.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/fixed_income/curves/plot_06_svensson.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_fixed_income_curves_plot_06_svensson.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_fixed_income_curves_plot_06_svensson.py:


Svensson
========

Lars Svensson (1994) added a second hump term to Nelson-Siegel, with its
own decay :math:`\tau_2`, to fit forward curves that bend twice. He built
it to estimate forward rates at the Swedish Riksbank, and central banks
still publish curves fitted with it. On such a curve, Nelson-Siegel
misses the second bend and Svensson does not.

.. GENERATED FROM PYTHON SOURCE LINES 13-27

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from financialkit.fixed_income import SvenssonCurve, fit_nelson_siegel, fit_svensson

    tenors = np.array([0.25, 0.5, 1, 2, 3, 4, 5, 7, 10, 12, 15, 20, 25, 30])
    true = SvenssonCurve(0.045, -0.02, -0.03, 0.045, 0.8, 7.0)
    rng = np.random.default_rng(1994)
    observed = true.zero_rate(tenors) + rng.normal(0, 0.0002, tenors.size)

    ns = fit_nelson_siegel(tenors, observed)
    sv = fit_svensson(tenors, observed)
    print(f"Nelson-Siegel RMSE {1e4 * ns.rmse:.2f} bp, Svensson RMSE {1e4 * sv.rmse:.2f} bp")





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Nelson-Siegel RMSE 4.70 bp, Svensson RMSE 1.29 bp




.. GENERATED FROM PYTHON SOURCE LINES 28-30

Zero and forward curves
-----------------------

.. GENERATED FROM PYTHON SOURCE LINES 30-45

.. code-block:: Python


    t = np.linspace(0.05, 30, 300)
    fig, axes = plt.subplots(1, 2, figsize=(10, 4))
    axes[0].plot(tenors, 100 * observed, "ko", label="observed")
    for name, res in (("Nelson-Siegel", ns), ("Svensson", sv)):
        axes[0].plot(t, 100 * res.curve.zero_rate(t), label=name)
        axes[1].plot(t, 100 * res.curve.instantaneous_forward(t), label=name)
    axes[1].plot(t, 100 * true.instantaneous_forward(t), "k:", label="true")
    axes[0].set_title("zero rates")
    axes[1].set_title("instantaneous forwards")
    for ax in axes:
        ax.set_xlabel("maturity (years)")
        ax.set_ylabel("rate (%)")
        ax.legend()
    plt.show()



.. image-sg:: /api/gallery/fixed_income/curves/images/sphx_glr_plot_06_svensson_001.png
   :alt: zero rates, instantaneous forwards
   :srcset: /api/gallery/fixed_income/curves/images/sphx_glr_plot_06_svensson_001.png
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.060 seconds)


.. _sphx_glr_download_api_gallery_fixed_income_curves_plot_06_svensson.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../../lite/lab/index.html?path=api/gallery/fixed_income/curves/plot_06_svensson.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_06_svensson.ipynb <plot_06_svensson.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_06_svensson.py <plot_06_svensson.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_06_svensson.zip <plot_06_svensson.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_