Correlation of coming limit price with order book in stock markets

Abstract

We examine the correlation of the limit price with the order book, when a limit order comes. We analyzed the Rebuild Order Book of Stock Exchange Electronic Trading Service, which is the centralized order book market of London Stock Exchange. As a result, the limit price is broadly distributed around the best price according to a power-law, and it isn't randomly drawn from the distribution, but has a strong correlation with the size of cumulative unexecuted limit orders on the price. It was also found that the limit price, on the coarse-grained price scale, tends to gather around the price which has a large size of cumulative unexecuted limit orders.

Empirical regularities of order placement in the Chinese stock market

“…For the positive relative prices, we obtain α + buy = 1.66±0.07 in the range 0.003 x 0.04 for the buy orders and α + sell = 1.80 ± 0.06 in the range 0.003 x 0.04 for the sell orders. These power-law exponents are greater than those of the London Stock Exchange [26,33]. When we focus on the distributions of negative relative prices, we have α − buy = 1.72 ± 0.03 in the range 0.003 x 0.04 for buy orders and α − sell = 1.15 ± 0.02 in the range 0.003 x 0.05 for sell orders.…”

“…The two distributions for Chinese stocks illustrated in Fig. 3(a) exhibit very different behavior when compared with other stock markets [26,30,31,32,33]. The most import idiosyncratic feature is that there exist kinks around x = ±0.1, which is induced by the 10% price limit trading rule in the Chinese market.…”

“…Potters and Bouchaud investigated the relative limit price distributions for inside-the-book orders of three Nasdaq stocks (June 1 to July 15, 2002) and found that the distributions exhibit power-law tails with an exponent α = 1 [32]. Maskawa analyzed 13 rebuild order books of Stock Exchange Electronic Trading Service from July to December in 2004 on the London Stock Exchange and found that the limit prices for all orders inside the book are broadly distributed with a power-law tail whose exponent is α = 1.5 [33], which is consistent with the results of Zovko and Farmer [30]. He also presented the distribution in the negative part for more aggressive order outside the book and found that the negative part decays much faster than the positive part.…”

On the probability distribution of stock returns in the Mike-Farmer model

“…Potters and Bouchaud investigated the relative limit price distributions for inside-the-book orders of three Nasdaq stocks (June 1 to July 15,2002) and found that the distributions exhibit power-law tails with an exponent α = 1 [41]. Maskawa analyzed 13 rebuild order books of Stock Exchange Electronic Trading Service from July to December in 2004 on the London Stock Exchange and found that the limit prices for all orders inside the book are broadly distributed with a power-law tail whose exponent is α = 1.5 [42], which is consistent with the results of Zovko and Farmer [39]. He also presented the distribution in the negative part for more aggressive order outside the book and found that the negative part decays much faster than the positive part.…”

Price Dynamics in an Order‐Driven Market with Bayesian Learning

“…Takahashi et al [44] employed an agentbased approach to analyze how the asset prices are affected by the investors and investment systems that are based on behavioral finance. Maskawa [45] considered the mimetic behavior of traders in a continuous double auction market and studied the fluctuations in the stock price and the power-law tail of the distribution of returns. LeBaron et al [46] introduced an order-driven market with heterogeneous investors, analyzed the markets with and without learning and adaptation, and showed that the interaction of purely fundamentalist agents with heterogeneous estimates is sufficient to generate fat tails and volatility clustering.…”