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NTN-B1

CommercialName

Bases: Enum

Commercial Name Enum used to identify the kind of used NTN-B1 in the scope of the calculation (Renda+ or Educa+).

cash_flows(settlement, maturity, commercial_name)

Generate the cash flows for NTN-B1 bonds between the settlement and maturity dates.

Parameters:

Name Type Description Default
settlement DateScalar

The settlement date (exclusive) to start generating the cash flows.

 required
maturity DateScalar

The maturity date of the bond.

 required
commercial_name CommercialName

The commercial name of the NTN-B1 bond (Renda+ or Educa+).

 required

Returns:

Type Description
DataFrame

pd.DataFrame: DataFrame with columns "PaymentDate" and "CashFlow".
Returned columns
  • PaymentDate: The payment date of the cash flow
  • CashFlow: Cash flow value for the bond

Examples:

>>> from pyield import ntnb1
>>> r_mais = ntnb1.CommercialName.RENDA_MAIS
>>> ntnb1.cash_flows("10-05-2024", "15-12-2060", r_mais)
shape: (240, 2)
┌─────────────┬──────────┐
│ PaymentDate ┆ CashFlow │
│ ---         ┆ ---      │
│ date        ┆ f64      │
╞═════════════╪══════════╡
│ 2041-01-15  ┆ 0.004167 │
│ 2041-02-15  ┆ 0.004167 │
│ 2041-03-15  ┆ 0.004167 │
│ 2041-04-15  ┆ 0.004167 │
│ 2041-05-15  ┆ 0.004167 │
│ …           ┆ …        │
│ 2060-08-15  ┆ 0.004167 │
│ 2060-09-15  ┆ 0.004167 │
│ 2060-10-15  ┆ 0.004167 │
│ 2060-11-15  ┆ 0.004167 │
│ 2060-12-15  ┆ 0.004167 │
└─────────────┴──────────┘
Source code in pyield/tn/ntnb1.py 
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def cash_flows(
    settlement: DateLike, maturity: DateLike, commercial_name: CommercialName
) -> pl.DataFrame:
    """
    Generate the cash flows for NTN-B1 bonds between the settlement and maturity dates.

    Args:
        settlement (DateScalar): The settlement date (exclusive) to start generating
            the cash flows.
        maturity (DateScalar): The maturity date of the bond.
        commercial_name (CommercialName): The commercial name of the NTN-B1 bond
            (Renda+ or Educa+).

    Returns:
        pd.DataFrame: DataFrame with columns "PaymentDate" and "CashFlow".

    Returned columns:
        - PaymentDate: The payment date of the cash flow
        - CashFlow: Cash flow value for the bond

    Examples:
        >>> from pyield import ntnb1
        >>> r_mais = ntnb1.CommercialName.RENDA_MAIS
        >>> ntnb1.cash_flows("10-05-2024", "15-12-2060", r_mais)
        shape: (240, 2)
        ┌─────────────┬──────────┐
        │ PaymentDate ┆ CashFlow │
        │ ---         ┆ ---      │
        │ date        ┆ f64      │
        ╞═════════════╪══════════╡
        │ 2041-01-15  ┆ 0.004167 │
        │ 2041-02-15  ┆ 0.004167 │
        │ 2041-03-15  ┆ 0.004167 │
        │ 2041-04-15  ┆ 0.004167 │
        │ 2041-05-15  ┆ 0.004167 │
        │ …           ┆ …        │
        │ 2060-08-15  ┆ 0.004167 │
        │ 2060-09-15  ┆ 0.004167 │
        │ 2060-10-15  ┆ 0.004167 │
        │ 2060-11-15  ┆ 0.004167 │
        │ 2060-12-15  ┆ 0.004167 │
        └─────────────┴──────────┘

    """
    if has_nullable_args(settlement, maturity, commercial_name):
        return pl.DataFrame({"PaymentDate": [], "CashFlow": []})

    # Validate and normalize dates
    settlement = cv.convert_dates(settlement)
    maturity = cv.convert_dates(maturity)

    # Get the coupon dates between the settlement and maturity dates
    p_dates = payment_dates(settlement, maturity, commercial_name)
    df = pl.DataFrame({"PaymentDate": p_dates})

    # Get bond parameters
    amort_payment, final_amort_payment, _ = _get_bond_parameters(commercial_name)

    # Set the cash flow at maturity to FINAL_PMT and the others to COUPON_PMT
    df = df.with_columns(
        pl.when(pl.col("PaymentDate") == maturity)
        .then(final_amort_payment)
        .otherwise(amort_payment)
        .alias("CashFlow")
    )

    # Return a dataframe with the payment dates and cash flows
    return df

duration(settlement, maturity, rate, commercial_name)

Calculate the Macaulay duration of the NTN-B bond in business years.

