Zero Coupon Gilts Pricers#

Zero Coupon Bond Pricers#

This section describes both public and private API for fift_analytics zero coupon bond pricers.

All methods and functions described within this section are used to re-evaluate zero coupon bond prices.

fift_analytics.gilts.zero_coupon.zc_pricers.get_zero_coupon_gilt_price(face_value: float, annual_yield: float, maturity_date: str, settlement_date: str | None = None) → float#

Calculate the theoretical price of a zero-coupon gilt using continuous compounding.

Parameters:

  • face_value (float) -- The face value (maturity value) of the bond.

  • annual_yield (float) -- The annual yield to maturity as a decimal (e.g., 0.04 for 4% or -0.01 for -1%).

  • maturity_date (str) -- The maturity date of the bond in 'YYYY-MM-DD' format.

  • settlement_date (Optional[str]) -- The settlement date in 'YYYY-MM-DD' format. Defaults to today if not provided.

Raises:

ValueError -- If inputs are invalid (e.g., negative face value or invalid dates).

Returns:

The theoretical price of the zero-coupon gilt rounded to 2 decimal places.

Return type:

float

Example:
>>> face_value = 1000  # £1,000 face value
>>> annual_yield = -0.01  # -1% annual yield
>>> maturity_date = "2025-02-19"  # Maturity date: February 17, 2035
>>> settlement_date = "2025-02-16"  # Settlement date: February 17, 2025
>>> price = get_zero_coupon_gilt_price(face_value, annual_yield, maturity_date, settlement_date)
>>> print(f"The theoretical price of the zero-coupon gilt is: £{price:.2f}")
fift_analytics.gilts.zero_coupon.zc_pricers.validate_inputs(face_value: float, maturity_date: str, settlement_date: str | None) → None#

Validate input parameters for correctness.

Parameters:

  • face_value -- Face value of the bond.

  • maturity_date -- Maturity date in 'YYYY-MM-DD' format.

  • settlement_date -- Settlement date in 'YYYY-MM-DD' format or None.

Raises:

ValueError -- If any input is invalid (e.g., negative face value or invalid dates).

fift_analytics.gilts.zero_coupon.zc_pricers.parse_settlement_date(settlement_date: str | None) → datetime#

Parse and return the settlement date. Defaults to today if not provided.

Parameters:

settlement_date -- Settlement date in 'YYYY-MM-DD' format or None.

Returns:

Settlement date as a datetime object.

fift_analytics.gilts.zero_coupon.zc_pricers.parse_maturity_date(maturity_date: str) → datetime#

Parse and return the maturity date.

Parameters:

maturity_date -- Maturity date in 'YYYY-MM-DD' format.

Returns:

Maturity date as a datetime object.

fift_analytics.gilts.zero_coupon.zc_pricers.calculate_time_to_maturity(settlement_date: datetime, maturity_date: datetime) → float#

Calculate time to maturity in years using Actual/Actual (ISMA) day count convention.

Parameters:

  • settlement_date -- Settlement date as a datetime object.

  • maturity_date -- Maturity date as a datetime object.

Returns:

Time to maturity in years.

Raises:

ValueError -- If the maturity date is earlier than or equal to the settlement date.

fift_analytics.gilts.zero_coupon.zc_pricers.is_leap_year(year: int) → bool#

Check if a given year is a leap year.

Parameters:

year -- Year to check.

Returns:

True if leap year, False otherwise.

fift_analytics.gilts.zero_coupon.zc_pricers.compute_continuous_price(face_value: float, annual_yield: float, time_to_maturity: float) → float#

Compute the price of a zero-coupon gilt using continuous compounding.

Parameters:

  • face_value (float) -- Face value of the bond.

  • annual_yield (float) -- Annual yield to maturity as a decimal (e.g., 0.04 for 4% or -0.01 for -1%).

  • time_to_maturity (float) -- Time to maturity in years.

Returns:

The price of the zero-coupon gilt rounded to 2 decimal places.

Return type:

float

Calculation Steps:

  • If time_to_maturity is very small (approaching zero), return face value directly.

  • Compute intermediate result using the continuous compounding formula: P = F * exp(-r * t)

  • Round intermediate result to six decimal places for precision.

  • Round final result to two decimal places for financial reporting standards.

Example:
>>> compute_continuous_price(1000, -0.01, 10)
1051.27