Both the direction of temporary equilibrium prices and the direction of the FCE price affect the price movement. The total share of insiders depends on the position of the FCE price in relation to the FIP.
Inventory and Adverse Selection Effects in a Limit Order Market
Introduction
Most of the literature on empirical microstructure related to limit order markets focuses on predictable patterns in order flow and the interactions between volume, market depth, liquidity and volatility (Bias, Hillion and Spatt, 1995), (Danielson and Payne, 2001 ), (Ahn, Bae and Chan, Limit Orders, Depth and Volatility: Evidence from the Hong Kong Stock Exchange, 2001), (Bollerslev & Melvin, 1994). We note and outline the problems associated with the tendency for trade initiation to remain on the same side of the market.
The Theory of the Bid-Ask Spread
- Effective Spreads and Quoted Spreads
- The Roll Model of the Effective Spread
- Glosten/Milgrom and Ho/Stoll
- The Stoll Decomposition of the Quoted Spread
Huang & Stoll, 1997) generalized the methodology of (Stoll, 1989) using trade indicator models to estimate bid-ask spread components for NYSE data. Combining equations (1.4) and (1.6), Huang and Stoll derive the basic trade indicator model in which changes in the bid-ask spread are modeled as a function of delayed order flow and expected order flow.
The ASX and Limit Order Markets
- Quality and Characteristics of ASX Data
- Applicability of Inventory and Adverse Selection Models
As a result, when the model is first estimated, Huang and Stoll find that the share of the half-spread due to adverse selection is negative. All consecutive trades initiated at the bid (ask) price and associated with the same bid (ask) ID number are considered part of the same trade.
Empirical Inconsistencies of the Roll and Stoll/Huang Stoll Models
- Quoted and Effective Spreads in ASX Data
- Explaining Differences Between Quoted and Effective Spreads
- The Tendency for Reversals
Each of the theories discussed in (Stoll, 1989) assumed that the probability of a change is at least .5. Basically, many small trades can accumulate on one side of the market before they affect the probability of a change in a meaningful way.
Methodology
- Predicting Changes in the Level and Slope of the Order Book
- A Graphical Interpretation
- Predicting Expected Order Flow
Similarly, the amount the bid price falls after a run against the bid price is the unrealized part of the flow spread after a bid run. After each run, we measure the amount the price changed on the same side of the market as the previous trade.
Results
- The Level of the Bid-Ask Spread
- The Slope of the Bid-ask Spread
For example, the smallest effect of unexpected shocks to the asking price at the asking price level was a whole order of magnitude smaller than the average effect among stocks. High transaction volumes at both bid and ask prices appear to increase market depth and liquidity.
Conclusions
Principles of Continuous Price Determination in an Experimental Environment
Introduction
Other researchers outside of finance, such as (Goode & Sunder, 1993) and (Brewer, Jiang, & Plott, 2003) show that price convergence to the Walrasian equilibrium can be achieved with "zero intelligence". The fourth section develops principles that are natural generalizations of classical principles and illustrates how they apply to the complex random arrival and departure environment.
The Random Arrival and Departure Environment
- Preference Inducement Methodology
- Incentive Parameter Structure (Latent Incentives and Realized Incentives)
Incentives come in the form of private orders to buy from the researchers (i.e. costs for potential sellers) or private orders to sell to the researchers (i.e. redemption values for potential buyers) in a market open only to the agent for whom the orders are intended. target (i.e. the agent's private market)3. The basic parameters are called 'latent buyer incentives' and 'latent seller incentives'. The latent buyer incentives consist of a probability density function gb(x), where x is a price.
Market Institutions
Models and Theory
- Temporal Equilibrium
- Flow Competitive Equilibrium
- Trader Behavior
Flow competitive demand (FCD) and flow competitive supply (FCS) curves, on the other hand, specify the arrival rates of buyers (sellers) with reserves above (below) a given price. Flow competitive supply and flow competitive demand reflect two.. components: 1) the distribution of latent reservation prices for buyers and sellers, and 2) the relative arrival rates of buyers and sellers. A flow-competitive equilibrium (FCE) is defined by 1) a price PFCE at which the arrival rate of buyers with reservation prices at or above PFCE equals the arrival rate of sellers with reserve prices at or below PFCE, and 2) a rate of trade related to PFCE.
All trades occur near or at the FCE price. Almost 100% of the additional surplus due to expectations has been realized.
Experimental Procedures and Design
- Experimental Procedures
- Experimental Design
However, due to the random nature of the environment and the slower speed of the computer, the actual market arrival rates were typically slower than the parameterized rates. The total arrival prices per minute are the arrival prices per person indicated in the table times the number of. The number of incentives sent to the market in Table 2.2 includes only those incentives that were on the market or arrived on the market during the interval in which the trader they were intended for was active.
In most experiments, adjusting for when traders were present in the market was not significant.
Results
- Overview
- Price Levels
- Efficiency
- Bid and Ask Placement/Improvement: Evidence of Expectations Formation . 70
Coincidentally, the two experiments with changing rates were the only experiments in which the FCE price was not equal to the mean of the distribution of latent incentives. The distribution modes in Figures 15 and 16 are generally slightly below the FCE price. Given both of these properties, entropy is a natural metric for measuring the “focal concentration” of the distribution of offer prices.
What we observe is that as long as the FCE remains constant, the entropy of the distribution decreases.
