Market forces II: Liquidity J. Doyne Farmer

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Market forces II: Liquidity

  • J. Doyne Farmer

  • 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?

  • Theory: Information

  • 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?
  • Go next step: Explain distribution in detail

Agent based models

  • Most agent-based models suffer from inability to calibrate behaviors of agents.

  • Easy to get lost in “wilderness of bounded rationality”.

    • Too many ad hoc models
  • 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

Return decomposition

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


  • 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.


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


  • 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


  • 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

Katalog: ~jdf

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