.. _sphx_glr_api_gallery_market_microstructure_information:

Information
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How informed traders move prices, and how to measure their presence.


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


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

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    <div class="sphx-glr-thumbcontainer" tooltip="Albert Kyle (1985) placed an insider who knows the liquidation value v \sim N(p_0, \sigma_v^2) in a market with noise traders whose orders u \sim N(0, \sigma_u^2) camouflage it. A competitive market maker sees only the total flow y = x + u and sets p = E[v \mid y] = p_0 + \lambda y. In equilibrium">

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  .. image:: /api/gallery/market_microstructure/information/images/thumb/sphx_glr_plot_01_kyle_thumb.png
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  :doc:`/api/gallery/market_microstructure/information/plot_01_kyle`

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      <div class="sphx-glr-thumbnail-title">Kyle's insider and the price impact lambda</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Lawrence Glosten and Paul Milgrom (1985) explained the spread with no inventory and no costs. A competitive dealer trades one unit at a time with traders who are informed with probability \alpha. Since a buy is more likely to come from someone who knows the value is high, the dealer sets the ask to E[V \mid \text{buy}] and the bid to E[V \mid \text{sell}], losing to the informed exactly what it gains from the uninformed. Each trade updates the dealer&#x27;s belief by Bayes&#x27; rule, so prices are a martingale that converges to the truth.">

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  .. image:: /api/gallery/market_microstructure/information/images/thumb/sphx_glr_plot_02_glosten_milgrom_thumb.png
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  :doc:`/api/gallery/market_microstructure/information/plot_02_glosten_milgrom`

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      <div class="sphx-glr-thumbnail-title">Glosten and Milgrom: a spread from adverse selection alone</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Joel Hasbrouck (1991) measured the information in trades with a vector autoregression of quote revisions r_t and signed trades x_t. Order flow is persistent and quotes also react to inventory, so a trade&#x27;s immediate price effect overstates what it reveals. The cumulative impulse response of the quote to an unexpected trade separates the two: it settles at the permanent impact, the information content, after the transitory part has decayed.">

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  .. image:: /api/gallery/market_microstructure/information/images/thumb/sphx_glr_plot_03_hasbrouck_var_thumb.png
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  :doc:`/api/gallery/market_microstructure/information/plot_03_hasbrouck_var`

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      <div class="sphx-glr-thumbnail-title">Hasbrouck's trade-impact VAR</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Easley, Kiefer, O&#x27;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 \alpha), informed traders add rate \mu to one side; otherwise only uninformed buys and sells arrive, at rates \varepsilon_b, \varepsilon_s. The fitted mixture gives the share of trades that are informed, \mathrm{PIN} = \alpha\mu / (\alpha\mu + \varepsilon_b + \varepsilon_s). Their finding: thinly traded stocks have a higher PIN, which explains their wider spreads.">

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  .. image:: /api/gallery/market_microstructure/information/images/thumb/sphx_glr_plot_04_pin_thumb.png
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  :doc:`/api/gallery/market_microstructure/information/plot_04_pin`

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      <div class="sphx-glr-thumbnail-title">Easley, Kiefer, O'Hara and Paperman: the probability of informed trading</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="High-frequency markets have too many trades and too few days for the PIN likelihood. Easley, López de Prado and O&#x27;Hara (2012) measured order imbalance in volume time instead: cut the trading record into buckets of equal volume, split each one-minute bar&#x27;s volume into buys and sells by bulk volume classification, V^B = V\Phi(\Delta P/\sigma_{\Delta P}), and average |V^B - V^S|/V over the last 50 buckets. Their VPIN rose for hours before the flash crash of 6 May 2010.">

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  .. image:: /api/gallery/market_microstructure/information/images/thumb/sphx_glr_plot_05_vpin_thumb.png
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  :doc:`/api/gallery/market_microstructure/information/plot_05_vpin`

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      <div class="sphx-glr-thumbnail-title">VPIN: flow toxicity in volume time</div>
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.. toctree::
   :hidden:

   /api/gallery/market_microstructure/information/plot_01_kyle
   /api/gallery/market_microstructure/information/plot_02_glosten_milgrom
   /api/gallery/market_microstructure/information/plot_03_hasbrouck_var
   /api/gallery/market_microstructure/information/plot_04_pin
   /api/gallery/market_microstructure/information/plot_05_vpin