Fix interpolated curves

Author: lsbardel

app/api/docs/yield_curve.md

@@ -1,13 +1,17 @@
 Fit a yield curve model to a set of (time-to-maturity, rate) pairs and return
 the calibrated curve plus interpolated rates.
 
-Four curve types are supported:
+Six curve types are supported:
 
-- **nelson_siegel**: the Nelson-Siegel parametric model, well suited for smooth
-  yield curves with a single hump. Good default choice.
+- **nelson_siegel_curve**: the Nelson-Siegel parametric model, well suited for
+  smooth yield curves with a single hump. Good default choice.
 - **cir_curve**: Cox-Ingersoll-Ross model, a mean-reverting short-rate model.
 - **vasicek_curve**: Vasicek model, a Gaussian mean-reverting short-rate model.
-- **no_discount**: flat discount curve (no discounting), useful as a baseline.
+- **interpolated_linear_curve**: piecewise linear interpolation of the zero rate
+  through the input maturities.
+- **interpolated_monotonic_cubic_curve**: shape-preserving monotone cubic (PCHIP)
+  interpolation of the zero rate.
+- **no_discount_curve**: flat discount curve (no discounting), useful as a baseline.
 
 Rates should be continuously compounded and expressed as decimals (e.g. 0.045 for 4.5%).
 Time to maturity is in years (e.g. 0.25 for 3 months, 2.0 for 2 years).

app/api/rates.py

@@ -31,7 +31,7 @@ async def yield_curve(
         ..., description="List of rates to fit the Nelson-Siegel model"
     ),
     curve_type: str = Query(
-        "nelson_siegel",
+        "nelson_siegel_curve",
         description="Type of curve to fit",
         enum=list(YieldCurve.curve_types()),
     ),

app/api/volatility.py

@@ -11,7 +11,7 @@
 from quantflow.options.inputs import VolSurfaceInputs
 from quantflow.options.surface import OptionInfo, VolSurfaceLoader
 from quantflow.rates.cir import CIRCurve
-from quantflow.rates.nelson_siegel import NelsonSiegel
+from quantflow.rates.nelson_siegel import NelsonSiegelCurve
 
 from .deps import RedisCache, RedisDep
 from .rates import YieldCurveResponse
@@ -86,13 +86,13 @@ async def _load_surface(asset: str) -> VolSurfaceLoader:
     if asset in DERIBIT_ASSETS:
         async with Deribit() as cli:
             loader = await cli.volatility_surface_loader(asset.lower(), inverse=True)
-        loader.calibrate_curves(quote_curve=CIRCurve, asset_curve=NelsonSiegel)
+        loader.calibrate_curves(quote_curve=CIRCurve, asset_curve=NelsonSiegelCurve)
         return loader
     else:
         async with Yahoo() as cli:
             loader = await cli.volatility_surface_loader(asset)
         loader.calibrate_spot()
-        loader.calibrate_curves(quote_curve=CIRCurve, asset_curve=NelsonSiegel)
+        loader.calibrate_curves(quote_curve=CIRCurve, asset_curve=NelsonSiegelCurve)
         return loader
 
 

docs/api/rates/index.md

@@ -12,9 +12,11 @@ The central concept is the [discount factor](../../glossary.md#discount-factor)
     f(\tau) = -\frac{\partial \ln D_\tau}{\partial \tau}
 \end{equation}
 
+**[Interpolated Curves](interpolated.md)** build the term structure directly from observed zero rates at a set of anchor dates. [InterpolatedLinearCurve][quantflow.rates.interpolated.InterpolatedLinearCurve] interpolates the zero rate piecewise linearly, while [InterpolatedMonotonicCubicCurve][quantflow.rates.interpolated.InterpolatedMonotonicCubicCurve] uses a shape-preserving cubic spline.
+
 **[CIRCurve](cir.md)** is a short-rate term-structure model derived from the Cox-Ingersoll-Ross process, with positive-rate dynamics and closed-form discount factors.
 
