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A Theory for Market Impact: How Order Flow Affects Stock Price

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  • Austin Gerig

Abstract

It is known that the impact of transactions on stock price (market impact) is a concave function of the size of the order, but there exists little quantitative theory that suggests why this is so. I develop a quantitative theory for the market impact of hidden orders (orders that reflect the true intention of buying and selling) that matches the empirically measured result and that reproduces some of the non-trivial and universal properties of stock returns (returns are percent changes in stock price). The theory is based on a simple premise, that the stock market can be modeled in a mechanical way - as a device that translates order flow into an uncorrelated price stream. Given that order flow is highly autocorrelated, this premise requires that market impact (1) depends on past order flow and (2) is asymmetric for buying and selling. I derive the specific form for the dependence in (1) by assuming that current liquidity responds to information about all currently active hidden orders (liquidity is a measure of the price response to a transaction of a given size). This produces an equation that suggests market impact should scale logarithmically with total order size. Using data from the London Stock Exchange I empirically measure market impact and show that the result matches the theory. Also using empirical data, I qualitatively specify the asymmetry of (2). Putting all results together, I form a model for market impact that reproduces three universal properties of stock returns - that returns are uncorrelated, that returns are distributed with a power law tail, and that the magnitude of returns is highly autocorrelated (also known as clustered volatility).

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File URL: http://arxiv.org/pdf/0804.3818
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 0804.3818.

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Date of creation: Apr 2008
Date of revision: Jul 2008
Handle: RePEc:arx:papers:0804.3818

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Web page: http://arxiv.org/

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Cited by:
  1. Karol Wawrzyniak & Wojciech Wi\'slicki, 2013. "Grand canonical minority game as a sign predictor," Papers 1309.3399, arXiv.org.
  2. Bence Toth & Imon Palit & Fabrizio Lillo & J. Doyne Farmer, 2011. "Why is order flow so persistent?," Papers 1108.1632, arXiv.org.
  3. Bence Toth & Fabrizio Lillo & J. Doyne Farmer, 2010. "Segmentation algorithm for non-stationary compound Poisson processes," Papers 1001.2549, arXiv.org, revised Feb 2011.
  4. repec:hal:wpaper:hal-00745317 is not listed on IDEAS
  5. Jean-Philippe Bouchaud & J. Doyne Farmer & Fabrizio Lillo, 2008. "How markets slowly digest changes in supply and demand," Papers 0809.0822, arXiv.org.
  6. Fabrizio Pomponio & Frédéric Abergel, 2013. "Multiple-limit trades : empirical facts and application to lead-lag measures," Post-Print hal-00745317, HAL.
  7. Jean-Philippe Bouchaud, 2011. "Panel Statement: The endogenous dynamics of markets: price impact and feedback loops," Chapters, European Central Bank, European Central Bank.
  8. Igor Skachkov, 2013. "Market Impact Paradoxes," Papers 1312.3349, arXiv.org.

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