The Dynamics of Price Adjustment in Experimental Random Arrival and
Introduction
Experimental research on price dynamics in continuous double auctions began with (Smith V., 1962) and (Smith V., 1965), who investigated the Walrasian theory that the speed of price movements was driven by the level of excess demand. They test modifications of the Walrasian hypothesis and find support that both the level and the derivatives of excess demand can play a role in price adjustment. We begin with a discussion of the important, if theoretically neglected, role played by price friction, which we relate to microstructural features of the continuous double-auction market.
We then examine univariate and multivariate classical theories of price dynamics using time series models.
Trading Environment and Known Results
- Incentive Parameter Structure (Latent Incentives and Realized Incentives)
- Types of Equilibrium
- Known Results
The FCE price is the price at which the supply flow equals the demand flow. AP1 Result 4: (i) Traded prices are distributed around both FCE and TE prices. ii) When trading prices deviate from the FCE price, they tend to deviate towards the TE price. AP1 Result 5: Both the direction of the temporal equilibrium prices and the direction of the FCE price influence the price movement.
AP1 Result 6: The mean squared error for price change forecasts based on the distance of current trade prices from the temporary equilibrium price and the FCE price declines for long forecast horizons.
Experiments Studied
At the end of each constant FCE interval, the FCE price moves up or down according to a discrete random walk by a certain amount. One realization of this process is shown in Figure 3.1, which shows the time paths of FCE, TE, and traded prices. In all the experiments presented here, subjects were told that incentives in their private markets would arrive randomly according to a certain rate and from some distribution that could change over time.
Description of Data
- Fat-Tails
- Conditional Heteroskedasticity
- Negative Autocorrelation
The distribution of price changes pooled from all experiments has an excess kurtosis of about 33, well above the kurtosis of the normal distribution. Evidence of conditional heteroskedasticity can be found in Figure 3.2c-d, which shows the ACF and PACF of the quadratic series of price changes. The first lag of the ACF is about 0.25, a value that would be expected if prices just randomly bounced back and forth between a fixed bid and ask price (Roll 1984).
At first glance, one might assume that this negative autocorrelation is due to the bid-ask spread as predicted by Roll, but upon closer examination, the second and third lags of the ACF as well as lags 1–7 of the PACF appear to be significant as well, a result that is not predicted by Roll's bid-ask bounce theory.
Results: Price Changes and the Dynamics of Price Movements
- Limit Order Book Friction
- Classical Models of Price Adjustment
- The Marshallian Nature of RA Environments
Here we regress squared price change on the length of the buy and sell order books. When the size of the relevant order book is sufficiently small, prices can change dramatically between trades. The first term is an interaction of the negative component of the independent variable by the size of the purchase order book.
The second is the interaction between the positive component of the explanatory variable and the size of the sales order book.
Conclusions
Large lower prices relative to any concept of equilibrium are likely to result in a faster rate of buy-side market orders, higher bid prices, and greater opportunity for bid improvement. Similarly, a large overvaluation relative to one equilibrium or the other is likely to result in a faster market order rate on the sell side, lower asking prices, and a large opportunity for improvement in the asking price.
Experimental Random Arrival Markets with Competing Insiders
Introduction
First, it is usually assumed that the market is created by (an) uninformed market maker(s). First, is information held by competitive insiders reflected in information efficiency and pricing.
Background and Trading Environment
For example, if private bids to buy and sell arrived at the market at a rate of 4 bids per minute, and the bids were uniformly distributed between 0 and 200 for the first half of the experiment and uniformly between 200 and 400 for the second half second. Given the above parameters, the FCE prices for the first and second half of the experiment would be 100 francs and 300 francs respectively, and trading would occur at a rate of 2 trades per minute. Since insiders know that prices will be higher in the second half of the experiment, the problem they face is that they would like to buy cheap units at the beginning of the experiment and sell them for more money during the second half.
This increases prices at the beginning of the experiment and decreases prices during the second half of the experiment, eroding insider profits.
Information Diffusion: Theory and Measurement
- A Theory of Information Diffusion
- Measuring Information Diffusion
Note that, assuming that all market speculation up to a certain point in time is due to insiders and that insiders interpret them. However, outsiders cannot identify the individual values of 𝑖∈𝑈𝑆𝑖𝑢(𝑝) and 𝑖∈𝑈𝑆𝑖 More aggregate surplus is available by trading at the full information price with a higher transaction rate than trading at a lower rate. slow for each of the individual FCE prices.
Since the amount of surplus available from trading at each of the individual FCEs does not depend on information, we can subtract this amount from the actual level of surplus extracted during an experiment to obtain the amount of rent achieved as to obtain as a result of.
Results
- Informational Efficiency
- Price Levels
- Inventories
- The Effects of Order Flow on Price Changes
The influence of FCE away from the full information price is likely the result of uncertainty about the full information price of non-insiders. Surprisingly, we find that traded prices continue to be skewed towards the FCE price even in the last period of each experiment. For each interval, we measure the average change in inventory per trades for both insiders and uninformed traders and the FIP and FCE price at the beginning of the interval.
Interestingly, relative to the overall level of speculation, outsider inventory accumulation does not depend at all on the relative location of the FCE relative to the FIP.
Conclusions
Bibliography
Expensive bidding and equilibrium properties of a multi-unit double auction under unpredictable changes in demand and supply. Dual auction markets with stochastic bid-ask schedules: Call markets and continuous auction trading mechanisms.
Appendices
Appendices from Chapter1
- Predicting the Size of Trade Initiation Runs
- Forecasting Variance of Run Sizes
- VAR Regressions of Bid-Ask Spread and Order Book
Appendices from Chapter 2
- Instructions for Random Arrival Experiments
Appendices from Chapter 4
- Help Information Given to All Traders
- Hand Outs for Insiders and Uninformed Subjects
