Spread Analytics

Compute interpolated swap spreads (I-spread) and asset swap spreads for bonds against calibrated curves. These measures quantify a bond's yield premium over the reference swap curve.

Setup

Create a 5-year fixed-rate bond and calibrate a discount curve for spread analysis. We also build a swap zero-rate curve (LineCurve) for I-spread computation.

import datetime
import math
from vade import (
    FixedRateBond, DiscountCurve, LineCurve, Deposit, IRS, Solver, AssetSwap,
)

effective = datetime.date(2025, 1, 15)
settlement = datetime.date(2025, 6, 16)

bond = FixedRateBond(
    effective=effective,
    termination="5y",
    coupon=0.045,
    frequency="s",
    settlement_days=1,
    convention="actactisda",
    face_value=100.0,
)

curve = DiscountCurve(
    {
        settlement: 1.0,
        datetime.date(2025, 9, 16): 1.0,
        datetime.date(2026, 6, 16): 1.0,
        datetime.date(2027, 6, 16): 1.0,
        datetime.date(2028, 6, 16): 1.0,
        datetime.date(2030, 6, 16): 1.0,
    },
    interpolation="log_linear",
    convention="act360",
    id="sofr",
)

dep = Deposit(effective=settlement, termination="3m", rate=0.0, convention="act360")
irs_1y = IRS(effective=settlement, termination="1y", frequency="a", fixed_rate=0.0, convention="act360", float_convention="act360")
irs_2y = IRS(effective=settlement, termination="2y", frequency="a", fixed_rate=0.0, convention="act360", float_convention="act360")
irs_3y = IRS(effective=settlement, termination="3y", frequency="a", fixed_rate=0.0, convention="act360", float_convention="act360")
irs_5y = IRS(effective=settlement, termination="5y", frequency="a", fixed_rate=0.0, convention="act360", float_convention="act360")

instruments = [
    (dep, 0.0440),
    (irs_1y, 4.20),
    (irs_2y, 4.10),
    (irs_3y, 4.00),
    (irs_5y, 3.90),
]

solver = Solver(curves=[curve], instruments=instruments)
result = solver.iterate()
assert result.converged

calibrated = solver.get_curve(0)

# Swap zero-rate curve for I-spread (interpolated swap rates)
swap_curve = LineCurve(
    {
        settlement: 0.044,
        datetime.date(2026, 6, 16): 0.042,
        datetime.date(2027, 6, 16): 0.041,
        datetime.date(2028, 6, 16): 0.040,
        datetime.date(2030, 6, 16): 0.039,
    },
    convention="act365f",
)

The I-spread (interpolated spread) is the difference between a bond's yield to maturity and the linearly interpolated swap rate at the bond's maturity. Unlike the Z-spread (which shifts the entire discount curve), the I-spread uses a single-point comparison against the swap curve.

See FixedRateBond.i_spread API reference.

i_sprd = bond.i_spread(settlement, swap_curve)

assert isinstance(i_sprd, float)
assert -0.05 < i_sprd < 0.05  # reasonable range

Asset Swap Spread

An asset swap packages a bond with an interest rate swap. The asset swap spread is the spread on the floating leg that makes the package NPV-neutral. It measures the bond's credit premium over the swap curve.

See AssetSwap API reference.

Par Asset Swap

A par asset swap assumes the bond trades at par. The spread compensates for the difference between the bond's fixed coupons and the swap curve.

par_asw = AssetSwap(bond=bond, asw_type="par")
par_spread = par_asw.rate(curves=calibrated)

assert isinstance(par_spread, float)
assert math.isfinite(par_spread)

Non-Par Asset Swap

A non-par (market value) asset swap uses the bond's actual dirty price rather than par. This adjusts the spread for the bond's premium or discount.

dirty = float(bond.dirty_price(calibrated, settlement=settlement))

non_par_asw = AssetSwap(bond=bond, asw_type="non_par", dirty_price=dirty)
non_par_spread = non_par_asw.rate(curves=calibrated)

assert isinstance(non_par_spread, float)
assert math.isfinite(non_par_spread)

Comparing Spread Measures

Different spread measures answer different questions. The Z-spread and I-spread use the bond's yield; asset swap spreads reflect the economics of a hedged position. Here they are side by side for the same bond.

clean = float(bond.price(calibrated, settlement=settlement))

z_sprd = float(bond.z_spread(calibrated, price=clean, settlement=settlement))
i_sprd_val = float(bond.i_spread(settlement, swap_curve))
asw_val = float(par_asw.rate(curves=calibrated))

assert isinstance(z_sprd, float)
assert isinstance(i_sprd_val, float)
assert isinstance(asw_val, float)

Next Steps

Callable Bonds -- Option-adjusted spread for bonds with embedded options
Bonds -- Core bond analytics and Z-spread