## Introduction section Examples of calculations

### Examples of calculations

### EXAMPLE OF INDEXATION COEFFICIENT CALCULATION FOR BTP INDEXED TO EUROPEAN INFLATION

The BTP indexed to European inflation has, as its reference value, "the Harmonized Index of Consumer Prices in the euro area **(HICP)**, excluding tobacco". This index is published monthly on Eurostat's website, at the following address:

https://ec.europa.eu/eurostat/databrowser/view/teicp240/default/table?lang=en

To get the indexation coefficient, each day's reference index must be divided by the value taken at the base time, according to the following formula:

IC_{d,m} = Reference Index _{d,m} Base Index

If, for example, we want to calculate the reference index for **May 15th, 2022**, the payment date of the first coupon of the BTP indexed to European inflation (BTP€i) maturing on May 15th, 2033, the formula will be:

IC_{d,m} = 112.60097 107.78267 = 1.04470

#### Calculation of the reference index

For **May 15th, 2022**, the Eurostat indexes to be used for calculation are those for February and March 2022:

REFERENCE MONTH | EUROSTAT INDEX | |
---|---|---|

February 2022 | (m-3) three months before the month in which the calculation is made |
111.35 |

March 2022 | (m-2) two months before the month in which the calculation is made |
114.12 |

Although the reference index is the one of the coupon payment day (May 15th, 2022), the coupon interest accrual period is 14 days, because the coupon payment day (May 15th, 2022) corresponds to the first interest accrual day of the next coupon, exactly as is the case for other BTPs. This value is then divided by the total number of days in the month (in this case May) for which the calculation is made, namely **31**.

The reference index is then obtained from the following formula:

RI_{d,m} = EI_{m-3} + (*d*-1) gg * (EI_{m-2}- EI_{m-3})

That is:

RI_{d,m} = 111.35 + (15 - 1) 31 * (114.12-111.35) = 112.6009677

The index should be truncated to the sixth decimal place (112.600967) and rounded to the fifth digit (**112.60097**).

#### Calculation of the base index

For the BTP indexed to European inflation with maturity date as of May 15th, 2033 and a real coupon of 0.10% per annum, the base day is **November 15th, 2021**, the date of the bond's accrual. For the calculation of the base index, the Eurostat indices to be used are those for August and September 2021:

REFERENCE MONTH | EUROSTAT INDEX | |
---|---|---|

August 2021 | (m-3) three months before the month in which the calculation is made |
107.54 |

March 2022 | (m-2) two months before the month in which the calculation is made |
108.06 |

Proceeding with the same formula used to calculate the reference index we will have:

BI = 107.54 + (15 - 1) 30 * (108.06-107.54) = 107.78266666

Again, the index should be truncated to the sixth decimal place (107.782666) and rounded to the fifth digit (**107.78267**).

Example of calculation of the indexation coefficient related to each day of May 2022:

DATE | REFERENCE INDEX | BASE INDEX | INDEXATION COEFFICIENT |
---|---|---|---|

01/05/2022 | 111.35000 | 107.78267 | 1.03310 |

02/05/2022 | 111.43935 | 107.78267 | 1.03393 |

03/05/2022 | 111.52871 | 107.78267 | 1.03476 |

04/05/2022 | 111.61806 | 107.78267 | 1.03558 |

05/05/2022 | 111.70742 | 107.78267 | 1.03641 |

06/05/2022 | 111.79677 | 107.78267 | 1.03724 |

07/05/2022 | 111.88613 | 107.78267 | 1.03807 |

08/05/2022 | 111.97548 | 107.78267 | 1.03890 |

09/05/2022 | 112.06484 | 107.78267 | 1.03973 |

10/05/2022 | 112.15419 | 107.78267 | 1.04056 |

11/05/2022 | 112.24355 | 107.78267 | 1.04139 |

12/05/2022 | 112.33290 | 107.78267 | 1.04222 |

13/05/2022 | 112.42226 | 107.78267 | 1.04305 |

14/05/2022 | 112.51161 | 107.78267 | 1.04387 |

15/05/2022 | 112.60097 | 107.78267 | 1.04470 |

16/05/2022 | 112.69032 | 107.78267 | 1.04553 |

17/05/2022 | 112.77968 | 107.78267 | 1.04636 |

18/05/2022 | 112.86903 | 107.78267 | 1.04719 |

19/05/2022 | 112.95839 | 107.78267 | 1.04802 |

20/05/2022 | 113.04774 | 107.78267 | 1.04885 |

21/05/2022 | 113.13710 | 107.78267 | 1.04968 |

22/05/2022 | 113.22645 | 107.78267 | 1.05051 |

23/05/2022 | 113.31581 | 107.78267 | 1.05134 |

24/05/2022 | 113.40516 | 107.78267 | 1.05217 |

25/05/2022 | 113.49452 | 107.78267 | 1.05299 |

26/05/2022 | 113.58387 | 107.78267 | 1.05382 |

27/05/2022 | 113.67323 | 107.78267 | 1.05465 |

28/05/2022 | 113.76258 | 107.78267 | 1.05548 |

29/05/2022 | 113.85194 | 107.78267 | 1.05631 |

30/05/2022 | 113.94129 | 107.78267 | 1.05714 |

31/05/2022 | 114.03065 | 107.78267 | 1.05797 |

Daily values of the indexation coefficient are available on the website of the Department of Treasury-Public Debt at the following address:

https://www.dt.mef.gov.it/en/debito_pubblico/dati_statistici/coefficienti_di_indicizzazione_btpei/