.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/credit/portfolio_loss/plot_02_creditrisk_plus.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_credit_portfolio_loss_plot_02_creditrisk_plus.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_credit_portfolio_loss_plot_02_creditrisk_plus.py:


CreditRisk+ and Panjer's recursion
==================================

Credit Suisse First Boston's CreditRisk+ (1997) treated defaults like
insurance claims: Poisson events with rates driven by a gamma-distributed
sector factor, and exposures rounded to multiples of a loss unit. The
default count is then negative binomial, and Panjer's (1981) recursion
produces the whole loss distribution exactly, without simulation. The
factor's volatility :math:`\sigma` fattens the tail without changing the
expected loss.

.. GENERATED FROM PYTHON SOURCE LINES 15-35

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from financialkit.credit import creditrisk_plus
    from financialkit.credit.visualizers import plot_loss_distribution

    rng = np.random.default_rng(0)
    exposures = np.round(rng.lognormal(np.log(2e5), 0.9, 300), -4)
    pds = np.clip(rng.lognormal(np.log(0.01), 0.8, 300), 1e-4, 0.2)
    unit = 50_000.0

    fig, ax = plt.subplots(1, 2, figsize=(12, 4))
    for a, sigma in zip(ax, (0.0, 1.0), strict=True):
        dist = creditrisk_plus(exposures, pds, sigma=sigma, unit=unit)
        plot_loss_distribution(dist, alpha=0.999, ax=a, log=True)
        a.set_title(f"sector volatility sigma = {sigma}")
        a.set_xlim(0, 2.5e7)
        a.set_ylim(1e-8, 1)
        print(f"sigma = {sigma}: EL {dist.mean:,.0f}, sd {dist.std:,.0f}, 99.9% UL {dist.unexpected_loss(0.999):,.0f}")




.. image-sg:: /api/gallery/credit/portfolio_loss/images/sphx_glr_plot_02_creditrisk_plus_001.png
   :alt: sector volatility sigma = 0.0, sector volatility sigma = 1.0
   :srcset: /api/gallery/credit/portfolio_loss/images/sphx_glr_plot_02_creditrisk_plus_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    sigma = 0.0: EL 1,168,615, sd 892,123, 99.9% UL 4,581,385
    sigma = 1.0: EL 1,168,614, sd 1,470,212, 99.9% UL 8,981,386




.. GENERATED FROM PYTHON SOURCE LINES 36-38

Tail probabilities
------------------

.. GENERATED FROM PYTHON SOURCE LINES 38-50

.. code-block:: Python


    fig, ax = plt.subplots(figsize=(7, 4))
    for sigma in (0.0, 0.5, 1.0, 1.5):
        d = creditrisk_plus(exposures, pds, sigma=sigma, unit=unit)
        ax.semilogy(d.losses, 1 - np.cumsum(d.pmf), label=f"sigma = {sigma}")
    ax.set_xlim(0, 3e7)
    ax.set_ylim(1e-6, 1)
    ax.set_xlabel("loss")
    ax.set_ylabel("P(loss > x)")
    ax.legend()

    plt.show()



.. image-sg:: /api/gallery/credit/portfolio_loss/images/sphx_glr_plot_02_creditrisk_plus_002.png
   :alt: plot 02 creditrisk plus
   :srcset: /api/gallery/credit/portfolio_loss/images/sphx_glr_plot_02_creditrisk_plus_002.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.318 seconds)


.. _sphx_glr_download_api_gallery_credit_portfolio_loss_plot_02_creditrisk_plus.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/credit/portfolio_loss/plot_02_creditrisk_plus.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_02_creditrisk_plus.ipynb <plot_02_creditrisk_plus.ipynb>`

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

      :download:`Download Python source code: plot_02_creditrisk_plus.py <plot_02_creditrisk_plus.py>`

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

      :download:`Download zipped: plot_02_creditrisk_plus.zip <plot_02_creditrisk_plus.zip>`


.. only:: html

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

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