.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/exotic_options/barriers/plot_03_double_barrier.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_exotic_options_barriers_plot_03_double_barrier.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_exotic_options_barriers_plot_03_double_barrier.py:


Ikeda-Kunitomo double barriers
==============================

A double knock-out dies if the price leaves a corridor :math:`(L, U)`.
Naoto Ikeda and Masaaki Kunitomo (1992) solved it, even for curved
(exponential) barriers, with an infinite series of images reflected
alternately through both boundaries. The terms decay like
:math:`e^{-2n^2\ln^2(U/L)/\sigma^2T}`, so two or three are plenty unless
the corridor is very narrow. Unlike a vanilla call, a double knock-out
call loses value as volatility rises: more paths hit a barrier.

.. GENERATED FROM PYTHON SOURCE LINES 15-27

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from financialkit.exotic_options import double_barrier_price, plot_barrier_paths
    from financialkit.integrators import gbm_paths

    K, L, U, T, r = 100.0, 80.0, 130.0, 0.5, 0.05

    fig, axes = plt.subplots(1, 3, figsize=(15, 4))
    t, paths = gbm_paths(100.0, r, 0.25, T, 100, 40, rng=0)
    plot_barrier_paths(t, paths, [L, U], ax=axes[0])




.. image-sg:: /api/gallery/exotic_options/barriers/images/sphx_glr_plot_03_double_barrier_001.png
   :alt: 12 of 40 paths knocked out
   :srcset: /api/gallery/exotic_options/barriers/images/sphx_glr_plot_03_double_barrier_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <Axes: title={'center': '12 of 40 paths knocked out'}, xlabel='time t', ylabel='price $S_t$'>



.. GENERATED FROM PYTHON SOURCE LINES 28-30

The corridor value and its volatility
-------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 30-38

.. code-block:: Python


    S = np.linspace(L, U, 300)
    for sigma in (0.1, 0.2, 0.3, 0.4):
        axes[1].plot(S, double_barrier_price(S, K, L, U, T, r, sigma), label=rf"$\sigma$ = {sigma:.0%}")
    axes[1].set_xlabel("spot S")
    axes[1].set_ylabel("double knock-out call")
    axes[1].legend()





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

 .. code-block:: none


    <matplotlib.legend.Legend object at 0x116d77a10>



.. GENERATED FROM PYTHON SOURCE LINES 39-42

How many images?
----------------
The error of the series truncated at :math:`|n| \le N`, against :math:`N = 20`.

.. GENERATED FROM PYTHON SOURCE LINES 42-52

.. code-block:: Python


    for width, (lo, hi) in (("wide", (60.0, 160.0)), ("medium", (80.0, 130.0)), ("narrow", (95.0, 110.0))):
        ref = double_barrier_price(100.0, 100.0, lo, hi, T, r, 0.3, n_terms=20)
        err = [abs(double_barrier_price(100.0, 100.0, lo, hi, T, r, 0.3, n_terms=n) - ref) + 1e-17 for n in range(0, 6)]
        axes[2].semilogy(range(0, 6), err, "o-", label=f"{width}: ({lo:g}, {hi:g})")
    axes[2].set_xlabel("terms N")
    axes[2].set_ylabel("truncation error")
    axes[2].legend()
    fig.tight_layout()
    plt.show()








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

   **Total running time of the script:** (0 minutes 0.730 seconds)


.. _sphx_glr_download_api_gallery_exotic_options_barriers_plot_03_double_barrier.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/exotic_options/barriers/plot_03_double_barrier.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_03_double_barrier.ipynb <plot_03_double_barrier.ipynb>`

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

      :download:`Download Python source code: plot_03_double_barrier.py <plot_03_double_barrier.py>`

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

      :download:`Download zipped: plot_03_double_barrier.zip <plot_03_double_barrier.zip>`


.. only:: html

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

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