tf_quant_finance.rates.nelson_seigel_svensson.interpolate

Last updated: 2023-03-16.

tf_quant_finance.rates.nelson_seigel_svensson.interpolate#

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Performs Nelson Seigel Svensson interpolation for supplied points.

tf_quant_finance.rates.nelson_seigel_svensson.interpolate(
    interpolation_times, svensson_parameters, dtype=None, name=None
)

Given a set of interpolation times and the parameters for the nelson seigel svensson model, this function returns the interpolated values for the yield curve. We assume that the parameters are already computed using a fitting technique.

r(T) = beta_0 +
       beta_1 * (1-exp(-T/tau_1))/(T/tau_1) +
       beta_2 * ((1-exp(-T/tau_1))/(T/tau_1) - exp(-T/tau_1)) +
       beta_3 * ((1-exp(-T/tau_2))/(T/tau_2) - exp_(-T/tau_2))

Where T represents interpolation times and beta_i’s and tau_i’s are paramters for the model.

Example#

import tf_quant_finance as tff
interpolation_times = [5., 10., 15., 20.]
svensson_parameters =
tff.rates.nelson_svensson.interpolate.SvenssonParameters(
      beta_0=0.05, beta_1=-0.01, beta_2=0.3, beta_3=0.02,
      tau_1=1.5, tau_2=20.0)
result = interpolate(interpolation_times, svensson_parameters)
# Expected_result
# [0.12531, 0.09667, 0.08361, 0.07703]

References:#

[1]: Robert Müller. A technical note on the Svensson model as applied to the Swiss term structure. BIS Papers No 25, Mar 2015. https://www.bis.org/publ/bppdf/bispap25l.pdf

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.

  • svensson_parameters: An instance of SvenssonParameters. All parameters within should be real tensors.

  • dtype: Optional tf.dtype for interpolation_times. 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 ‘nelson_svensson_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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