way or the other. In some cases, convexity adjustment may be needed.

**3. Inflation Curve Construction**

Inflation curves can be bootstrapped from liquid inflation instruments, such as inflation indexed bonds, zero coupon swaps, or inflation swaps.

Given inflation curves, pricing inflation products become straightforward. Also one can derive breakeven yields to maturity or breakeven inflation zero rates from the inflation curves. Futhermore, he can generate breakeven inflation swap rates.

4. Related Topics |