.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "generated_examples\economic\plot_ex2_short_rate_mean_variance.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_ex2_short_rate_mean_variance.py>`
        to download the full example code

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

.. _sphx_glr_generated_examples_economic_plot_ex2_short_rate_mean_variance.py:


Short rate mean and variance
===================================

The means and variances of the simulated short rates.

For each :math:`t_i`,
the mean and the variance of the short rate :math:`r(t_i)` should converge to
:math:`E\{r(t_i) | \mathcal{F}_{0}\}` and :math:`Var\{r(t_i) | \mathcal{F}_{0}\}`.

.. 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 16-34



.. image-sg:: /generated_examples/economic/images/sphx_glr_plot_ex2_short_rate_mean_variance_001.png
   :alt: Mean 1000 scenarios, Mean 10000 scenarios, Variance 1000 scenarios, Variance 10000 scenarios
   :srcset: /generated_examples/economic/images/sphx_glr_plot_ex2_short_rate_mean_variance_001.png
   :class: sphx-glr-single-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=False)

    for size, h in zip([1000, 10000], [0, 1]):
        HW.scen_size = size
        axs[0, h].plot(range(HW.step_size + 1), HW.E_rt(), "b-")
        axs[0, h].plot(range(HW.step_size + 1), HW.mean_short_rate(), "r--")
        axs[0, h].set_title('Mean ' + str(size) + ' scenarios')
        axs[1, h].plot(range(HW.step_size + 1), HW.Var_rt(), "b-")
        axs[1, h].plot(range(HW.step_size + 1), HW.var_short_rate(), "r--")
        axs[1, h].set_title('Variance ' + str(size) + ' scenarios')





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

   **Total running time of the script:** ( 0 minutes  0.395 seconds)


.. _sphx_glr_download_generated_examples_economic_plot_ex2_short_rate_mean_variance.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_ex2_short_rate_mean_variance.py <plot_ex2_short_rate_mean_variance.py>`

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

      :download:`Download Jupyter notebook: plot_ex2_short_rate_mean_variance.ipynb <plot_ex2_short_rate_mean_variance.ipynb>`


.. only:: html

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

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