.. _sphx_glr_api_gallery_exotic_options_asian:

Asian options
-------------

Options on an average price: the geometric closed form, the arithmetic
average by Monte Carlo with the geometric control variate, and
lognormal moment matching.


.. 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="An average-rate option pays on the average price over its life, which makes it cheaper than a vanilla option and harder to manipulate at expiry. Angelien Kemna and Ton Vorst (1990) observed that a geometric average of lognormal prices is lognormal, with volatility \sigma/\sqrt3 under continuous averaging, so its option has a Black-Scholes formula. The arithmetic average traded in practice has none, but the geometric option is so tightly correlated with it that it makes a near-perfect Monte Carlo control variate.">

.. only:: html

  .. image:: /api/gallery/exotic_options/asian/images/thumb/sphx_glr_plot_01_kemna_vorst_thumb.png
    :alt:

  :doc:`/api/gallery/exotic_options/asian/plot_01_kemna_vorst`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Kemna-Vorst Asian options</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Stuart Turnbull and Lee Wakeman (1991) priced the arithmetic average A as if it were lognormal with the right first two moments: Black&#x27;s formula on the forward E[A] with volatility">

.. only:: html

  .. image:: /api/gallery/exotic_options/asian/images/thumb/sphx_glr_plot_02_turnbull_wakeman_thumb.png
    :alt:

  :doc:`/api/gallery/exotic_options/asian/plot_02_turnbull_wakeman`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Turnbull-Wakeman Asian approximation</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /api/gallery/exotic_options/asian/plot_01_kemna_vorst
   /api/gallery/exotic_options/asian/plot_02_turnbull_wakeman