BCB Resolution No. 416 — Procedures for Calculating Fixed Rates “Pm” and “PMm”

BCB RESOLUTION NO. 416, OF SEPTEMBER 27, 2024

Provides for the procedures for calculating the fixed rates “Pm” and “PMm”, as provided for in Article 2 of CMN Resolution No. 5,180, of September 27, 2024.

The Collegiate Board of the Central Bank of Brazil, in an extraordinary session held on September 27, 2024, based on Article 3 of Law No. 13,483, of September 21, 2017,

R E S O L V E S:

Article 1. The fixed rates “Pm” and “PMm”, as provided for in Article 2 of CMN Resolution No. 5,180, of September 27, 2024, shall be calculated based, respectively, on the rates related to the five-year – TDP and three-year – TDPM terms, calculated every business day, from the term structure of interest rates of fixed-yield National Treasury bonds, National Treasury Letters – LTN and National Treasury Notes Series F – NTN-F, according to the formulas below, expressed in annual form, in percentage terms, considering the convention of 252 business days, with two decimal places:

I -

, where:

a) TDPi corresponds to the i-th interest rate related to the five-year term calculated every business day from the term structure of interest rates of fixed-yield National Treasury bonds, LTN and NTN-F, available in the three months immediately preceding the day of calculation of the “Pm” rate, counted from date to date, expressed in annual form, considering the convention of 252 business days, with two decimal places; and

b) n corresponds to the number of business days with TDP rates available in the three months immediately preceding the day of calculation of the “Pm” rate, counted from date to date; and

II -

, where:

a) TDPMi corresponds to the i-th interest rate related to the three-year term calculated every business day from the term structure of interest rates of fixed-yield National Treasury bonds, LTN and NTN-F, available in the three months immediately preceding the day of calculation of the “PMm” rate, counted from date to date, expressed in annual form, considering the convention of 252 business days, with two decimal places; and

b) n corresponds to the number of business days with TDPM rates available in the three months immediately preceding the day of calculation of the “PMm” rate, counted from date to date.

Article 2. The TDP and TDPM rates mentioned, respectively, in the main text and items I and II of Article 1, shall be calculated from the term structure of interest rates of LTN and NTN-F to be estimated daily based on the following formula:

, where:

I -

corresponds to the term, in years, considering the convention of 252 business days;

II -

,

,

,

,

and

correspond to the parameters calculated from a methodology for minimizing errors generated in the estimation process; and

III - corresponds to the spot interest rate, with continuous compounding, related to the term

expressed in annual form, considering the convention of 252 business days.

Sole Paragraph. For the purpose of calculating the interest rates referred to in the main text, conversion to the annual compounding regime shall be applied, considering the convention of 252 business days.

Article 3. For each maturity of LTN and NTN-F that makes up the database referred to in Article 3, the average interest rate – TM, shall be calculated every business day, according to the formula below, expressed in annual form, in percentage terms, considering the convention of 252 business days:

, where:

I - Fj corresponds to the financial amount of the j-th definitive operation of the k-th maturity of LTN and NTN-F;

II - ij corresponds to the interest rate of the j-th definitive operation of the k-th maturity of LTN and NTN-F, expressed in annual form, in percentage terms, considering the convention of 252 business days; and

III - n corresponds to the number of definitive operations with the k-th maturity of LTN and NTN-F.

Article 4. The parameters

,

,

,

and

mentioned in Article 2 shall be calculated daily from the minimization of the mean of the squared estimation errors.

§ 1. The estimation errors consist of the difference between the average price of each maturity of LTN and NTN-F that makes up the calculation base and the respective theoretical price.

§ 2. The average price of each maturity of LTN and NTN-F corresponds to the sum of its payments discounted by the average interest rate calculated according to Article 3.

§ 3. The theoretical price of each maturity of LTN and NTN-F corresponds to the sum of its payments discounted by the estimated interest rates according to the term structure of interest rates referred to in Article 2 for each payment term.

§ 4. The square of the estimation error of each maturity of LTN and NTN-F shall be weighted by the inverse value of the measure of the duration of the title to which it refers.

Article 5. The Open Market Operations Department – Demab shall adopt the necessary measures for the execution of the provisions of this Resolution.

Article 6. This Resolution enters into force on the date of its publication.

DIOGO ABRY GUILLEN
Substitute Director of Monetary Policy