Add CIR curve tests

frontend/src/yield-curve.md

@@ -13,7 +13,7 @@ import * as d3 from "npm:d3";
 ```
 
 ```js
-const curveType = view(Inputs.select(["nelson_siegel", "vasicek_curve"], {label: "Curve type"}));
+const curveType = view(Inputs.select(["nelson_siegel", "vasicek_curve", "cir_curve"], {label: "Curve type"}));
 ```
 
 ```js

quantflow/rates/cir.py

@@ -136,23 +136,28 @@ def jacobian(self, ttm: FloatArrayLike) -> FloatArray | None:
 
     @classmethod
     def calibrate(cls, ttm: ArrayLike, rates: ArrayLike) -> Self:
-        """Fit the CIR curve to continuously compounded rates via least squares."""
+        """Fit the CIR curve to continuously compounded rates via least squares.
+
+        The Feller condition is enforced by reparametrising sigma as
+        sigma = ratio * sqrt(2 * kappa * theta), with ratio in [0, 1].
+        """
         ttm_arr = np.asarray(ttm, dtype=float)
         rates_arr = np.asarray(rates, dtype=float)
 
         def residuals(params: np.ndarray) -> np.ndarray:
-            curve = cls(
-                rate=params[0], kappa=params[1], theta=params[2], sigma=params[3]
-            )
+            rate, kappa, theta, sigma_ratio = params
+            sigma = sigma_ratio * np.sqrt(2.0 * kappa * theta)
+            curve = cls(rate=rate, kappa=kappa, theta=theta, sigma=sigma)
             df = np.asarray(curve.discount_factor(ttm_arr), dtype=float)
             fitted = -np.log(df) / ttm_arr
             return fitted - rates_arr
 
-        x0 = np.array([rates_arr[0], 1.0, rates_arr[-1], 0.1])
+        x0 = np.array([rates_arr[0], 1.0, rates_arr[-1], 0.5])
         result = least_squares(
             residuals,
             x0,
-            bounds=([0.0, 1e-4, 0.0, 1e-4], [1.0, 50.0, 1.0, 2.0]),
+            bounds=([0.0, 1e-4, 1e-6, 1e-4], [1.0, 50.0, 1.0, 1.0]),
         )
-        r, k, th, s = result.x
+        r, k, th, sr = result.x
+        s = sr * np.sqrt(2.0 * k * th)
         return cls(rate=r, kappa=k, theta=th, sigma=s)

quantflow_tests/test_cir_curve.py

@@ -0,0 +1,88 @@
+from __future__ import annotations
+
+from decimal import Decimal
+
+import numpy as np
+import pytest
+
+from quantflow.rates.cir import CIRCurve
+
+
+def test_cir_process_mapping() -> None:
+    curve = CIRCurve(
+        rate=Decimal("0.03"),
+        kappa=Decimal("1.2"),
+        theta=Decimal("0.04"),
+        sigma=Decimal("0.1"),
+    )
+    process = curve.process()
+    assert process.rate == pytest.approx(0.03)
+    assert process.kappa == pytest.approx(1.2)
+    assert process.theta == pytest.approx(0.04)
+    assert process.sigma == pytest.approx(0.1)
+
+
+def test_cir_forward_and_discount_shapes() -> None:
+    curve = CIRCurve(
+        rate=Decimal("0.03"),
+        kappa=Decimal("0.8"),
+        theta=Decimal("0.05"),
+        sigma=Decimal("0.1"),
+    )
+    ttms = np.array([0.0, 0.5, 1.0, 2.0])
+    fwd = np.asarray(curve.instantaneous_forward_rate(ttms))
+    df = np.asarray(curve.discount_factor(ttms))
+    assert fwd.shape == ttms.shape
+    assert df.shape == ttms.shape
+    assert df[0] == pytest.approx(1.0)
+    assert df[-1] < df[1]
+
+
+def test_cir_forward_rate_at_zero() -> None:
+    curve = CIRCurve(
+        rate=Decimal("0.05"),
+        kappa=Decimal("1.0"),
+        theta=Decimal("0.04"),
+        sigma=Decimal("0.2"),
+    )
+    fwd = curve.instantaneous_forward_rate(0.0)
+    assert fwd == pytest.approx(0.05, rel=1e-6)
+
+
+def test_cir_calibrate_recovers_curve() -> None:
+    true_curve = CIRCurve(
+        rate=Decimal("0.03"),
+        kappa=Decimal("1.5"),
+        theta=Decimal("0.04"),
+        sigma=Decimal("0.06"),
+    )
+    ttm = np.array([0.25, 0.5, 1.0, 2.0, 3.0, 5.0], dtype=float)
+    rates = -np.log(np.asarray(true_curve.discount_factor(ttm))) / ttm
+    fitted = CIRCurve.calibrate(ttm, rates)
+    fitted_df = np.asarray(fitted.discount_factor(ttm))
+    true_df = np.asarray(true_curve.discount_factor(ttm))
+    np.testing.assert_allclose(fitted_df, true_df, atol=3e-3)
+
+
+def test_cir_calibrate_feller_condition() -> None:
+    """Calibration must always produce parameters satisfying the Feller condition."""
+    ttm = np.array([0.25, 0.5, 1.0, 2.0, 5.0, 10.0], dtype=float)
+    rates = np.array([0.05, 0.048, 0.045, 0.042, 0.040, 0.039], dtype=float)
+    fitted = CIRCurve.calibrate(ttm, rates)
+    process = fitted.process()
+    assert process.feller_condition >= 0.0
+    assert process.is_positive is True
+
+
+def test_cir_continuously_compounded_rate() -> None:
+    curve = CIRCurve(
+        rate=Decimal("0.04"),
+        kappa=Decimal("1.0"),
+        theta=Decimal("0.05"),
+        sigma=Decimal("0.15"),
+    )
+    ttm = np.array([1.0, 5.0, 10.0])
+    df = np.asarray(curve.discount_factor(ttm))
+    expected_rates = -np.log(df) / ttm
+    computed_rates = np.asarray(curve.continuously_compounded_rate(ttm))
+    np.testing.assert_allclose(computed_rates, expected_rates, rtol=1e-10)