copyright © 2000, bios group, inc. 1/10/01 dr vince darley, ocado ltd [email protected] in...

Copyright © 2000, Bios Group, Inc.

1/10/01

Dr Vince Darley, Ocado [email protected]

In collaboration with Sasha Outkin, Mike Brown, Al Berkeley, Tony Plate, Frank Gao, Richard Palmer, Isaac Saias, Mary Montoya

AMLCF workshop July 20, 2009

Agent-Based Modeling of the Nasdaq Stock Market and Predicting the

Impact of Rule Changes


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Problem Statement

• Nasdaq had to consider decimalization and its impacts in 1998.

• How reducing the tick size may affect the market behavior? Why should it have any effect?– How a change to decimals can be modeled?– What is the mechanism through which changed tick

size would affect the market? • Via individual market participants (agents) decisions?• Via changes to market infrastructure– order matching?

– Given specific mechanisms, what other (second order?) effects may occur?


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• Investigate effects of possible policy and environment changes:

– Ex: Evaluate the effects of changing the tick size (decimalization) and of parasitism

• Evaluate the influence of market rules and structure on market dynamics and strategies

• Demonstrate that that simulated market participants and aggregate market parameters are “sufficiently similar” to those in the real world to validate model empirically

Goals


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Problem Architecture


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Construct and analyze an agent-based model of the market:

• Populate with agents (investors and market makers).

• Simulate market infrastructure and rules.

• Calibrate with the actual stock market data:

- To ensure that the simulated distribution of trade sizes, volumes, prices and other statistical parameters is similar to that observed in the real world.

- To simulate real-world behaviors of and interactions of market makers and investors using data sets of historical quotes and trades.

• Design it to reflect the look and feel of the then existing Level 2 Nasdaq system.

Model Implementation


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Philosophical Observations

• By definition, almost tautologically, “the market” is an agent-based system.

• The question is what predictive power such a model representation has? For what kinds of problems?

• What are the theoretical reasons for agent-based representation to work?

• Crucial differences from existing approaches: – Modeling processes and mechanisms, rather than the outcomes

and states.– Heterogeneous rather than homogenous model– Focus on emergent behaviors – potentially, counter intuitively,

invalidating the initial model.• Nasdaq decimalization study: an empirical example.

– Study done during 1998-2000.– Decimalization occurred in April 2001.


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Agent Details

• Market makers

• Investors

• Market Agent Features:– Autonomous– Adaptive/learning/handcrafted strategies– Various levels of sophistication/adaptability/

access to information


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Simulation Basics

• Market agents are trading in a single stock• Investors have a price target which follows a

Poisson process, random walk, etc.

• Investors: – Receive noisy information about this target– Decide whether to trade by

• Comparing this target with available price• Incorporating market trends• Performing sophisticated technical trading, etc.

• Market makers:– Receive buy and sell orders – Must learn how to set their quotes profitably


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Investor – Market Maker Interaction and Parasitism

Parasitic strategy:– Attempts to undercut the current bid/offer by a

small increment (tick size)– Is not a major source of liquidity for the market


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Market MakersLimit OrderBook/ECN

Exchange,Rules

Database

Model Structure

Investors

Nasdaq


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Model Features

• Trading in:– Market orders– Limit orders– Negotiated orders

• Market rules/ parameters:– Order handling rules– Tick size, etc.

• Market agents’ modes of interaction:– Quote Montage– ECNs– Limit order books– Preferencing, etc.


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Model Calibration

• Calibrated the model to• Individual strategies

• Aggregate market parameters

• Simulated strategies are able to replicate the real-world ones (with precision up to 60-70%)

• Created self-calibrating software to use data as it comes in


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Questions Investigated

• Effects of tick-size changes and parasitism

• Market dynamics effects:– Presence and origin of “fat tails”– Spread clustering and its causes

• Effects of market maker and investor learning and strategy evolution


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Tick size effects

As tick size is reduced, parasitic strategies increasingly impede price discovery / market’s ability to generate useful information

Standard Deviation of (Price - True Value)

11.051.1

1.151.2

1.251.3

1.351.4

1.45

4 100

Inverse of the tick size

Sta

nd

ard

De

via

tio

n

Simulation with asmall number ofparasites

Simulation withsignificant number ofparasites


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Tick Size Effects, Many Parasites

Tick size 1/100Tick size 1/16


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Fat Tail Results

• “Fat tails”:– A large probability of extreme events by

comparison with a Gaussian distribution

• Origins are uncertain– Herd effects, other?

