.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/market_microstructure/dealers/plot_03_avellaneda_stoikov.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_market_microstructure_dealers_plot_03_avellaneda_stoikov.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_market_microstructure_dealers_plot_03_avellaneda_stoikov.py:


Avellaneda and Stoikov: market making in a limit order book
===========================================================

Marco Avellaneda and Sasha Stoikov (2008) let a market maker quote
around a Brownian mid price :math:`s`, with fills arriving at rate
:math:`A e^{-k\delta}` at distance :math:`\delta`. A trader with
exponential utility first computes the *reservation price*
:math:`r = s - q\gamma\sigma^2(T - t)`, the mid price adjusted for its
inventory :math:`q`, and then quotes a spread
:math:`\gamma\sigma^2(T-t) + \frac{2}{\gamma}\ln(1 + \gamma/k)` around it.
The example reproduces the comparison of their Table 1: the inventory
strategy gives up a little expected profit for a much smaller variance.

.. GENERATED FROM PYTHON SOURCE LINES 17-25

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from financialkit.market_microstructure import AvellanedaStoikov, SymmetricQuotes, simulate_market_making
    from financialkit.market_microstructure.visualizers import plot_market_making

    s0, sigma, T, n_steps, A, k = 100.0, 2.0, 1.0, 200, 140.0, 1.5








.. GENERATED FROM PYTHON SOURCE LINES 26-28

One trading session
-------------------

.. GENERATED FROM PYTHON SOURCE LINES 28-33

.. code-block:: Python


    res = simulate_market_making(AvellanedaStoikov(0.1, sigma, k, T), s0, sigma, T, n_steps, A, k, n_paths=1, rng=5)
    axes = plot_market_making(res)
    axes[0].set_title(f"inventory strategy, gamma = 0.1: profit {res.pnl[0]:.1f}")




.. image-sg:: /api/gallery/market_microstructure/dealers/images/sphx_glr_plot_03_avellaneda_stoikov_001.png
   :alt: inventory strategy, gamma = 0.1: profit 66.3
   :srcset: /api/gallery/market_microstructure/dealers/images/sphx_glr_plot_03_avellaneda_stoikov_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    Text(0.5, 1.0, 'inventory strategy, gamma = 0.1: profit 66.3')



.. GENERATED FROM PYTHON SOURCE LINES 34-40

Inventory against symmetric quoting
-----------------------------------

The symmetric strategy quotes the same average spread centred on the
mid price. Paper values for :math:`\gamma = 0.1`: profit 62.94 (sd 5.89)
against 67.21 (sd 13.43).

.. GENERATED FROM PYTHON SOURCE LINES 40-51

.. code-block:: Python


    print(f"{'gamma':>6s} {'strategy':>10s} {'spread':>7s} {'profit':>7s} {'sd':>6s} {'q(T)':>6s} {'sd q':>6s}")
    for g in (0.01, 0.1, 0.5):
        inv = simulate_market_making(AvellanedaStoikov(g, sigma, k, T), s0, sigma, T, n_steps, A, k, n_paths=1000, rng=6)
        half = float(np.mean(inv.ask - inv.bid)) / 2
        sym = simulate_market_making(SymmetricQuotes(half), s0, sigma, T, n_steps, A, k, n_paths=1000, rng=6)
        for name, r in [("inventory", inv), ("symmetric", sym)]:
            q = r.inventory[:, -1]
            print(f"{g:6.2f} {name:>10s} {2 * half:7.2f} {r.pnl.mean():7.2f} {r.pnl.std():6.2f} {q.mean():6.2f} {q.std():6.2f}")

    plt.show()




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

 .. code-block:: none

     gamma   strategy  spread  profit     sd   q(T)   sd q
      0.01  inventory    1.35   68.26   8.82   0.10   5.16
      0.01  symmetric    1.35   68.37  13.53   0.10   8.56
      0.10  inventory    1.49   64.84   6.55   0.04   2.88
      0.10  symmetric    1.49   68.24  13.48   0.12   8.36
      0.50  inventory    2.16   48.21   5.94   0.04   1.90
      0.50  symmetric    2.16   59.40  12.13   0.17   6.94





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

   **Total running time of the script:** (0 minutes 0.082 seconds)


.. _sphx_glr_download_api_gallery_market_microstructure_dealers_plot_03_avellaneda_stoikov.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/market_microstructure/dealers/plot_03_avellaneda_stoikov.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_03_avellaneda_stoikov.ipynb <plot_03_avellaneda_stoikov.ipynb>`

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

      :download:`Download Python source code: plot_03_avellaneda_stoikov.py <plot_03_avellaneda_stoikov.py>`

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

      :download:`Download zipped: plot_03_avellaneda_stoikov.zip <plot_03_avellaneda_stoikov.zip>`


.. only:: html

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

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