.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "generated_examples\smithwilson\plot_smithwilson.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        Click :ref:`here <sphx_glr_download_generated_examples_smithwilson_plot_smithwilson.py>`
        to download the full example code

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

.. _sphx_glr_generated_examples_smithwilson_plot_smithwilson.py:


Smith-Wilson extrapolation with various alphas
==============================================

This notebook reads in the **smithwilson** model,
and extrapolates forward rates
using the Smith-Wilson method with various alphas, and draws
the forward rates.
See :doc:`/projects/smithwilson` for the details of the **smithwilson** model.

The source of the input data is Switzerland EIOPA spot rates
with LLP 25 years available from the following source.

Source: RFR_spot_no_VA tab in EIOPA_RFR_20190531_Term_Structures.xlsx,
archived in EIOPA_RFR_20190531.zip, avaialble on
`EIOPA's Risk-Free Interest Rate Term Structures web site`_.

.. _EIOPA's Risk-Free Interest Rate Term Structures web site: https://wayback.archive-it.org/org-1495/20191229100044/https:/eiopa.europa.eu/regulation-supervision/insurance/solvency-ii-technical-information/risk-free-interest-rate-term-structures

.. GENERATED FROM PYTHON SOURCE LINES 22-26

.. code-block:: default


    import modelx as mx
    import pandas as pd








.. GENERATED FROM PYTHON SOURCE LINES 27-30

The code below reads the ``smithwilson`` model from *"model"* folder,
and assign ``SmithWilson`` space in the model to
a global variable named ``space``.

.. GENERATED FROM PYTHON SOURCE LINES 30-33

.. code-block:: default


    space = mx.read_model("model").SmithWilson








.. GENERATED FROM PYTHON SOURCE LINES 34-38

The code below is for parametrizing  the ``SmithWilson`` space by ``x``.
The parameter ``x`` takes integer values, and they can be positive and negative.
the alpha in the ``SmithWilson[x]`` space is adjusted from the original alpha
by ``x`` times 10%.

.. GENERATED FROM PYTHON SOURCE LINES 38-44

.. code-block:: default


    def parametrize(x):
        return {"refs": {"alpha": alpha * (1 + 0.1*x)}}

    space.formula = parametrize








.. GENERATED FROM PYTHON SOURCE LINES 45-48

The code below creates the ``ForwardRates`` cells,
which calculates extrapolated forward rates from
the present values of bond prices.

.. GENERATED FROM PYTHON SOURCE LINES 48-54

.. code-block:: default


    @mx.defcells
    def ForwardRates(t):
        return P(t) / P(t+1) - 1









.. GENERATED FROM PYTHON SOURCE LINES 55-57

The code below plots the extrapolated forward rates
with various alphas.

.. GENERATED FROM PYTHON SOURCE LINES 57-64

.. code-block:: default


    d = {"{0:.3}".format(space.alpha * (1 + 0.1*x)):
             [space[x].ForwardRates[t] for t in range(1, 101)]
         for x in range(-6, 5)}

    df = pd.DataFrame(d, index=range(1, 101))

    df.plot.line()


.. image-sg:: /generated_examples/smithwilson/images/sphx_glr_plot_smithwilson_001.png
   :alt: plot smithwilson
   :srcset: /generated_examples/smithwilson/images/sphx_glr_plot_smithwilson_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** ( 0 minutes  0.739 seconds)


.. _sphx_glr_download_generated_examples_smithwilson_plot_smithwilson.py:

.. only:: html

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


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

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

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

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


.. only:: html

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

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