Transcript Bios Group Nasdaq Market Simulation

Agent-Based Modeling of the Nasdaq Stock
Market and Predicting the
Impact of Rule Changes
Dr Vince Darley, Ocado Ltd
[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
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1/10/01
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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Goals
• 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
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Problem Architecture
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Model Implementation
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.
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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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Model Structure
Nasdaq
Limit Order
Book/ECN
Market Makers
Exchange,
Rules
Investors
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Database
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Model Features
• Trading in:
– Market orders
– Limit orders
– Negotiated orders
• Market rules/
parameters:
• Market agents’ modes of
interaction:
–
–
–
–
Quote Montage
ECNs
Limit order books
Preferencing, etc.
– Order handling rules
– Tick size, 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 6070%)
• 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
Standard Deviation of (Price - True Value)
1.45
1.4
1.35
1.3
1.25
1.2
1.15
1.1
1.05
1
Simulation with a
small number of
parasites
Simulation with
significant number of
parasites
4
100
Inverse of the tick size
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Tick Size Effects, Many Parasites
Tick size 1/16
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Tick size 1/100
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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 Simulated
Average Price Dynamics
frequency
20000
15000
10000
5000
- -0 0-. .02- 1.0-91.0-81.0-71.0-61.0-51.0-41.0 3-1.-0210-.1.0-1 0.0-90.0-80.0-70.0-60.0-50.0-40.0 30. 020 ..10 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70. 0800.9.01 1.0 11.0 21.0 31.0 41.0 51.0 61.0 71. 081 .9 2
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)
frequency
20000
15000
10000
5000
difference in the logarithms of the average price
- 0 .-002. 0- 10 9. 0- 10 8. 00
1.
7 0- 10 6. 0- 10 5. 0- 10 4. 00
1.
3 0- 10 2. 0-101. -0 01 . 0
-09
. 0- 00 8. 0- 00 7. 0- 00 6. 00.
5 0- 00 4. 0- 00 3. 0- 00 2. 0 0 0
1 .0 . 0 0 .
1 0 00 2. 0 00 3. 0 0 4
. 0 00 5. 0 00 6. 0 00 7. 0 0 8
. 0 0 09 . 001. 0 10 1. 0 1
02
. 0 10 3. 0 10 4. 0 10 5. 0 0
1.
6 0 10 7. 0 10 8. 0 109. 0 2
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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
Simulation data
200
Frequency
Frequency
• Spread = difference
between smallest offer
and largest bid
• Spread clustering
occurs when some
spread values occur
much more frequently
than others
250
150
100
50
1 7 9 1 9 5 2 1 1 12 3 3 2 Spread
51 32 7 7 2 91 53 1 2 3 3size
1 7 3 5 9 3 7 1 93 9 5 4 12 1 4 3 1 14 5 2 3 4 7
1€€€€€€€
€€€€€ €€€ €€€€€€€€€ €€€€€ €€€€€€€€€€€€€€€€€ €€€€€€€€€€€€
€€ €€€€€€ €€€€€€€€€€€€€€€ €€€€€ €€€€€€€€€€€€€€€€€ €€€€€€€€€€€€€€
€ €€€€€€€€€€€€€€€€€€€€ €€€€€€€€€€€€€€€€€ €€€€€€€€€€€€
€€ €€€€€€ €€€€€€€€€€€
€€€€€€€€€€€€€€€€€€€€€€€€€€€€€ €€
1 6 8 1 6 41 6 81 6 2 1 6 8 1 6 41 6 81 6 1 6 8 1 6 41 6 8 1 6 2 1 6 8 1 6 41 6 8 1 6
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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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Learning in the Simulation
4
5
x 10
Spread Learning Dealer
New Volume Dealer
Basic Inv Dealer
Assets $
4
3
2
1
0
0
0.5
1
1.5
time
2
2.5
3
4
x 10
• Spread Learning market maker is the most profitable
dealer on the market under many circumstances
• Known exceptions: high volatility, tough parasites
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Phase Transitions
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Summary of Findings
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%.
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Comparisons with Data
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.
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Comparisons with Data (Cont.)
5 of the 6 likely outcomes actually occurred.
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%.
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1/10/01
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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1/10/01
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