.. _sphx_glr_api_gallery_monte_carlo_multilevel:

Multilevel Monte Carlo
----------------------

Giles's telescoping sum over Euler discretisations of increasing
resolution, and its cost against standard Monte Carlo.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Pricing with a discretised SDE has two errors: the bias of the time step and the statistical error. Balancing them with Euler&#x27;s scheme costs O(\varepsilon^{-3}). Michael Giles (2008), borrowing the idea of multigrid (and of Heinrich&#x27;s multilevel integration), wrote the finest approximation as a telescoping sum,">

.. only:: html

  .. image:: /api/gallery/monte_carlo/multilevel/images/thumb/sphx_glr_plot_01_giles_mlmc_thumb.png
    :alt:

  :doc:`/api/gallery/monte_carlo/multilevel/plot_01_giles_mlmc`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Giles multilevel Monte Carlo</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /api/gallery/monte_carlo/multilevel/plot_01_giles_mlmc