Publisher Summary This chapter discusses the new approach to the classic problem of tâtonnement —the dynamic process through which markets seek to reach equilibrium. The foundation of this approach is based on several empirical observations about financial markets. The most important of which is long memory in the fluctuations of supply and demand. This is exhibited in the placement of trading orders and corresponds to long-term, slowly decaying positive correlations in the initiation of buying versus selling. It is observed in all the stock markets studied so far at very high levels of statistical significance. It appears that the primary cause of this long memory is the incremental execution of large hidden trading orders. The fact that the long memory of order flow must coexist with market efficiency has a profound influence on price formation, causing dynamic adjustments of liquidity that are strongly asymmetric between buyers and sellers. This has important consequences for market impact. This work has also important consequences about the interpretation and effect of information in financial markets. In particular, the explanation for market impact is that the shape of the impact function is determined by differences in the information content of trades.

https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1266681_code463929.pdf?abstractid=1266681&mirid=1&type=2

How markets slowly digest changes in supply and demand

The role of a dealer in securities markets is to provide liquidity on the exchange by quoting bid and ask prices at which he is willing to buy and sell a specific quantity of assets. Traditionally,...

/pdf/high-frequency-trading-in-a-limit-order-book-1ckbzw5782.pdf

High-frequency trading in a limit order book

We consider optimal execution strategies for block market orders placed in a limit order book (LOB). We build on the resilience model proposed by Obizhaeva and Wang (2005) but allow for a general shape of the LOB defined via a given density function. Thus, we can allow for empirically observed LOB shapes and obtain a nonlinear price impact of market orders. We distinguish two possibilities for modeling the resilience of the LOB after a large market order: the exponential recovery of the number of limit orders, i.e., of the volume of the LOB, or the exponential recovery of the bid-ask spread. We consider both of these resilience modes and, in each case, derive explicit optimal execution strategies in discrete time. Applying our results to a block-shaped LOB, we obtain a new closed-form representation for the optimal strategy, which explicitly solves the recursive scheme given in Obizhaeva and Wang (2005). We also provide some evidence for the robustness of optimal strategies with respect to the choice of the shape function and the resilience-type.

Optimal execution strategies in limit order books with general shape functions

We study the cause of large fluctuations in prices on the London Stock Exchange. This is done at the microscopic level of individual events, where an event is the placement or cancellation of an order to buy or sell. We show that price fluctuations caused by individual market orders are essentially independent of the volume of orders. Instead, large price fluctuations are driven by liquidity fluctuations, variations in the market's ability to absorb new orders. Even for the most liquid stocks there can be substantial gaps in the order book, corresponding to a block of adjacent price levels containing no quotes. When such a gap exists next to the best price, a new order can remove the best quote, triggering a large midpoint price change. Thus, the distribution of large price changes merely reflects the distribution of gaps in the limit order book. This is a finite size effect, caused by the granularity of order flow: in a market where participants place many small orders uniformly across prices, such large...

What really causes large price changes

Buying and selling stocks causes price changes, which are described by the price impact function. To explain the shape of this function, we study the Island ECN orderbook. In addition to transaction data, the orderbook contains information about potential supply and demand for a stock. The virtual price impact calculated from this information is four times stronger than the actual one and explains it only partially. However, we find a strong anticorrelation between price changes and order flow, which strongly reduces the virtual price impact and provides for an explanation of the empirical price impact function.

Order book approach to price impact

Buying and selling stocks causes price changes, which are described by the price impact function. To explain the shape of this function, we study the Island ECN orderbook. In addition to transaction data, the orderbook contains information about potential supply and demand for a stock. The virtual price impact calculated from this information is four times stronger than the actual one and explains it only partially. However, we find a strong anticorrelation between price changes and order flow, which strongly reduces the virtual price impact and provides for a quantitative explanation of the empirical price impact function.

https://arxiv.org/pdf/cond-mat/0311457.pdf

We analyse large stock price changes of more than five standard deviations for (i) TAQ data for the year 1997 and (ii) order book data from the Island ECN for the year 2002. We argue that a large trading volume alone is not a sufficient explanation for large price changes. Instead, we find that a low density of limit orders in the order book, i.e. a small liquidity, is a necessary prerequisite for the occurrence of extreme price fluctuations. Taking into account both order flow and liquidity, large stock price fluctuations can be explained quantitatively.

https://home.uni-leipzig.de/rosenow/Bernd_Rosenow/Financial_markets_files/largeevents.pdf

Large stock price changes: volume or liquidity?

In order to investigate the origin of large price fluctuations, we analyze stock price changes of ten frequently traded NASDAQ stocks in the year 2002. Though the influence of the trading frequency on the aggregate return in a certain time interval is important, it cannot alone explain the heavy-tailed distribution of stock price changes. For this reason, we analyze intervals with a fixed number of trades in order to eliminate the influence of the trading frequency and investigate the relevance of other factors for the aggregate return. We show that in tick time the price follows a discrete diffusion process with a variable step width while the difference between the number of steps in positive and negative direction in an interval is Gaussian distributed. The step width is given by the return due to a single trade and is long-term correlated in tick time. Hence, its mean value can well characterize an interval of many trades and turns out to be an important determinant for large aggregate returns. We also present a statistical model reproducing the cumulative distribution of aggregate returns. For an accurate agreement with the empirical distribution, we also take into account asymmetries of the step widths in different directions together with cross correlations between these asymmetries and the mean step width as well as the signs of the steps.

Analysis of aggregated tick returns: evidence for anomalous diffusion.

We analyze large stock price changes of more than five standard deviations for i) TAQ data for the year 1997 and ii) order book data from the Island ECN for the year 2002. We argue that large price changes are not due to large trading volumes. Instead, we find that extreme price fluctuations are mainly caused by a low density of limit orders stored in the order book, i.e. a small liquidity.

Philipp Weber

Papers

Order book approach to price impact

Order book approach to price impact

Large stock price changes: volume or liquidity?

Analysis of aggregated tick returns: evidence for anomalous diffusion.

Large stock price changes: volume or liquidity?