.. _sphx_glr_api_gallery_options_greeks:

Greeks and hedging
------------------

The sensitivities that the Black-Scholes argument hedges away, and what
happens when the hedge is rebalanced only a finite number of times.


.. 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="The Black-Scholes argument hedges an option with \Delta = \partial V/\partial S shares; the other partial derivatives measure how that hedge and the option&#x27;s value respond to everything else. The Greeks, named by traders after the 1973 paper, satisfy the pricing PDE itself,">

.. only:: html

  .. image:: /api/gallery/options/greeks/images/thumb/sphx_glr_plot_01_greeks_thumb.png
    :alt:

  :doc:`/api/gallery/options/greeks/plot_01_greeks`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">The Black-Scholes Greeks</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Black and Scholes priced an option by showing that a dealer who sells it and holds \Delta shares, rebalancing continuously, carries no risk. Real hedges are rebalanced a finite number of times. The dealer&#x27;s terminal P&amp;L then has mean zero but a spread that shrinks like 1/\sqrt{n} in the number of rebalances (Boyle and Emanuel 1980), and the hedge works whatever the stock&#x27;s real-world drift.">

.. only:: html

  .. image:: /api/gallery/options/greeks/images/thumb/sphx_glr_plot_02_delta_hedging_thumb.png
    :alt:

  :doc:`/api/gallery/options/greeks/plot_02_delta_hedging`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Delta hedging in discrete time</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /api/gallery/options/greeks/plot_01_greeks
   /api/gallery/options/greeks/plot_02_delta_hedging