fift_analytics.gilts.zero_coupon.curve_yield_extrapolation.derive_yield_from_zero_curve

fift_analytics.gilts.zero_coupon.curve_yield_extrapolation.derive_yield_from_zero_curve(zero_curve: list[tuple[int, float]], target_maturity: float) → float

Derive the implicit yield for a given maturity using a zero-coupon bond curve.

Formula:

\[y = y1 + ((t - t1) * (y2 - y1)) / (t2 - t1)\]

Interpolates between two maturities.

• for maturities less than 3 months, uses 3 months.

• for maturities greater than largest tenor point on the curve, it extrapolates.

Parameters:

• zero_curve (list) -- A list of tuples representing the zero-coupon bond curve. Each tuple contains (maturity_in_months, annual_yield). Example: [(3, 0.01), (6, 0.015), (12, 0.02), (18, 0.025)]

• target_maturity (float) -- The target maturity in months for which to derive the yield.

Returns:

The interpolated or extrapolated yield for the given maturity.

Return type:

float

Example:

>>> zero_curve = [(3, 0.01), (6, 0.015), (12, 0.02), (18, 0.025)]
>>> derive_yield_from_zero_curve(zero_curve, 9)
0.0175
>>> derive_yield_from_zero_curve(zero_curve, 2)
0.01
>>> derive_yield_from_zero_curve(zero_curve, 24)
0.03