Chapter 3 The Dynamics of Price Adjustment in Experimental Random Arrival and
3.5 Results: Price Changes and the Dynamics of Price Movements
3.5.1 Limit Order Book Friction
needed for declining price movement. The need for existing orders to be cleared or changed effectively slows the process of price adjustment. If existing orders are not cancelled fast enough to reflect current market conditions, the market necessarily
“pauses” while existing orders become engaged in transactions created by new order flow. Not only does the limit order book induce serial correlation in transaction prices, Bollerslev & Domowitz have even shown that limit order books can induce serial correlation in price volatilities as well.
The extent to which the limit order book will slow price movement will depend on the relative size of market orders compared to the size of the book itself.
Interestingly, the book has the function of creating liquidity by aggregating orders over time, but this same function of liquidity provision has the side effect of slowing market adjustments.
In the experiments described here, market orders are small, nearly all are less than 20 units. Most market orders, nearly 70%, are single unit orders. There are no discernible differences between the size of market orders to buy versus market orders to sell. Both the distributions of buy and sell order book lengths are non-negative, fat tailed distributions. The means and variances of the buy and sell order book lengths are 28.4, 426.2 and 16.1, 198.6 respectively. It is therefore a priori postulated that the friction effects of market micro structure will be large.
Result 1: Price changes are relatively insensitive to excess demand between individual trades due to limit order book friction.
Support: Figure 3.3a-d shows four different scatter plots which describe how price changes at varying levels of dt, co-vary with excess demand. Result 1 is illustrated by Figure 3.3a, which shows the price changes between individual trades. On this level,—
the level at which theory most often assumes that adjustments take place—there is both visually and statistically no discernable evidence that price changes co-vary with temporal excess demand at all.
When we look at price changes over the course of 50, 100 or 300 trades
(approximately 10, 20 and 60 minutes of trading respectively), the positive relationship between excess demand and price changes appears. We also begin to notice distinct
“clusters” of data. This is partly because the larger the value of dt we choose, the higher the level of induced auto correlation between data points. The data also appears to cluster between experiments as well.
Figure 3.3: The Effect of Excess Demand for Varying Levels of dt
Source: using data from experiments 070208 through 071004
Unfortunately, limit order books are multi-dimensional market structures, characterized by a large number of parameters such as their level, depth and curvature.
Because of the dimensionality of limit orders books, showing exactly how they slow price adjustment is difficult. Figure 3.4 shows a scatter plot of dP squared versus the lengths of the buy and sell order book. Here, we refer to the “length” of an order book as the total number of units offered for sale or purchase on that order book within 200 francs of the current trading price. The length of a book is merely one dimension of an order book and does not take into account other features such as the price level of the best offer or the depth of the market at any particular price, but, for our purposes, serves as an acceptable summary statistic. The choice of 200 francs is admittedly ad hoc,
but reflects a tradeoff between including prices too far away from the market, making the measure less meaningful, and choosing a price interval so tight around the current price that there are too few units available to measure.
Also included in Figure 3.4 is an estimated hyperplane, which helps to illustrate the relationship between price volatility and limit order book friction. The regression results used to generate the hyperplane are listed in Table 3.2. As can be seen in Figure 3.4 below, the level of limit order book friction is positively related to the lengths of both order books. Large price movements/high volatility occurs systematically more often when either one or both of the limit order books is small compared to when they are large.
Table 3.2 shows the results of the regression used to create the hyperplane visible in Figure 3.4. Here, we regress squared price change on the lengths of the buy and sell order books.
Figure 3.4: Limit Order Book Friction as a Function of Order Book Depths
Source: using data from experiments 070208 through 071004
Table 3.2: Limit Order Book Friction as a Function of Order Book Depths
Variable Coefficient Confidence Interval
Constant 2087.11 [1495.45, 2678.77]
Length of Buy Order Book -18.20 [-33.56, -2.84]
Length of Sell Order Book -40.17 [-62.13, -18.22]
Source: using data from experiments 070208 through 071004
Three key features are visible in Figure 3.4. First, there are noticeably more units posted on the buy-order book than the sell order book, a feature which is true in every experiment. Second, price changes are heteroskedastic in the length of the order books,
0 20
40 60
80 100
0 40 20
60 100 80
0 2000 4000 6000 8000 10000
Length of Buy Order Book
Length of Sell Order Book
dP2
as illustrated by the slope of the estimated hyperplane drawn in the figure. The sell- order book slows upward price movement, while the buy-order book slows downward price movement. When the size of the relevant order book is sufficiently small, prices can change dramatically between trades.
The third feature visible in Figure 3.4 is that the buy-order book, while typically larger, does not increase order book friction to the same extent that the sell-order book does. As we will see later, a possible explanation for this lies in the fact that bids tend to arrive further away from current trading prices than do asks. This results in the buy order book having a steeper slope than the sell order book, and hence an asymmetric price response function.
3.5.2 Classical Models of Price Adjustment