Market forces II: Liquidity Santa Fe Institute La Sapienza March 15, 2006
Empirical behavioral model: collaborators
Price impact on longer time scales
What is liquidity Roughly speaking, it is the inverse slope of the demand (- supply) curve (price impact). - Large price change for given demand -> high
- Small price change for given demand -> low
Component of supply and demand having to do with “how many people are around to trade with”. - Identified with fluctuating component
Farmer et al. 2004, Weber & Rosenow 2006 - Liquidity fluctuations drive large price changes
- time scale?
What causes volatility? Alternatively, can made an impact theory (Clarke) - Each trade has a price impact
- Price diffusion is proportional to trading volume
- Standard dogma in finance literature
We find liquidity fluctuations are more important - Gillemot, Lillo, and Farmer, “There’s more to volatility than volume”
Volatility at 2 hour timescale - AZN - Size of standing orders is power law distributed
- Standing orders executed at a fixed rate
- N standing orders, replenished when removed
What are microscopic determinants of volatility? Assume random walk model: N = number of price changes N = fn, I.e. - n = number of trades
- f = fraction that penetrate
How well does this model explain price changes? How much does each factor account for?
Explaining power law distribution of price flucutaitons Power law distribution of price fluctuations is viewed by physicists as a sign that markets are “out of equilibrium”. Now many different models: - SFI, Brock and Hommes, minority game, Lux and Marchesi, Iori, ….
- Many of them “explain stylized facts”
- Which is right?
Agent based models Most agent-based models suffer from inability to calibrate behaviors of agents. Easy to get lost in “wilderness of bounded rationality”. Behavioral economics?
Elements of model Assume continuous double auction Must model people’s actions: - Signs of orders (buy or sell)
- Prices where orders are placed
- Cancellation
Stochastic representative agent model - Model for conditional probability of above behaviors; art is to find right variables to condition on
- Order placement and cancellation fully determine prices via mechanistic rules of market
(1) Autocorrelation of order signs
Long memory raises several questions Efficiency paradox - All else equal, long-memory of orders implies strong linear predictability of prices.
- Prices aren’t predictable -- why isn’t this transmitted to prices?
- Exploiting inefficiency does not remove it.
What causes long memory?
Model of strategic order splitting Assumptions: Hidden order size is power law distributed. Hidden order arrival is IID Execution rate is independent of hidden order size. Matches empirical results based on comparison of upstairs and downstairs markets Implies lack of market clearing -- slow tatonnement
Long-memory efficiency paradox
Liquidity imbalance
Sign imbalance and liquidity imbalance vs. time
Price impact appears permanent
Strategic motivation? We understand how paradox is resolved: Why is it resolved? Our idea: Liquidity matching. E.g., suppose liquidity provider matches liquidity taker: Suggests two way “liquidity matching game”
(2) Prices for order placement Where is the best price for an order? Depends on many factors: - Time horizon of opportunity
- Market conditions
- Cost of not making transaction
- …
Situation is very different for aggressive vs. non-aggressive orders
Continuous double auction
Cancellation Total probability of cancellation is almost independent of number of orders in book Implies probability of cancellation per order is inversely proportional to number of orders.
Cancellation
Empirical behavioral model Generate order sign with order splitting model. Generate limit price with unconditional distribution p(x). Assume all orders have same size. If limit price equals or crosses opposite best, generate transaction. Cancel orders based on relative distance to opposite best, order imbalance in book, and total number of orders in book. Ad hoc: Require at least two orders in book at all times.
The ugly Simulation blows up if tick size is too big relative to price. - Due to spread dynamics, when tick size is large, market orders do not remove sufficient orders from book
- Implies we are missing a key element for these stocks, probably in cancellation model
Threshold for model convergence
Comments Flaws: - High volatility or large tick size stocks
- Not enough clustered volatility
- Not efficient w.r.t. observing order signs (doesn’t capture liquidity imbalance dynamics)
Promise: - Equation of state linking order flow and prices
- Fundamental implications for price formation
Testing prediction of spread Equation of state from mean field theory
Conclusions Regularities in order placement and cancellation. - Strategic equilibria or “behavioral regularities”?
“Explains” many aspects of price formation Raises fundamental questions about causality - Information arrival vs. internal dynamics of market
Regulatory applications - Should markets encourage provision of liquidity?
- Screening of specialists
Intermediate level of modeling - Between econometrics and microeconomics
- Divide and conquer strategy
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