.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "generated_examples\economic\plot_ex3_disc_factor_convergence.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        Click :ref:`here <sphx_glr_download_generated_examples_economic_plot_ex3_disc_factor_convergence.py>`
        to download the full example code

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

.. _sphx_glr_generated_examples_economic_plot_ex3_disc_factor_convergence.py:


Discount factor convergence
===================================

The convergence of the stochastic discount factors generated by the Hull-White model.

The charts below examine the convergence of the discount factors
for various combinations of :math:`\sigma` and :math:`a`, first by changing :math:`\sigma` and secondly by changing :math:`a`.
As Balaraman's study shows, the convergence gets worse as :math:`\sigma/a` gets larger than 1, and gets better as :math:`\sigma/a` gets smaller than 1.

.. seealso::
    * :mod:`~economic.BasicHullWhite.HullWhite` in :mod:`~economic.BasicHullWhite`
    * :doc:`/libraries/economic/hull-white-simulation` notebook in the :mod:`~economic` library

.. GENERATED FROM PYTHON SOURCE LINES 16-36



.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /generated_examples/economic/images/sphx_glr_plot_ex3_disc_factor_convergence_001.png
         :alt: $a=$0.1, $\sigma=$0.05, $\sigma/a=$0.50, $\sigma=$0.075, $\sigma/a=$0.75, $\sigma=$0.1, $\sigma/a=$1.00, $\sigma=$0.125, $\sigma/a=$1.25
         :srcset: /generated_examples/economic/images/sphx_glr_plot_ex3_disc_factor_convergence_001.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /generated_examples/economic/images/sphx_glr_plot_ex3_disc_factor_convergence_002.png
         :alt: $\sigma=$0.125, $a=$0.05, $\sigma/a=$2.00, $a=$0.1, $\sigma/a=$1.00, $a=$0.15, $\sigma/a=$0.67, $a=$0.2, $\sigma/a=$0.50
         :srcset: /generated_examples/economic/images/sphx_glr_plot_ex3_disc_factor_convergence_002.png
         :class: sphx-glr-multi-img





.. code-block:: default

    import modelx as mx
    import matplotlib.pyplot as plt

    HW = mx.read_model("BasicHullWhite").HullWhite

    fig, axs = plt.subplots(2, 2, sharex=True, sharey=True)
    fig.suptitle(r"$a=$" + str(HW.a))
    for sigma, (h, v) in zip([0.05, 0.075, 0.1, 0.125], [(0, 0), (0, 1), (1, 0), (1, 1)]):
        HW.sigma = sigma
        axs[h, v].set_title(r"$\sigma=$" + str(sigma) +  r", $\sigma/a=$" + "%.2f" % (sigma/HW.a))
        axs[h, v].plot(range(HW.step_size+1), [HW.mkt_zcb(i) for i in range(HW.step_size+1)], "b-")
        axs[h, v].plot(range(HW.step_size+1), HW.mean_disc_factor(), "r--")

    fig, axs = plt.subplots(2, 2, sharex=True, sharey=True)
    fig.suptitle(r"$\sigma=$" + str(HW.sigma))
    HW.sigma = 0.1
    for a, (h, v) in zip([0.05, 0.1, 0.15, 0.2], [(0, 0), (0, 1), (1, 0), (1, 1)]):
        HW.a = a
        axs[h, v].set_title(r"$a=$" + str(a) +  r", $\sigma/a=$" + "%.2f" % (HW.sigma/HW.a))
        axs[h, v].plot(range(HW.step_size+1), [HW.mkt_zcb(i) for i in range(HW.step_size+1)], "b-")
        axs[h, v].plot(range(HW.step_size+1), HW.mean_disc_factor(), "r--")

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

   **Total running time of the script:** ( 0 minutes  0.940 seconds)


.. _sphx_glr_download_generated_examples_economic_plot_ex3_disc_factor_convergence.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_ex3_disc_factor_convergence.py <plot_ex3_disc_factor_convergence.py>`

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

      :download:`Download Jupyter notebook: plot_ex3_disc_factor_convergence.ipynb <plot_ex3_disc_factor_convergence.ipynb>`


.. only:: html

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

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