.. 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_02_reiner_rubinstein.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_02_reiner_rubinstein.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_02_reiner_rubinstein.py:


Reiner-Rubinstein barrier options
=================================

Eric Reiner and Mark Rubinstein (1991) wrote down closed forms for all
eight single-barrier options -- calls and puts, down and up, in and out
-- each with a cash rebate. Every one is a sum of six building blocks
:math:`A, \dots, F`: the vanilla option, the vanilla struck at the
barrier, their reflections through the barrier and the two rebates.
Without rebates, a knock-in and a knock-out with the same terms add up
to the vanilla option.

.. GENERATED FROM PYTHON SOURCE LINES 15-21

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from financialkit.exotic_options import barrier_price
    from financialkit.options import black_scholes_price








.. GENERATED FROM PYTHON SOURCE LINES 22-26

Haug's table
------------
Haug (2007), Table 4-13: S = 100, T = 0.5, r = 8%, b = 4%, sigma = 25%,
a rebate of 3, H = 95 for down barriers and 105 for up barriers.

.. GENERATED FROM PYTHON SOURCE LINES 26-33

.. code-block:: Python


    K = np.array([90.0, 100.0, 110.0])
    for option_type in ("call", "put"):
        for barrier_type, H in (("down-and-out", 95.0), ("down-and-in", 95.0), ("up-and-out", 105.0), ("up-and-in", 105.0)):
            v = barrier_price(100.0, K, H, 0.5, 0.08, 0.25, q=0.04, option_type=option_type, barrier_type=barrier_type, rebate=3.0)
            print(f"{barrier_type:>12} {option_type}: " + "  ".join(f"{x:8.4f}" for x in v))





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

 .. code-block:: none

    down-and-out call:   9.0246    6.7924    4.8759
     down-and-in call:   7.7627    4.0109    2.0576
      up-and-out call:   2.6789    2.3580    2.3453
       up-and-in call:  14.1112    8.4482    4.5910
    down-and-out put:   2.2798    2.2947    2.6252
     down-and-in put:   2.9586    6.5677   11.9752
      up-and-out put:   3.7760    5.4932    7.5187
       up-and-in put:   1.4653    3.3721    7.0846




.. GENERATED FROM PYTHON SOURCE LINES 34-36

Knock-in plus knock-out is the vanilla option
---------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 36-54

.. code-block:: Python


    S = np.linspace(60.0, 140.0, 300)
    T, r, sigma, Kc = 1.0, 0.05, 0.3, 100.0
    fig, axes = plt.subplots(1, 2, figsize=(12, 4), sharey=True)
    for ax, direction, H in ((axes[0], "down", 85.0), (axes[1], "up", 125.0)):
        out = barrier_price(S, Kc, H, T, r, sigma, barrier_type=f"{direction}-and-out")
        inn = barrier_price(S, Kc, H, T, r, sigma, barrier_type=f"{direction}-and-in")
        ax.plot(S, out, label=f"{direction}-and-out")
        ax.plot(S, inn, label=f"{direction}-and-in")
        ax.plot(S, out + inn, "k--", lw=2, label="sum")
        ax.plot(S, black_scholes_price(S, Kc, T, r, sigma), ":", color="C3", lw=3, label="vanilla call")
        ax.axvline(H, color="0.5", lw=1)
        ax.set_xlabel("spot S")
        ax.set_title(f"{direction} barrier H = {H:g}")
        ax.legend()
    axes[0].set_ylabel("value")
    fig.tight_layout()
    plt.show()



.. image-sg:: /api/gallery/exotic_options/barriers/images/sphx_glr_plot_02_reiner_rubinstein_001.png
   :alt: down barrier H = 85, up barrier H = 125
   :srcset: /api/gallery/exotic_options/barriers/images/sphx_glr_plot_02_reiner_rubinstein_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.081 seconds)


.. _sphx_glr_download_api_gallery_exotic_options_barriers_plot_02_reiner_rubinstein.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_02_reiner_rubinstein.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_02_reiner_rubinstein.ipynb <plot_02_reiner_rubinstein.ipynb>`

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

      :download:`Download Python source code: plot_02_reiner_rubinstein.py <plot_02_reiner_rubinstein.py>`

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

      :download:`Download zipped: plot_02_reiner_rubinstein.zip <plot_02_reiner_rubinstein.zip>`


.. only:: html

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

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