.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/market_microstructure/information/plot_04_pin.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_information_plot_04_pin.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_information_plot_04_pin.py:


Easley, Kiefer, O'Hara and Paperman: the probability of informed trading
========================================================================

Easley, Kiefer, O'Hara and Paperman (1996) turned the Glosten-Milgrom
logic into an estimator that needs only daily counts of buys and sells.
On a day with private news (probability :math:`\alpha`), informed
traders add rate :math:`\mu` to one side; otherwise only uninformed buys
and sells arrive, at rates :math:`\varepsilon_b, \varepsilon_s`. The
fitted mixture gives the share of trades that are informed,
:math:`\mathrm{PIN} = \alpha\mu / (\alpha\mu + \varepsilon_b + \varepsilon_s)`.
Their finding: thinly traded stocks have a higher PIN, which explains
their wider spreads.

.. GENERATED FROM PYTHON SOURCE LINES 17-22

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from financialkit.market_microstructure import fit_pin, simulate_pin








.. GENERATED FROM PYTHON SOURCE LINES 23-25

Three kinds of days
-------------------

.. GENERATED FROM PYTHON SOURCE LINES 25-42

.. code-block:: Python


    true = dict(alpha=0.35, delta=0.45, mu=60.0, eps_b=80.0, eps_s=75.0)
    B, S = simulate_pin(250, **true, rng=11)
    res = fit_pin(B, S)
    pin_true = true["alpha"] * true["mu"] / (true["alpha"] * true["mu"] + true["eps_b"] + true["eps_s"])
    print(f"alpha {res.alpha:.3f}, delta {res.delta:.3f}, mu {res.mu:.1f}, eps_b {res.eps_b:.1f}, eps_s {res.eps_s:.1f}")
    print(f"PIN {res.pin:.3f} ± {res.pin_se:.3f} (true {pin_true:.3f})")

    fig, ax = plt.subplots(figsize=(5, 5))
    ax.plot(B, S, ".", color="0.4")
    for (cb, cs), name in [((res.eps_b, res.eps_s), "no news"), ((res.eps_b, res.eps_s + res.mu), "bad news"), ((res.eps_b + res.mu, res.eps_s), "good news")]:
        ax.plot(cb, cs, "o", ms=12, mfc="none", mew=2, label=name)
    ax.set_xlabel("buys per day")
    ax.set_ylabel("sells per day")
    ax.legend()
    fig.tight_layout()




.. image-sg:: /api/gallery/market_microstructure/information/images/sphx_glr_plot_04_pin_001.png
   :alt: plot 04 pin
   :srcset: /api/gallery/market_microstructure/information/images/sphx_glr_plot_04_pin_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    alpha 0.391, delta 0.572, mu 58.8, eps_b 78.4, eps_s 75.5
    PIN 0.130 ± 0.009 (true 0.119)




.. GENERATED FROM PYTHON SOURCE LINES 43-48

Active and inactive stocks
--------------------------

Uninformed volume scales up across stocks while information events stay
similar, so PIN falls with activity, as in the paper's volume deciles.

.. GENERATED FROM PYTHON SOURCE LINES 48-62

.. code-block:: Python


    scales = [0.25, 0.5, 1.0, 2.0, 4.0]
    pins = []
    for i, sc in enumerate(scales):
        b_, s_ = simulate_pin(250, 0.3, 0.5, 30.0 * np.sqrt(sc), 20.0 * sc, 20.0 * sc, rng=20 + i)
        pins.append(fit_pin(b_, s_))
    fig, ax = plt.subplots(figsize=(6, 3.5))
    ax.errorbar([40 * s for s in scales], [p.pin for p in pins], yerr=[2 * p.pin_se for p in pins], fmt="o-", capsize=3)
    ax.set_xscale("log")
    ax.set_xlabel("average uninformed trades per day")
    ax.set_ylabel("estimated PIN (± 2 se)")
    fig.tight_layout()

    plt.show()



.. image-sg:: /api/gallery/market_microstructure/information/images/sphx_glr_plot_04_pin_002.png
   :alt: plot 04 pin
   :srcset: /api/gallery/market_microstructure/information/images/sphx_glr_plot_04_pin_002.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.700 seconds)


.. _sphx_glr_download_api_gallery_market_microstructure_information_plot_04_pin.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/information/plot_04_pin.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_04_pin.ipynb <plot_04_pin.ipynb>`

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

      :download:`Download Python source code: plot_04_pin.py <plot_04_pin.py>`

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

      :download:`Download zipped: plot_04_pin.zip <plot_04_pin.zip>`


.. only:: html

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

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