On the origin of power-law tails in price fluctuations

By J. D. Farmer, Fabrizio Lillo. 2003

162 citations recorded by the source corpus.

In a recent Nature paper, Gabaix et al. \cite{Gabaix03} presented a theory to explain the power law tail of price fluctuations. The main points of their theory are that volume fluctuations, which have a power law tail with exponent roughly -1.5, are modulated by the average market impact function, which describes the response of prices to transactions. They argue that the average market impact function follows a square root law, which gives power law tails for prices with exponent roughly -3. We demonstrate that the long-memory nature of order flow invalidates their statistical analysis of market impact, and present a more careful analysis that properly takes this into account. This makes it clear that the functional form of the average market impact function varies from market to market, and in some cases from stock to stock. In fact, for both the London Stock Exchange and the New York Stock Exchange the average market impact function grows much slower than a square root law; this implies that the exponent for price fluctuations predicted by modulations of volume fluctuations is much too big. We find that for LSE stocks the distribution of transaction volumes does not even have a power law tail. This makes it clear that volume fluctuations do not determine the power law tail of price returns.

Subfields: Condensed Matter Physics, Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/1c6a4027739960d02b8ac9f10d308ecf42ff7152

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In Condensed Matter Physics

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Citations in the corpus

The Long Memory of the Efficient Market (2003, background): “Once we adjust for scale, this seems to be roughly the same for all the stocks in the sample (see also [30]).”
Limit order books (2010, background): “For example, the effective sample size of a long-memory process is significantly smaller than the number of data points, so statistical estimators often converge at an extremely slow rate (Farmer and Lillo 2004).”
The Impact of Heterogeneous Trading Rules on the Limit Order Book and Order Flows (2007, background): “11 (right) we find instead an almost linear relationship between 11 the Hill exponent of returns distributions and the Hill exponent of the gap distribution, indicating, as suggested by Farmer and Lillo (2004), that the presence of large gaps at the best price is what drives large price changes.”