def test_interpolated_yields_with_yields(self, interpolation_times,
reference_times, yields,
expected):
dtypes = [np.float32, np.float64]
for dtype in dtypes:
expected = np.array(expected, dtype=dtype)
actual = self.evaluate(
monotone_convex.interpolate_yields(interpolation_times,
reference_times,
yields=yields,
dtype=dtype))
np.testing.assert_allclose(actual, expected, rtol=1e-5)
def test_interpolated_yields_consistency(self):
dtypes = [np.float32, np.float64]
for dtype in dtypes:
reference_times = np.array([1.0, 2.0, 3.0, 4.0], dtype=dtype)
yields = np.array([5.0, 4.75, 4.53333333, 4.775], dtype=dtype)
# Times for which the interpolated values are required.
interpolation_times_1 = tf.constant([0.25, 0.5, 1.0, 2.0, 3.0],
dtype=dtype)
interpolation_times_2 = tf.constant([1.1, 2.5, 2.9, 3.6, 4.0],
dtype=dtype)
expected = np.array([
5.1171875, 5.09375, 5.0, 4.75, 4.533333, 4.9746, 4.624082,
4.535422, 4.661777, 4.775
],
dtype=dtype)
actual_1 = monotone_convex.interpolate_yields(
interpolation_times_1, reference_times, yields=yields)
actual_2 = monotone_convex.interpolate_yields(
interpolation_times_2, reference_times, yields=yields)
actual = self.evaluate(tf.concat([actual_1, actual_2], axis=0))
np.testing.assert_allclose(actual, expected, rtol=1e-5)
def _compute_pv(cashflows, cashflow_times, reference_rates, reference_times):
times = tf.concat(cashflow_times, axis=0)
groups = tf.concat([
tf.zeros_like(cashflow, dtype=tf.int32) + i
for i, cashflow in enumerate(cashflows)
],
axis=0)
rates = monotone_convex.interpolate_yields(times,
reference_times,
yields=reference_rates)
discounts = tf.math.exp(-times * rates)
cashflows = tf.concat(cashflows, axis=0)
return tf.math.segment_sum(discounts * cashflows, groups)
def test_interpolated_yields_zero_time(self):
"""Checks the interpolation for yield curve is non-NaN for 0 time."""
dtypes = [np.float32, np.float64]
for dtype in dtypes:
reference_times = np.array([0.3, 1.0, 1.43, 3.7, 9.2, 12.48], dtype=dtype)
yields = np.array([3.0, 3.1, 2.9, 4.1, 4.3, 5.1], dtype=dtype)
# Times for which the interpolated values are required.
interpolation_times = tf.constant([0.0], dtype=dtype)
actual = self.evaluate(
monotone_convex.interpolate_yields(
interpolation_times, reference_times, yields=yields))
np.testing.assert_allclose(actual, [0.0], rtol=1e-8)
def one_step(converged, failed, iteration, expiry_discounts):
"""One step of the iteration."""
expiry_rates = -tf.math.log(expiry_discounts) / expiry_times
failed = tf.math.reduce_any(
tf.math.is_nan(expiry_rates) | tf.math.is_nan(expiry_discounts))
calc_rates = monotone_convex.interpolate_yields(
calc_times, expiry_times, yields=expiry_rates)
calc_discounts = tf.math.exp(-calc_rates * calc_times)
next_expiry_discounts = -tf.math.segment_sum(
calc_bond_cashflows * calc_discounts,
calc_groups) / expiry_bond_cashflows
discount_diff = tf.math.abs(next_expiry_discounts - expiry_discounts)
converged = (~tf.math.reduce_any(tf.math.is_nan(discount_diff)) &
(tf.math.reduce_max(discount_diff) < discount_tolerance))
return converged, failed, iteration + 1, next_expiry_discounts
def test_interpolated_yields_flat_curve(self):
"""Checks the interpolation for flat curves."""
dtypes = [np.float32, np.float64]
for dtype in dtypes:
reference_times = np.array([0.3, 1.0, 1.43, 3.7, 9.2, 12.48], dtype=dtype)
yields = np.array([8.0] * 6, dtype=dtype)
# Times for which the interpolated values are required.
interpolation_times = tf.constant(
[0.1, 1.1, 1.22, 0.45, 1.8, 3.8, 7.45, 7.73, 9.6, 11.7, 12.],
dtype=dtype)
expected = np.array([8.0] * 11, dtype=dtype)
actual = self.evaluate(
monotone_convex.interpolate_yields(
interpolation_times, reference_times, yields=yields))
np.testing.assert_allclose(actual, expected, rtol=1e-5)
def test_interpolated_yields_with_discrete_forwards(self):
dtypes = [np.float32, np.float64]
for dtype in dtypes:
reference_times = tf.constant([1.0, 2.0, 3.0, 4.0], dtype=dtype)
discrete_forwards = tf.constant([5, 4.5, 4.1, 5.5], dtype=dtype)
test_times = tf.constant(
[0.25, 0.5, 1.0, 2.0, 3.0, 1.1, 2.5, 2.9, 3.6, 4.0], dtype=dtype)
expected = np.array([
5.1171875, 5.09375, 5.0, 4.75, 4.533333, 4.9746, 4.624082, 4.535422,
4.661777, 4.775
],
dtype=dtype)
actual = self.evaluate(
monotone_convex.interpolate_yields(
test_times, reference_times, discrete_forwards=discrete_forwards))
np.testing.assert_allclose(actual, expected, rtol=1e-5)
