Curves

Discount curve construction and interpolation. All curve objects are equinox.Module pytrees — fully differentiable for key-rate duration computation.

DiscountCurve

class DiscountCurve(eqx.Module):
    pillar_dates: Int[Array, "n_pillars"]       # sorted ordinal dates
    discount_factors: Float[Array, "n_pillars"] # DF at each pillar
    reference_date: Int[Array, ""]              # valuation date
    day_count: str = "act_365"                  # static field

Fields:

Field	Type	Static	Description
pillar_dates	Int[Array, "n"]	No	Ordinal dates for curve nodes, sorted ascending.
discount_factors	Float[Array, "n"]	No	Discount factors at each pillar. First should be 1.0. Differentiable.
reference_date	Int[Array, ""]	No	Valuation date as ordinal.
day_count	str	Yes	Day count convention name.

Interpolation: Log-linear (linear in log-DF space), equivalent to piecewise-constant continuously-compounded forward rates. Flat extrapolation beyond curve range.

Usage:

# Callable — interpolate at arbitrary dates
df = curve(date)           # single date
dfs = curve(date_array)    # vectorized

Differentiability

discount_factors are differentiable leaves. jax.grad through any function that uses a DiscountCurve gives sensitivities to each pillar — this is how key-rate durations work.

forward_rate

forward_rate(curve, start, end) -> Float[Array, ""]

Simply-compounded forward rate between two ordinal dates:

\[F(t_1, t_2) = \frac{DF(t_1)/DF(t_2) - 1}{\tau(t_1, t_2)}\]

zero_rate

zero_rate(curve, date) -> Float[Array, ""]

Continuously-compounded zero rate to a given date:

\[r(t) = -\frac{\ln DF(t)}{\tau(\text{ref}, t)}\]