• Our model generates fat tails with no herd effects


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Fat Tails in SimulatedAverage Price Dynamics

-0.2-0.19-0.18-0.17-0.16-0.15-0.14-0.13-0.12-0.11-0.1-0.09-0.08-0.07-0.06-0.05-0.04-0.03-0.02-0.010.0.010.020.030.040.050.060.070.080.090.10.110.120.130.140.150.160.170.180.190.2

5000

10000

15000

20000

freq

uenc

y

difference in the logarithms of the average price


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Time Correlations and Fat Tails

The fat tails seem to disappear when the data points are taken far apart (50 periods here)

-0.02-0.019-0.018-0.017-0.016-0.015-0.014-0.013-0.012-0.011-0.01-0.009-0.008-0.007-0.006-0.005-0.004-0.003-0.002-0.0010.0.0010.0020.0030.0040.0050.0060.0070.0080.0090.010.0110.0120.0130.0140.0150.0160.0170.0180.0190.02

5000

10000

15000

20000

difference in the logarithms of the average price

freq

uenc

y


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Why Fat Tails in the Simulation?

• Possible explanations:– Interaction and self-interaction through

price

– Existence of spread

– Memory of traders, investors, etc.

• No explicit “herd” effects included


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Spread Clustering

• Nasdaq dealers collusion accusations -Christie and Schulz (1994)

• SEC investigation into quoting behavior on Nasdaq (1996) and subsequent settlement

• Clustering in various financial markets - Hasbrouck (1998)


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Spread Clustering

• Spread = difference between smallest offer and largest bid

• Spread clustering occurs when some spread values occur much more frequently than others

Fre

qu

ency

117€€€€€€€€169€€€€€819€€€€€€€€165€€€€€421€€€€€€€€1611€€€€€€€€823€€€€€€€€163€€€€€225€€€€€€€€1613€€€€€€€€827€€€€€€€€167€€€€€429€€€€€€€€1615€€€€€€€€831€€€€€€€€16

233€€€€€€€€1617€€€€€€€€835€€€€€€€€169€€€€€437€€€€€€€€1619€€€€€€€€839€€€€€€€€165€€€€€241€€€€€€€€1621€€€€€€€€843€€€€€€€€1611€€€€€€€€445€€€€€€€€1623€€€€€€€€847€€€€€€€€16

50

100

150

200

250

Spread size

Fre

quen

cy

Simulation data


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Importance of Spread Clustering

• Emergent property in the simulation: no collusion is present, yet the spread clustering occurs

• Real-world issue: Nasdaq, Forex


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0 0.5 1 1.5 2 2.5 3

x 104

0

1

2

3

4

5x 10

4

Spread Learning DealerNew Volume Dealer Basic Inv Dealer

Learning in the Simulation

• Spread Learning market maker is the most profitable dealer on the market under many circumstances

• Known exceptions: high volatility, tough parasites

time

Ass

ets

$


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Phase Transitions


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1. Decimalization (tick size reduction) will negatively impact the price discovery process.

2. Ambiguous investor wealth effects may be observed. (Investors’ average wealth may actually decrease in the simulation, but the effect is not statistically significant).

3. Phase transitions will occur in the space of market-maker strategies.

4. Spread clustering may be more frequent with tick size reductions.

5. Parasitic strategies may become more effective as a result of tick size reductions.

6. Volume will increase, potentially ranging from 15% to 600%.

Summary of Findings


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Tick size was officially reduced from a 1/16th to $.01 (in phases) in March, 2001.

Nasdaq economists captured actual data from this transition and put the findings in their Economic Research study report.

BiosGroup compared our model’s results with the findings from the Nasdaq report.

Comparisons with Data


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1. Decimalization (tick size reduction) will negatively impact the price discovery process.

2. Ambiguous investor wealth effects may be observed. (Investors’ average wealth may actually decrease in the simulation, but the effect is not statistically significant).

3. Phase transitions will occur in the space of market-maker strategies.

4. Spread clustering may be more frequent with tick size reductions.

5. Parasitic strategies may become more effective as a result of tick size reductions.

6. Volume will increase, potentially ranging from 15% to 600%.

5 of the 6 likely outcomes actually occurred.

Comparisons with Data (Cont.)


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Nasdaq Book


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Longer-Term Effects

• Not only the participants strategies change, but the market institutions change as the result.


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Future Directions

• Systematising the work• Best features of ABMs combined with best features

of more traditional approaches.– ABMs to explain / derive parameters of stochastic

processes in finance. For example, what features of agents / institutions give raise to specific market behaviors?

• How strongly macro laws are coupled with the micro laws?– Is it possible to have the same macro behaviors when

micro behaviors are different?


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Summary and Conclusions

• Predicting complex outcomes is possible!

• Building and validating any “big ABM model” such as this is difficult and time-consuming

• Machine learning agents were an important part of that.

• Ensuring sufficient accuracy and rigour is very difficult. Careful involvement and feedback from market participants/regulators was essential – one benefit of this being (expensive) paid consulting work was that this was not optional

Any questions?

copyright © 2000, bios group, inc. 1/10/01 dr vince darley, ocado ltd [email protected] in...

Documents

market dynamics

market behavior

nasdaq stock market

bios group

interactions of market

aggregate market parameters

influence of market

actual stock market