.. 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_03_chooser.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_03_chooser.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_03_chooser.py:


Rubinstein choosers
===================

"Pay now, choose later": the holder of a simple chooser decides at a
date :math:`t` whether the option is a call or a put, both struck at
:math:`K` and expiring at :math:`T`. Mark Rubinstein (1991) used
put-call parity to write the choice as a call plus a put:

.. math:: \max(c, p) = c + (K e^{-r(T-t)} - S_t e^{-q(T-t)})^+
          \;\Rightarrow\; V = c(S, K, T) + e^{-q(T-t)}\, p(S, K e^{-(r-q)(T-t)}, t).

Choosing today is worth the better of the two options; choosing at
expiry is a straddle. In between the value rises with the time left to
choose.

.. GENERATED FROM PYTHON SOURCE LINES 19-38

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from financialkit.exotic_options import chooser_price
    from financialkit.options import black_scholes_price

    S, T, r, sigma = 100.0, 1.0, 0.05, 0.25
    print(f"Haug (2007), 4.4.1: {chooser_price(50.0, 50.0, 0.25, 0.5, 0.08, 0.25):.4f}")
    t = np.linspace(0.0, T, 60)

    fig, axes = plt.subplots(1, 2, figsize=(12, 4))
    for K in (90.0, 100.0, 110.0):
        line = axes[0].plot(t, chooser_price(S, K, t, T, r, sigma), label=f"K = {K:g}")[0]
        c, p = black_scholes_price(S, K, T, r, sigma), black_scholes_price(S, K, T, r, sigma, option_type="put")
        axes[0].plot([0, T], [max(c, p), c + p], "o", color=line.get_color())
    axes[0].set_xlabel("choice date t (dots: better option, straddle)")
    axes[0].set_ylabel("chooser value")
    axes[0].legend()




.. image-sg:: /api/gallery/exotic_options/compound/images/sphx_glr_plot_03_chooser_001.png
   :alt: plot 03 chooser
   :srcset: /api/gallery/exotic_options/compound/images/sphx_glr_plot_03_chooser_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    Haug (2007), 4.4.1: 6.1071

    <matplotlib.legend.Legend object at 0x116f11be0>



.. GENERATED FROM PYTHON SOURCE LINES 39-41

A Monte Carlo check of the decision rule
----------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 41-56

.. code-block:: Python


    K, tc = 100.0, 0.5
    rng = np.random.default_rng(0)
    z = rng.standard_normal((2, 50_000))
    St = S * np.exp((r - 0.5 * sigma**2) * tc + sigma * np.sqrt(tc) * z[0])
    ST = St * np.exp((r - 0.5 * sigma**2) * (T - tc) + sigma * np.sqrt(T - tc) * z[1])
    pick_call = black_scholes_price(St, K, T - tc, r, sigma) >= black_scholes_price(St, K, T - tc, r, sigma, option_type="put")
    y = np.exp(-r * T) * np.where(pick_call, np.maximum(ST - K, 0), np.maximum(K - ST, 0))
    print(f"chooser {chooser_price(S, K, tc, T, r, sigma):.4f}, Monte Carlo {y.mean():.4f} +/- {y.std() / np.sqrt(y.size):.4f}")
    axes[1].hist(St[pick_call], bins=60, alpha=0.6, label="choose the call")
    axes[1].hist(St[~pick_call], bins=60, alpha=0.6, label="choose the put")
    axes[1].set_xlabel(f"price at the choice date t = {tc}")
    axes[1].legend()
    fig.tight_layout()
    plt.show()




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

 .. code-block:: none

    chooser 17.0412, Monte Carlo 17.0335 +/- 0.0811





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

   **Total running time of the script:** (0 minutes 0.085 seconds)


.. _sphx_glr_download_api_gallery_exotic_options_compound_plot_03_chooser.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_03_chooser.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_03_chooser.ipynb <plot_03_chooser.ipynb>`

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

      :download:`Download Python source code: plot_03_chooser.py <plot_03_chooser.py>`

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

      :download:`Download zipped: plot_03_chooser.zip <plot_03_chooser.zip>`


.. only:: html

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

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