tf_quant_finance.rates.constant_fwd.interpolate

Last updated: 2023-03-16.

tf_quant_finance.rates.constant_fwd.interpolate#

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Performs the constant forward interpolation for supplied points.

tf_quant_finance.rates.constant_fwd.interpolate(
    interpolation_times, reference_times, reference_yields, dtype=None, name=None
)

Given an interest rate yield curve whose maturities and the corresponding (continuously compounded) yields are in reference_times and reference_yields, this function returns interpolated yields at interpolation_times using the constant forward interpolation.

Let t_i, i=1,...,n and y_i, i=1,...,n denote the reference_times and reference_yields respectively. If t is a maturity for which the interpolation is desired such that t_{i-1} <= t <= t_i, then constant forward interpolation produces the corresponding yield, y_t, such that the forward rate in the interval [t_{i-1},t] is the same as the forward rate in the interval [t_{i-1},t_i]. Mathematically, this is the same as linearly interpolating t*y_t using the curve t_i, t_i*y_i.

reference_times must be strictly increasing but reference_yields don’t need to be because we don’t require the rate curve to be monotonic.

Examples#

interpolation_times = [1, 3, 6, 7, 8, 15, 18, 25, 30]
# `reference_times` must be increasing, but `reference_yields` don't need to
# be.
reference_times = [0.0, 2.0, 6.0, 8.0, 18.0, 30.0]
reference_yields = [0.01, 0.02, 0.015, 0.014, 0.02, 0.025]
result = interpolate(interpolation_times, reference_times, reference_yields)

Args:#

  • interpolation_times: The times at which interpolation is desired. A N-D Tensor of real dtype where the first N-1 dimensions represent the batching dimensions.

  • reference_times: Maturities in the input yield curve. A N-D Tensor of real dtype where the first N-1 dimensions represent the batching dimensions. Should be sorted in increasing order.

  • reference_yields: Continuously compounded yields corresponding to reference_times. A N-D Tensor of real dtype. Should have the compatible shape as x_data.

  • dtype: Optional tf.dtype for interpolation_times, reference_times, and reference_yields`. If not specified, the dtype of the inputs will be used.

  • name: Python str. The name prefixed to the ops created by this function. If not supplied, the default name ‘constant_fwd_interpolation’ is used.

Returns:#

A N-D Tensor of real dtype with the same shape as interpolations_times containing the interpolated yields.

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