Parameters:

Name Type Description Default
settlement DateScalar

The settlement date of the operation.

 required
maturity DateScalar

The maturity date of the NTN-B bond.

 required
rate float

The discount rate used to calculate the duration.

 required
commercial_name CommercialName

The commercial name of the NTN-B1 bond (Renda+ or Educa+).

 required

Returns:

Name Type Description
float float

The Macaulay duration of the NTN-B bond in business years.

Examples:

>>> from pyield import ntnb1
>>> r_mais = ntnb1.CommercialName.RENDA_MAIS
>>> ntnb1.duration("23-06-2025", "15-12-2084", 0.0686, r_mais)
47.10493458167134
Source code in pyield/tn/ntnb1.py 
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def duration(
    settlement: DateLike,
    maturity: DateLike,
    rate: float,
    commercial_name: CommercialName,
) -> float:
    """
    Calculate the Macaulay duration of the NTN-B bond in business years.

    Args:
        settlement (DateScalar): The settlement date of the operation.
        maturity (DateScalar): The maturity date of the NTN-B bond.
        rate (float): The discount rate used to calculate the duration.
        commercial_name (CommercialName): The commercial name of the NTN-B1 bond
            (Renda+ or Educa+).

    Returns:
        float: The Macaulay duration of the NTN-B bond in business years.

    Examples:
        >>> from pyield import ntnb1
        >>> r_mais = ntnb1.CommercialName.RENDA_MAIS
        >>> ntnb1.duration("23-06-2025", "15-12-2084", 0.0686, r_mais)
        47.10493458167134
    """
    # Return NaN if any input is nullable
    if has_nullable_args(settlement, maturity, rate, commercial_name):
        return float("nan")

    df = cash_flows(settlement, maturity, commercial_name)
    s_byears = bday.count(settlement, df["PaymentDate"]) / 252
    s_dcf = df["CashFlow"] / (1 + rate) ** s_byears
    duration = (s_dcf * s_byears).sum() / s_dcf.sum()

    # Truncate duration to 14 decimal places for result reproducibility
    return bt.truncate(duration, 14)

dv01(settlement, maturity, rate, vna, commercial_name=CommercialName.RENDA_MAIS)

Calculate the DV01 (Dollar Value of 01) for an NTN-B1 in R$.

Represents the price change in R$ for a 1 basis point (0.01%) increase in yield.

Parameters:

Name Type Description Default
settlement DateScalar

The settlement date in 'DD-MM-YYYY' format or a pandas Timestamp.

 required
maturity DateScalar

The maturity date in 'DD-MM-YYYY' format or a pandas Timestamp.

 required
rate float

The discount rate used to calculate the present value of the cash flows, which is the yield to maturity (YTM) of the NTN-B.

 required
vna float

The nominal value of the NTN-B bond.

 required
commercial_name CommercialName

The commercial name of the NTN-B1 bond

 RENDA_MAIS

Returns:

Name Type Description
float float

The DV01 value, representing the price change for a 1 basis point increase in yield.

Examples:

>>> from pyield import ntnb1
>>> r_mais = ntnb1.CommercialName.RENDA_MAIS
>>> ntnb1.dv01("23-06-2025", "15-12-2084", 0.0686, 4299.160173, r_mais)
0.7738490000000127
Source code in pyield/tn/ntnb1.py 
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def dv01(
    settlement: DateLike,
    maturity: DateLike,
    rate: float,
    vna: float,
    commercial_name: CommercialName = CommercialName.RENDA_MAIS,
) -> float:
    """
    Calculate the DV01 (Dollar Value of 01) for an NTN-B1 in R$.

    Represents the price change in R$ for a 1 basis point (0.01%) increase in yield.

