.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/exotic_options/compound/plot_01_geske_compound.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_compound_plot_01_geske_compound.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_compound_plot_01_geske_compound.py:


Geske compound options
======================

Robert Geske (1979) priced an option on an option. His motivation was
corporate finance: if equity is a call on the firm's assets, a stock
option is a call on a call, and its implied volatility should rise as
the stock falls and leverage grows. The compound call is exercised at
:math:`T_1` only if the underlying option is worth more than the
compound strike, which happens above a critical spot :math:`I`, and the
joint law of the price at :math:`T_1` and :math:`T_2` brings in the
bivariate normal distribution with correlation :math:`\sqrt{T_1/T_2}`.

.. GENERATED FROM PYTHON SOURCE LINES 16-26

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from financialkit.exotic_options import compound_option_price, critical_price
    from financialkit.options import black_scholes_price

    K1, K2, T1, T2, r, sigma = 5.0, 100.0, 0.25, 1.0, 0.05, 0.3
    S = np.linspace(60.0, 150.0, 200)
    print(f"Haug (2007), 4.6, put on call: {compound_option_price(500.0, 50.0, 520.0, 0.25, 0.5, 0.08, 0.35, q=0.03, option_type='put'):.4f}")





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

 .. code-block:: none

    Haug (2007), 4.6, put on call: 21.1964




.. GENERATED FROM PYTHON SOURCE LINES 27-29

The four compound options
-------------------------

.. GENERATED FROM PYTHON SOURCE LINES 29-42

.. code-block:: Python


    fig, axes = plt.subplots(1, 2, figsize=(12, 4))
    for underlying in ("call", "put"):
        I = critical_price(K1, K2, T2 - T1, r, sigma, underlying_type=underlying)
        for option_type in ("call", "put"):
            axes[0].plot(
                S, compound_option_price(S, K1, K2, T1, T2, r, sigma, option_type=option_type, underlying_type=underlying), label=f"{option_type} on {underlying}"
            )
        axes[0].axvline(I, color="C0" if underlying == "call" else "C2", ls=":", lw=1)
    axes[0].set_xlabel("spot S (dotted: critical spots I)")
    axes[0].set_ylabel("value")
    axes[0].legend()




.. image-sg:: /api/gallery/exotic_options/compound/images/sphx_glr_plot_01_geske_compound_001.png
   :alt: plot 01 geske compound
   :srcset: /api/gallery/exotic_options/compound/images/sphx_glr_plot_01_geske_compound_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <matplotlib.legend.Legend object at 0x116f13cb0>



.. GENERATED FROM PYTHON SOURCE LINES 43-47

Compound put-call parity
------------------------
Call on call minus put on call is the call minus the discounted
compound strike, whatever the spot.

.. GENERATED FROM PYTHON SOURCE LINES 47-56

.. code-block:: Python


    cc = compound_option_price(S, K1, K2, T1, T2, r, sigma)
    pc = compound_option_price(S, K1, K2, T1, T2, r, sigma, option_type="put")
    axes[1].plot(S, cc - pc, lw=3, label="call on call - put on call")
    axes[1].plot(S, black_scholes_price(S, K2, T2, r, sigma) - K1 * np.exp(-r * T1), "k--", label=r"$c(S) - K_1 e^{-rT_1}$")
    axes[1].set_xlabel("spot S")
    axes[1].legend()
    fig.tight_layout()
    plt.show()








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

   **Total running time of the script:** (0 minutes 0.071 seconds)


.. _sphx_glr_download_api_gallery_exotic_options_compound_plot_01_geske_compound.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/compound/plot_01_geske_compound.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_01_geske_compound.ipynb <plot_01_geske_compound.ipynb>`

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

      :download:`Download Python source code: plot_01_geske_compound.py <plot_01_geske_compound.py>`

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

      :download:`Download zipped: plot_01_geske_compound.zip <plot_01_geske_compound.zip>`


.. only:: html

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

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