.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/fixed_income/immunization/plot_01_redington_immunization.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_immunization_plot_01_redington_immunization.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_immunization_plot_01_redington_immunization.py:


Redington immunization
======================

Frank Redington (1952), an actuary, asked how a life office could hold
assets so that a change in interest rates leaves its surplus unharmed.
His answer has three conditions: match the present values, match the
durations, and make the assets more convex than the liabilities. Then the
surplus has a local minimum at today's rates. Assets that straddle the
liabilities satisfy the third condition. Assets bunched inside them do
not.

.. GENERATED FROM PYTHON SOURCE LINES 15-34

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from financialkit.fixed_income import CashFlows, bond_cash_flows, redington_immunize
    from financialkit.fixed_income.visualizers import plot_surplus

    curve = 0.04
    liabilities = CashFlows([3.0, 6.0, 9.0, 12.0], [250.0, 250.0, 250.0, 250.0])

    straddle = redington_immunize(liabilities, [bond_cash_flows(1.0, 0.0, 1.0), bond_cash_flows(1.0, 0.0, 20.0)], curve)
    inside = redington_immunize(liabilities, [bond_cash_flows(1.0, 0.0, 6.5), bond_cash_flows(1.0, 0.0, 8.0)], curve)

    for name, res in (("1y/20y zeros", straddle), ("6.5y/8y zeros", inside)):
        print(
            f"{name}: holdings {res.holdings.round(1)}, PV {res.pv_assets:.2f} vs {res.pv_liabilities:.2f}, "
            f"D {res.duration_assets:.3f} vs {res.duration_liabilities:.3f}, "
            f"C {res.convexity_assets:.1f} vs {res.convexity_liabilities:.1f}, Redington: {res.redington_satisfied}"
        )





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

 .. code-block:: none

    1y/20y zeros: holdings [530.2 529.9], PV 747.50 vs 747.50, D 7.052 vs 7.052, C 128.1 vs 60.8, Redington: True
    6.5y/8y zeros: holdings [612.8 378.7], PV 747.50 vs 747.50, D 7.052 vs 7.052, C 50.3 vs 60.8, Redington: False




.. GENERATED FROM PYTHON SOURCE LINES 35-37

Surplus under parallel shifts
-----------------------------

.. GENERATED FROM PYTHON SOURCE LINES 37-45

.. code-block:: Python


    fig, ax = plt.subplots()
    shifts = np.linspace(-0.03, 0.03, 61)
    plot_surplus(straddle, shifts, ax=ax)
    plot_surplus(inside, shifts, ax=ax)
    ax.legend(["assets straddle liabilities", "_", "assets inside liabilities"])
    ax.set_title("Surplus = assets - liabilities")
    plt.show()



.. image-sg:: /api/gallery/fixed_income/immunization/images/sphx_glr_plot_01_redington_immunization_001.png
   :alt: Surplus = assets - liabilities
   :srcset: /api/gallery/fixed_income/immunization/images/sphx_glr_plot_01_redington_immunization_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.029 seconds)


.. _sphx_glr_download_api_gallery_fixed_income_immunization_plot_01_redington_immunization.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/immunization/plot_01_redington_immunization.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_01_redington_immunization.ipynb <plot_01_redington_immunization.ipynb>`

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

      :download:`Download Python source code: plot_01_redington_immunization.py <plot_01_redington_immunization.py>`

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

      :download:`Download zipped: plot_01_redington_immunization.zip <plot_01_redington_immunization.zip>`


.. only:: html

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

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