    Args:
        settlement (DateScalar): The settlement date in 'DD-MM-YYYY' format
            or a pandas Timestamp.
        maturity (DateScalar): The maturity date in 'DD-MM-YYYY' format or
            a pandas Timestamp.
        rate (float): The discount rate used to calculate the present value of
            the cash flows, which is the yield to maturity (YTM) of the NTN-B.
        vna (float): The nominal value of the NTN-B bond.
        commercial_name (CommercialName): The commercial name of the NTN-B1 bond

    Returns:
        float: The DV01 value, representing the price change for a 1 basis point
            increase in yield.

    Examples:
        >>> from pyield import ntnb1
        >>> r_mais = ntnb1.CommercialName.RENDA_MAIS
        >>> ntnb1.dv01("23-06-2025", "15-12-2084", 0.0686, 4299.160173, r_mais)
        0.7738490000000127
    """
    if has_nullable_args(settlement, maturity, rate, vna, commercial_name):
        return float("nan")

    quotation1 = quotation(settlement, maturity, rate, commercial_name)
    quotation2 = quotation(settlement, maturity, rate + 0.0001, commercial_name)
    price1 = price(vna, quotation1)
    price2 = price(vna, quotation2)
    return price1 - price2

payment_dates(settlement, maturity, commercial_name)

Generate all remaining amortization dates between a given date and the maturity date. The dates are inclusive. Payments are made from January 15th of the year of conversion to December 15 of maturity year.

Parameters:

Name Type Description Default
settlement DateLike

The settlement date (exclusive) to start generating the amortization dates.

 required
maturity DateLike

The maturity date.

 required
commercial_name CommercialName

The commercial name of the NTN-B1 bond (Renda+ or Educa+).

 required

Returns:

Type Description
Series

pl.Series: Series of coupon dates within the specified range.

Examples:

>>> from pyield import ntnb1
>>> r_mais = ntnb1.CommercialName.RENDA_MAIS
>>> ntnb1.payment_dates("10-05-2024", "15-12-2050", r_mais)
shape: (240,)
Series: 'payment_dates' [date]
[
    2031-01-15
    2031-02-15
    2031-03-15
    2031-04-15
    2031-05-15
    …
    2050-08-15
    2050-09-15
    2050-10-15
    2050-11-15
    2050-12-15
]
Source code in pyield/tn/ntnb1.py 
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def payment_dates(
    settlement: DateLike, maturity: DateLike, commercial_name: CommercialName
) -> pl.Series:
    """
    Generate all remaining amortization dates between a given date and the maturity
    date.
    The dates are inclusive. Payments are made from January 15th of the year of
    conversion to December 15 of maturity year.

    Args:
        settlement (DateLike): The settlement date (exclusive) to start generating
            the amortization dates.
        maturity (DateLike): The maturity date.
        commercial_name (CommercialName): The commercial name of the NTN-B1 bond
            (Renda+ or Educa+).

    Returns:
        pl.Series: Series of coupon dates within the specified range.

    Examples:
        >>> from pyield import ntnb1
        >>> r_mais = ntnb1.CommercialName.RENDA_MAIS
        >>> ntnb1.payment_dates("10-05-2024", "15-12-2050", r_mais)
        shape: (240,)
        Series: 'payment_dates' [date]
        [
            2031-01-15
            2031-02-15
            2031-03-15
            2031-04-15
            2031-05-15
            …
            2050-08-15
            2050-09-15
            2050-10-15
            2050-11-15
            2050-12-15
        ]
    """
    if has_nullable_args(settlement, maturity, commercial_name):
        return pl.Series("payment_dates", dtype=pl.Date)

    # Validate and normalize dates
    settlement = cv.convert_dates(settlement)
    maturity = cv.convert_dates(maturity)

    if maturity <= settlement:
        raise ValueError("Maturity date must be after the settlement date.")

    maturity = maturity.replace(day=15)

    # Get bond parameters
    _, _, n_amortizations = _get_bond_parameters(commercial_name)

    amtz_dates = [maturity - pd.DateOffset(months=i) for i in range(n_amortizations)]

    if len(amtz_dates) == 0:
        raise ValueError("No amortization dates found after settlement date.")

    pmt_dates = pl.Series(name="payment_dates", values=amtz_dates).cast(pl.Date)

    return pmt_dates.filter(pmt_dates > settlement).sort()

price(vna, quotation)

Calculate the NTN-B1 price using Brazilian Treasury rules.

