Fluctuations and response in financial markets: the subtle nature of ‘random’ price changes

By Jean-Philippe Bouchaud, Y. Gefen, Marc Potters, Matthieu Wyart. 2003

513 citations recorded by the source corpus.

Using trades and quotes data from the Paris stock market, we show that the random walk nature of traded prices results from a very delilcated interplay between two opposite tendencies: long-range correlated market orders that lead to super-diffusion (or persistence), and mean revrting limit orders that lead to sub-diffusion (or anti-persistence). We define and study a model where the price, at any instant, is the result of the impact of all past trades, mediated by a non-constant ‘propagator’ in time that describes the response of the market to a single trade. Within this model, the market is shown to be, in a precise sense, at a critical point, where the price is purely diffusive and the average response function almost constant. We find empirically, and discuss theoretically, a fluctuation-response relation. We also discuss the fraction of truly informed market orders, that correctly anticipate short-term moves, and find that it is quite small.

Subfields: Computer Networks and Communications, Condensed Matter Physics, Economics and Econometrics

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Citations in the corpus

Universal features of price formation in financial markets: perspectives from deep learning (2018, positive): “There is a trove of empirical evidence going against this hypothesis, and pointing to long-range dependence in financial time series (Mandelbrot et al. 1997, Bouchaud et al. 2004, Lillo and Farmer 2004, Bacry et al. 2008, Taranto et al. 2014).”
Optimal execution with non-linear transient market impact (2014, background): “[15, 14]; the above continuous time formulation (2.”
An empirical behavioral model of liquidity and volatility (2007, background): “Journal of economic dynamics and control, 21(8-9), 1471–1491.”
The Price Impact of Order Book Events (2010, unknown): “[9] associated the decay of price impact of trades with limit orders, arguing that there is a “delicate interplay between two opposite tendencies: strongly correlated market orders that lead to super-diffusion (or persistence), and mean reverting limit orders that lead to sub-diffusion (or anti-pers”
Relation between bid–ask spread, impact and volatility in order-driven markets (2006, methodology): “Such a strong relation was first noted for the case of FranceTelecom (Bouchaud et al. 2004), and independently on the stocks of the FTSE-100 (Zumbach 2004), but no theoretical argument was given in favour of this relation.”
The price impact of order book events: market orders, limit orders and cancellations (2009, methodology): “…express exactly the variance of the price at lag ‘, D(‘)¼h(ptþ‘ pt)2i, in terms of the G’s and the C’s, generalizing the corresponding result obtained by Bouchaud et al. (2004): Dð‘ Þ ¼ hðptþ‘ ptÞ2i ¼ X 0 n5‘ X 1 G 1 ð‘ nÞ2Pð 1Þ þ X n40 X 1 ½G 1ð‘þ nÞ G 1ðnÞ 2Pð 1Þ þ 2 X 0 n5n 05‘ X 1, 2 G 1ð‘…”
Anomalous price impact and the critical nature of liquidity in financial markets (2011, background): “However, we know from empirical data [3,21,26] that the signs of transactions t are in fact long-ranged correlated, i.”
No-dynamic-arbitrage and market impact (2010, unknown): “…1: By considering the tail of the limit-order book and a high trading rate price manipulation strategy, we deduced that :¼ 2 log 3 log 2 0:415: ð15Þ Bouchaud et al. (2004) have shown that, for a stateindependent market impact process like (1) with G( ) , the exponent of the power law of…”
Does herding affect volatility? Implications for the Spanish stock market (2012, background): “Bouchaud et al. (2004) find that the sign of the trades shows surprisingly long-range correlations that can be subtly ‘corrected’ by a mean reversion process in prices induced by liquidity providers.”
Optimal execution strategies in limit order books with general shape functions (2007, background): “In fact, it has been observed in the empirical studies [9, 17, 10, 21] that average shapes of typical order books have a maximum at or close to the best quotes and then decay as a function of the distance to the best quotes, which would conform to our assumption.”