Zero-Coupon Curve

Calculates the zero-coupon (spot) yield curve of a country by bootstrapping its government bond par yields. A par yield is the coupon at which a bond trades at par, so it mixes the discount rates of every coupon date; the zero-coupon rate of a maturity is the single rate that discounts a payment at that date. Zero-coupon rates are what bonds and other cash flows are discounted with, and what forward rates and the curve models (Nelson-Siegel, Vasicek) are built on.

Maturities up to one year are treasury bills, which pay no coupon, so their yield only needs converting to annual compounding: US bill yields are bond-equivalent yields (simple interest up to half a year), Canadian bill yields simple interest on a 365-day year and Swedish bill yields simple interest on a 360-day year. Beyond that the par yields are interpolated linearly to every coupon date and each discount factor follows from the earlier ones:

P(t_n) = (1 - c/f Σ_{i<n} P(t_i)) / (1 + c/f)

with c the par yield of maturity t_n and f the coupons per year (two, and one for Sweden and Norway). The curves of the Euro Area and Germany are estimated as zero-coupon curves by the ECB and the Bundesbank, which publish them continuously compounded; they are converted to annual compounding like the others. A curve needs a maturity of a year or less to start from, so the United Kingdom, Norway and Australia (and Canada before its bill yields start) are not covered.

Also known as: spot curve, zero curve, bootstrapped curve, discount curve.

Zero-Coupon Curve in Python or via the MCP

Install the Finance Toolkit with:

pip install financetoolkit -U

Then call get_zero_coupon_curve as shown below.

from financetoolkit import FixedIncome

fixedincome = FixedIncome(start_date='2026-10-19', end_date='2026-10-23')

zero_curve = fixedincome.get_zero_coupon_curve()

zero_curve['United States'][['1Y', '2Y', '5Y', '10Y', '20Y', '30Y']]

Or, after setting up the Finance Toolkit MCP, ask:

Which returns:

Parameters

get_zero_coupon_curve accepts the following parameters.

Related Yield Curves