.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/pde_methods/accuracy/plot_02_tavella_randall_grid.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_pde_methods_accuracy_plot_02_tavella_randall_grid.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_pde_methods_accuracy_plot_02_tavella_randall_grid.py:


Tavella-Randall non-uniform grids
=================================

Away from the strike a vanilla option is almost linear, so a uniform
grid spends most of its nodes where nothing happens. Tavella and Randall
(2000) map a uniform coordinate through a hyperbolic sine to cluster the
nodes around the strike, keeping the grid smooth so the three-point
differences stay second order.
:func:`~financialkit.pde_methods.tavella_randall_grid` builds the grid, and
``grid="tavella_randall"`` prices on it: the same accuracy with a fraction
of the nodes.

.. GENERATED FROM PYTHON SOURCE LINES 16-32

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from financialkit.options import black_scholes_price
    from financialkit.pde_methods import CrankNicolson, tavella_randall_grid, uniform_grid
    from financialkit.pde_methods.visualizers import plot_grid

    S, K, T, r, sigma = 100.0, 100.0, 0.5, 0.05, 0.2
    exact = black_scholes_price(S, K, T, r, sigma)

    fig, axes = plt.subplots(1, 2, figsize=(11, 4))
    plot_grid(uniform_grid(0.0, 400.0, 60), ax=axes[0], label="uniform")
    for alpha in (30.0, 15.0, 5.0):
        plot_grid(tavella_randall_grid(0.0, 400.0, 60, K, alpha), ax=axes[0], K=K, label=f"sinh, alpha = {alpha:g}")
    axes[0].set_title("node spacing, 60 intervals")




.. image-sg:: /api/gallery/pde_methods/accuracy/images/sphx_glr_plot_02_tavella_randall_grid_001.png
   :alt: node spacing, 60 intervals
   :srcset: /api/gallery/pde_methods/accuracy/images/sphx_glr_plot_02_tavella_randall_grid_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    Text(0.5, 1.0, 'node spacing, 60 intervals')



.. GENERATED FROM PYTHON SOURCE LINES 33-35

Error against the number of spot intervals
------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 35-45

.. code-block:: Python


    ms = np.array([20, 40, 80, 160])
    for grid, kw in (("uniform", {}), ("tavella_randall", {"concentration": 0.15})):
        err = [abs(CrankNicolson(m, 400, rannacher_steps=2, s_max=400.0, grid=grid, **kw).price(S, K, T, r, sigma).price - exact) for m in ms]
        axes[1].loglog(ms, err, "o-", label=grid)
    axes[1].set_xlabel("spot intervals M")
    axes[1].set_ylabel("absolute error")
    axes[1].legend()
    fig.tight_layout()
    plt.show()








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

   **Total running time of the script:** (0 minutes 0.142 seconds)


.. _sphx_glr_download_api_gallery_pde_methods_accuracy_plot_02_tavella_randall_grid.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/pde_methods/accuracy/plot_02_tavella_randall_grid.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_02_tavella_randall_grid.ipynb <plot_02_tavella_randall_grid.ipynb>`

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

      :download:`Download Python source code: plot_02_tavella_randall_grid.py <plot_02_tavella_randall_grid.py>`

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

      :download:`Download zipped: plot_02_tavella_randall_grid.zip <plot_02_tavella_randall_grid.zip>`


.. only:: html

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

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