Circular No. 3884 — Procedure for Calculating the NTNm Interest Rate under Article 4 of Resolution No. 4,645 of March 16, 2018

CIRCULAR No. 3,884, OF MARCH 22, 2018

Establishes the procedure for calculating the "NTNm" interest rate referred to in Article 4 of Resolution No. 4,645 of March 16, 2018.

The Collegiate Board of the Central Bank of Brazil, in a session held on March 22, 2018, based on Article 2 of Law No. 9,365 of December 16, 1996, and in view of the provisions of Resolution No. 4,645 of March 16, 2018,

RESOLVES:

Article 1. The "NTNm" rate referred to in Article 4 of Resolution No. 4,645 of March 16, 2018, shall be calculated based on the rates relative to the three-year term (TT) ascertained on each business day from the term structure of interest rates of the National Treasury Notes, Series B (NTN-B), according to the formula below, and expressed in annual form, in percentage terms, considering the convention of 252 business days, with two decimal places:

NTNm = (Σ TTi) / n, from i=1 to n, where:

I - TTi corresponds to the i-th interest rate relative to the three-year term ascertained on each business day from the term structure of interest rates of the NTN-B, available in the six months immediately preceding the day of calculation of the "NTNm" rate, counted date to date, expressed in annual form, in percentage terms, considering the convention of 252 business days, with two decimal places;

II - n corresponds to the number of business days with TT rates available in the six months immediately preceding the day of calculation of the "NTNm" rate, counted date to date.

Article 2. The TT rates mentioned in item I of Article 1 shall be calculated from the term structure of interest rates of the NTN-B to be estimated daily based on the following formula, as determined by Article 5 of Resolution No. 4,645 of 2018:

r(τ) = β0 + β1 ((1 - e^(-λ1τ)) / (λ1τ)) + β2 ((1 - e^(-λ1τ)) / (λ1τ) - e^(-λ1τ)) + β3 ((1 - e^(-λ2τ)) / (λ2τ) - e^(-λ2τ)), where:

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

II - β0, β1, β2, β3, λ1 and λ2 correspond to the parameters calculated from the methodology of minimization of errors generated in the estimation process referred to in Article 5;

III - r(τ) corresponds to the spot interest rate, with continuous compounding, relative to the term τ expressed in annual form, in percentage terms, considering the convention of 252 business days.

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

Article 3. The database for the estimation of the term structure of interest rates referred to in Article 2 shall be the definitive operations with NTN-B carried out in the secondary market, recorded in the Special Settlement and Custody System (SELIC), excluding operations that present discrepant rates, according to statistical treatment.

§ 1. The maturity of NTN-B that systematically does not present negotiations in the secondary market shall be excluded from the database.

§ 2. If a certain maturity of NTN-B does not present a sufficient number of transactions that allow the adequate estimation of its rate, an indicative interest rate that has broad acceptance as a price reference in the national financial market shall be used, for the NTN-B of that maturity.

Article 4. For each maturity of NTN-B that makes up the database referred to in Article 3, the average interest rate (TM) shall be calculated, on each business day, according to the formula below, expressed in annual form, in percentage terms, considering the convention of 252 business days:

TMk = (Σ Fj * ij) / (Σ Fj), from j=1 to n, where:

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

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

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

Article 5. The parameters β0, β1, β2, β3, λ1 and λ2 mentioned in Article 2 shall be calculated daily from the minimization of the mean of the squares of the estimation errors.

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

§ 2. The average price of each maturity of NTN-B corresponds to the sum of its payments discounted by the average interest rate calculated in accordance with Article 4.

§ 3. The theoretical price of each maturity of NTN-B 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 NTN-B shall be weighted by the inverse value of the measure of the duration of the security to which it refers.

§ 5. In the event of impossibility of estimation, for a given day, of the parameters mentioned in the caput, including due to insufficient information on negotiations in the secondary market and, simultaneously, absence of the indicative rates mentioned in § 2 of Article 3, the parameters used on the immediately preceding business day shall be adopted in the calculation of the interest rate relative to the three-year term.

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

Reinaldo Le Grazie
Director of Monetary Policy

This text does not replace the published in the DOU of 3/26/2018, Section 1, p. 27/28, republished in the DOU of 3/27/2018, Section 1, p. 31, and in Sisbacen.