Parameters:

Name Type Description Default
vna float

The nominal value of the NTN-B bond.

 required
quotation float

The NTN-B quotation in base 100.

 required

Returns:

Name Type Description
float float

The NTN-B1 price truncated to 6 decimal places.
References
  • SEI Proccess 17944.005214/2024-09

Examples:

>>> from pyield import ntnb1
>>> ntnb1.price(4299.160173, 99.3651 / 100)
4271.864805
>>> ntnb1.price(4315.498383, 100.6409 / 100)
4343.156412
Source code in pyield/tn/ntnb1.py 
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def price(
    vna: float,
    quotation: float,
) -> float:
    """
    Calculate the NTN-B1 price using Brazilian Treasury rules.

    Args:
        vna (float): The nominal value of the NTN-B bond.
        quotation (float): The NTN-B quotation in base 100.

    Returns:
        float: The NTN-B1 price truncated to 6 decimal places.

    References:
         - SEI Proccess 17944.005214/2024-09

    Examples:
        >>> from pyield import ntnb1
        >>> ntnb1.price(4299.160173, 99.3651 / 100)
        4271.864805
        >>> ntnb1.price(4315.498383, 100.6409 / 100)
        4343.156412
    """
    if has_nullable_args(vna, quotation):
        return float("nan")
    return bt.truncate(vna * quotation, 6)

quotation(settlement, maturity, rate, commercial_name)

Calculate the NTN-B quotation in base 100 using Anbima rules.

Parameters:

Name Type Description Default
settlement DateScalar

The settlement date of the operation.

 required
maturity DateScalar

The maturity date of the NTN-B bond.

 required
rate float

The discount rate used to calculate the present value of the cash flows, which is the yield to maturity (YTM) of the NTN-B.

 required
commercial_name CommercialName

The commercial name of the NTN-B1 bond (Renda+ or Educa+).

 required

Returns:

Name Type Description
float float

The NTN-B quotation truncated to 6 decimal places.
References
  • https://www.anbima.com.br/data/files/A0/02/CC/70/8FEFC8104606BDC8B82BA2A8/Metodologias%20ANBIMA%20de%20Precificacao%20Titulos%20Publicos.pdf

Examples:

>>> from pyield import ntnb1
>>> r_mais = ntnb1.CommercialName.RENDA_MAIS
>>> ntnb1.quotation("18-06-2025", "15-12-2084", 0.07010, r_mais)
0.038332
Source code in pyield/tn/ntnb1.py 
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def quotation(
    settlement: DateLike,
    maturity: DateLike,
    rate: float,
    commercial_name: CommercialName,
) -> float:
    """
    Calculate the NTN-B quotation in base 100 using Anbima rules.

    Args:
        settlement (DateScalar): The settlement date of the operation.
        maturity (DateScalar): The maturity date of the NTN-B bond.
        rate (float): The discount rate used to calculate the present value of
            the cash flows, which is the yield to maturity (YTM) of the NTN-B.
        commercial_name (CommercialName): The commercial name of the NTN-B1 bond
            (Renda+ or Educa+).

    Returns:
        float: The NTN-B quotation truncated to 6 decimal places.

    References:
        - https://www.anbima.com.br/data/files/A0/02/CC/70/8FEFC8104606BDC8B82BA2A8/Metodologias%20ANBIMA%20de%20Precificacao%20Titulos%20Publicos.pdf

    Examples:
        >>> from pyield import ntnb1
        >>> r_mais = ntnb1.CommercialName.RENDA_MAIS
        >>> ntnb1.quotation("18-06-2025", "15-12-2084", 0.07010, r_mais)
        0.038332
    """
    if has_nullable_args(settlement, maturity, rate, commercial_name):
        return float("nan")

    cf_df = cash_flows(settlement, maturity, commercial_name)
    cf_dates = cf_df["PaymentDate"]
    cf_values = cf_df["CashFlow"]

    # Calculate the number of business days between settlement and cash flow dates
    b_days = bday.count(settlement, cf_dates)

    # Calculate the number of periods truncated as per Anbima rules
    num_of_years = bt.truncate(b_days / 252, 14)

    discount_factor = (1 + rate) ** num_of_years

    # Calculate the present value of each cash flow (DCF) rounded as per Anbima rules
    cf_present_value = (cf_values / discount_factor).round(10)

    # Return the quotation (the dcf sum) truncated as per Anbima rules
    return bt.truncate(cf_present_value.sum(), 6)