Circular No. 3850 — Procedure for Calculating the Interest Rate "Jm" Under Article 2 of Resolution No. 4,600 of September 25, 2017

CIRCULAR NO. 3,850, OF SEPTEMBER 26, 2017

Provides for the procedure for calculating the interest rate "Jm" referred to in Article 2 of Resolution No. 4,600, of September 25, 2017.

The Collegiate Board of the Central Bank of Brazil, in a session held on September 26, 2017, having regard to the provisions of Article 6 of Resolution No. 4,600, of September 25, 2017,

RESOLVES:

Article 1. The interest rate "Jm" referred to in Article 2 of Resolution No. 4,600, of September 25, 2017, shall be calculated based on the rates relative to the five-year term, assessed on each business day from the term structure of interest rates of the National Treasury Notes, Series B (NTNB) – TD, according to the following formula:

Jm = (∑ from i=1 to n of TDi) / n, where:

I - TDi corresponds to the i-th interest rate relative to the five-year term, assessed from the term structure of interest rates of the NTNB, available in the three months immediately preceding the day of assessment of the "Jm" rate, counted date to date, expressed in annual form, considering the convention of 252 business days, with two decimal places;

II - n corresponds to the number of business days with TD rates available in the three months immediately preceding the day of assessment of the "Jm" rate, counted date to date.

Sole Paragraph. The "Jm" rate shall be expressed in annual form, considering the convention of 252 business days, with two decimal places.

Article 2. The TD rates mentioned in item I of Article 1 shall be calculated from the term structure of interest rates of the NTNB to be estimated daily based on the following formula, as determined by Article 3 of Resolution No. 4,600, of 2017:

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, considering the convention of 252 business days.

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

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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 NTNB 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 NTNB that systematically does not present negotiations in the secondary market shall be excluded from the database.

§ 2. If a certain NTNB maturity does not present negotiation in the secondary market on the day or does not present a sufficient number of transactions that allows 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 NTNB of that maturity.

Article 4. For each NTNB maturity 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 following formula:

TMk = (∑ from j=1 to m of Fj x ij) / (∑ from j=1 to m of Fj), where:

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

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

III - m corresponds to the number of definitive operations with the k-th maturity of NTNB.

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 NTNB maturity that makes up the calculation base and the respective theoretical price.

§ 2. The average price of each NTNB maturity corresponds to the sum of its payments discounted by the average interest rate calculated according to Article 4.

§ 3. The theoretical price of each NTNB maturity 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 NTNB maturity shall be weighted by the inverse value of the measure of the duration of the title to which it refers.

§ 5. In the event of impossibility of estimating, for a given day, the parameters mentioned in the caput, including due to insufficient information, the parameters used on the immediately preceding business day shall be adopted in the calculation of the interest rate relative to the five-year term.

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Article 6. The Department of Open Market Operations (Demab) is authorized to adopt the measures deemed necessary for the execution of the provisions of this Circular.

Article 7. This Circular enters into force on the date of its publication.

Reinaldo Le Grazie
Monetary Policy Director

This text does not replace that published in the DOU of 9/28/2017, Section 1, p. 55, and in Sisbacen.