.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/risk/var/plot_05_hybrid_var.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_risk_var_plot_05_hybrid_var.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_risk_var_plot_05_hybrid_var.py:


Boudoukh-Richardson-Whitelaw hybrid VaR
=======================================

Historical simulation gives every day in the window the same weight, so
after a jump in volatility it takes months to notice and then drops the
crisis days abruptly when they leave the window. Boudoukh, Richardson
and Whitelaw (1998) weighted the outcome :math:`i` days old by
:math:`\lambda^i`, combining RiskMetrics' exponential smoothing with
historical simulation's distribution-free tail: "the best of both worlds".

.. GENERATED FROM PYTHON SOURCE LINES 14-25

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from financialkit.risk import historical_var, hybrid_var
    from financialkit.risk.visualizers import plot_var

    rng = np.random.default_rng(11)
    vol = np.r_[np.full(500, 0.008), np.full(150, 0.025), np.full(350, 0.008)]
    pnl = vol * rng.standard_t(5, vol.size) / np.sqrt(5 / 3)
    window = 250








.. GENERATED FROM PYTHON SOURCE LINES 26-28

Rolling forecasts through a turbulent spell
-------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 28-42

.. code-block:: Python


    days = np.arange(window, pnl.size)
    hs = [historical_var(pnl[t - window : t], 0.99).var for t in days]
    bw = [hybrid_var(pnl[t - window : t], 0.99, lam=0.98).var for t in days]
    fig, ax = plt.subplots(figsize=(8, 3.8))
    ax.plot(np.arange(pnl.size), pnl, color="0.75", lw=0.6)
    ax.plot(days, -np.array(hs), label="historical (equal weights)")
    ax.plot(days, -np.array(bw), label="hybrid, lambda = 0.98")
    ax.plot(np.arange(pnl.size), -2.326 * vol, "k:", lw=1, label="true 99% normal-equivalent")
    ax.set_xlabel("day")
    ax.set_ylabel("P&L and minus VaR")
    ax.legend(loc="lower left", fontsize=8)
    fig.tight_layout()




.. image-sg:: /api/gallery/risk/var/images/sphx_glr_plot_05_hybrid_var_001.png
   :alt: plot 05 hybrid var
   :srcset: /api/gallery/risk/var/images/sphx_glr_plot_05_hybrid_var_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 43-48

The weighted distribution on the first turbulent days
-----------------------------------------------------

Twenty days into the turbulent period the hybrid method already puts
a third of its probability mass on them.

.. GENERATED FROM PYTHON SOURCE LINES 48-55

.. code-block:: Python


    t = 520
    res = hybrid_var(pnl[t - window : t], 0.99, 0.98)
    print(f"weight on last 20 days: {res.weights[-20:].sum():.2f}  (equal weighting: {20 / window:.2f})")
    plot_var(res)

    plt.show()



.. image-sg:: /api/gallery/risk/var/images/sphx_glr_plot_05_hybrid_var_002.png
   :alt: hybrid
   :srcset: /api/gallery/risk/var/images/sphx_glr_plot_05_hybrid_var_002.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    weight on last 20 days: 0.33  (equal weighting: 0.08)





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

   **Total running time of the script:** (0 minutes 0.099 seconds)


.. _sphx_glr_download_api_gallery_risk_var_plot_05_hybrid_var.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/risk/var/plot_05_hybrid_var.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_05_hybrid_var.ipynb <plot_05_hybrid_var.ipynb>`

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

      :download:`Download Python source code: plot_05_hybrid_var.py <plot_05_hybrid_var.py>`

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

      :download:`Download zipped: plot_05_hybrid_var.zip <plot_05_hybrid_var.zip>`


.. only:: html

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

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