-**[NelsonSiegel](nelson_siegel.md)** is a concrete `YieldCurve` implementation that fits a smooth parametric curve to observed zero-coupon rates using the Nelson-Siegel functional form.
+**[NelsonSiegelCurve](nelson_siegel.md)** is a concrete `YieldCurve` implementation that fits a smooth parametric curve to observed zero-coupon rates using the Nelson-Siegel functional form.
 
 **[VasicekCurve](vasicek.md)** is a Gaussian mean-reverting short-rate model with analytical formulas for discount factors and instantaneous forward rates.
 

docs/api/rates/interpolated.md

@@ -0,0 +1,17 @@
+# Interpolated Curves
+
+Interpolated curves build the term structure directly from observed continuously compounded zero rates at a set of anchor dates, interpolating between them rather than fitting a parametric form.
+
+The [InterpolatedYieldCurve][quantflow.rates.interpolated.InterpolatedYieldCurve] base class holds the interpolation nodes and derives the discount factor and instantaneous forward rate from the interpolated zero rate. Subclasses choose how the zero rate is interpolated between nodes.
+
+[InterpolatedLinearCurve][quantflow.rates.interpolated.InterpolatedLinearCurve] interpolates the zero rate piecewise linearly, giving a forward rate that is linear on each segment.
+
+[InterpolatedMonotonicCubicCurve][quantflow.rates.interpolated.InterpolatedMonotonicCubicCurve] uses a shape-preserving PCHIP cubic spline, giving a smooth zero rate and forward rate that introduces no spurious local extrema between nodes.
+
+::: quantflow.rates.interpolated.InterpolatedYieldCurve
+
+::: quantflow.rates.interpolated.InterpolatedLinearCurve
+
+::: quantflow.rates.interpolated.InterpolatedMonotonicCubicCurve
+
+::: quantflow.rates.interpolated.InterpolatedYieldCurveCalibration

docs/api/rates/nelson_siegel.md

@@ -1,5 +1,5 @@
 # Nelson Siegel Curve
 
-::: quantflow.rates.nelson_siegel.NelsonSiegel
+::: quantflow.rates.nelson_siegel.NelsonSiegelCurve
 
 ::: quantflow.rates.nelson_siegel.NelsonSiegelCalibration

docs/api/rates/yield_curve.md

@@ -4,4 +4,4 @@
 ::: quantflow.rates.yield_curve.YieldCurve
 
 
-::: quantflow.rates.no_discount.NoDiscount
+::: quantflow.rates.no_discount.NoDiscountCurve

docs/examples/fixtures/volsurface_btc.json

@@ -2,11 +2,11 @@
   "asset": "btc",
   "asset_curve": {
     "ref_date": "2026-05-21T10:04:10.269985Z",
-    "curve_type": "no_discount"
+    "curve_type": "no_discount_curve"
   },
   "quote_curve": {
     "ref_date": "2026-05-21T10:04:10.269985Z",
-    "curve_type": "nelson_siegel",
+    "curve_type": "nelson_siegel_curve",
     "beta1": "-1.3242608183",
     "beta2": "1.3324170039",
     "beta3": "1.6559934427",

docs/examples/fixtures/volsurface_eth.json

@@ -2,11 +2,11 @@
   "asset": "eth",
   "asset_curve": {
     "ref_date": "2026-05-21T10:08:42.397057Z",
-    "curve_type": "no_discount"
+    "curve_type": "no_discount_curve"
   },
   "quote_curve": {
     "ref_date": "2026-05-21T10:08:42.397057Z",
-    "curve_type": "nelson_siegel",
+    "curve_type": "nelson_siegel_curve",
     "beta1": "0.0430852145",
     "beta2": "-0.0189909065",
     "beta3": "-0.0679762918",

docs/theory/forwards.md

@@ -8,7 +8,7 @@ one unit of currency delivered at time $\tau$.
 In quantflow, discount factors are provided by a
 [YieldCurve][quantflow.rates.yield_curve.YieldCurve]. Different implementations capture
 different term structures: a flat zero-rate curve, a fitted
-[Nelson-Siegel][quantflow.rates.nelson_siegel.NelsonSiegel] curve, or any custom term
+[Nelson-Siegel][quantflow.rates.nelson_siegel.NelsonSiegelCurve] curve, or any custom term
 structure.
 
 ## Forward Price