oliver hein, goethe university, frankfurt, financial agent-based computational economics (finace)...

Oliver Hein, Goethe University, Frankfurt, Financial Agent-based Computational Economics (FINACE)

Kommunikations-Netzwerk-Topologie und

Marktverhalten

15. Februar 2008

von

Oliver Hein

Forschungskolloquium 2008


1. Frankfurt Artificial Stock Market- Components- Agent Types- Auction Method

2. Networks- Network Topologies- Network Centralization Measures

3. Simulation- Parameters- Simulation Results:

• Centralization against Volatility and Distortion• Agent Type Performance

4. Outlook

Contents


Frankfurt Artificial Stock Market

The Frankfurt Artificial Stock Market (FASM) 1.6 is available for download at:

www.finace.org

But there is no documentation yet! Only articles exist that describe the system.


Frankfurt Artificial Stock Market(FASM) ver. 1.6


Handelsablauf


Kommunikationsnetzwerke

BörseMeistausführungsprinzip

Blau=kaufen, Rot=verkaufen

Scale-Free-NetzwerkZufallsnetzwerk


Fundamental Agents

• Fundamental agent k observes an exogenous inner value pf (random walk) and the last traded price p.

• Fundamental agent k possesses a risk premium γk.

• The order volume depends on abs(pf – p). Higher differences lead to higher order volumes.

• One buy and one sell order per fundamental agent k and per trading day are generated with:

Limit pf - γk for the buy order

Limit pf + γk for the sell order


Trend Agents

• Trend agent k observes at time t the prices pt-xkto pt-1

• Every trading day, trend agent k computes a daily moving average mk of xk days of price p.

• If p > mk a buy order and if p < mk a sell order is generated at time t with:

Limit pt-1 ± μ

• μ is a small random number that is positive if there has been more buy orders than sell orders for pt-1 (G=Geld) and vice-versa (B=Brief).

• The order volume depends on abs(py – p). py is the price when a

switch from buy to sell or vice-versa occurred. Higher differences lead to higher order volumes.


Retail Agents (1)

• Retail Agents are initially not endowed with a trading strategy

• They are able to adopt both trading strategies (trend, fundamental)

• They are initially inactive and get activated by an individual price increase at the stock exchange

• Once activated retail agents may adopt a trading strategy only from their direct neighbors within the communication network.

Three cases are possible:

1. no neighbor with strategy no trading, wait

2. neighbor has strategy adopt and start trading

3. several neighbors with strategy adopt the best one and start trading


• Retail agents stop trading and go into hibernation if an individual price decrease at the stock exchange occurred (e.g. 10%)

• They sell all their shares over a defined period (e.g. 10 days) and remain inactive for an individual number of days (e.g. 90 days)

• When the hibernation period is over, they may get activated again depending on their individual

threshold

Retail Agents (2)


Distribution of Agent Types

Green=Retail Agents, Yellow=Fundamental Agents, Red=Trend Agents


Double Auction Batch Limit Order Book

The maximum possible trade volume defines the new price at 1019.

Orders Possible Trade Volume


NETWORKS


Random Network

Red=Retail Agents, Yellow=Fundamental Agents, Blue=Trend Agents


Small-World Network

Red=Retail Agents, Blue=Fundamental Agents, Yellow=Trend Agents


Scale-Free Network

Red=Retail Agents, Yellow=Fundamental Agents, Blue=Trend Agents


Degree Centralization

The degree centralization measures the variation of the degree of a network member in relation to all other network members. (g=number of nodes, n*=node with highest degree)

The degree centralization varies between 0 and 1. The star network has a degree-centralization of 1.

*

1

1 2

g n iD Di

D

C CC

g g

Freeman, L. C. (1978/79). "Centrality in Social Networks. Conceptual Clarification." Social Networks 1, p. 215-239.


Betweeness Centralization

Interactions between two nonadjacent nodes A and B depend on other nodes that exist on the path from node A to node B. The betweenness centralization measures the frequency of a node appearing on the path between the two nonadjacent nodes in relation to the other nodes of the network.

The betweenness centralization varies between 0 and 1, it reaches a maximum if a node is on all shortest paths between all other nodes (star network).

sjk equals the amount of shortest paths between nodes j and k.

pjk(i) equals the probability that node i is on the path between node j and k

jkiB

jkj k

p iC

s

*

12

2

1 2

g n iB Bi

B

C CC

g g



Closeness Centralization

The closeness centralization measures how close a node is to the other nodes of a network in relation to the other nodes of the network. It shows how quickly (shortest paths to other nodes) one node can be reached from other nodes.

d(i, j) being the distance (length of the shortest path) betweennode i and j.

1

1

,g

iC i j

j

C d n n

*

1

1 2 / 2 3

g n iC Ci

C

C CC

g g g



Used Centralization Measures

Network TypesBetweenness

CentralizationCloseness

CentralizationDegree

Centralization

Random 0.0306 0,0994 0.0121

Small-World 0.0461 0.0672 0.0040

Scale-Free 1 0.4048 0.3520 0.1067

Scale-Free 2 0.4574 0.5930 0.6841


SIMULATIONS AND RESULTS


Simulation Parameters

General agents’ parameters agent type # τ time window initial cash initial shares

fundamental 29 0.5% - 3.5% − 5 - 8 mil. 5,000 - 8, 000

trend 18 − 10 - 70 days 1 - 2 mil. 2,000 - 3, 000

retail 453 − − 1 – 1.5 mil. 0

Retail agents’ specific parameters

activation threshold

de-activation threshold

hibernation profit window sell period

5% - 10% 10% - 18% 60 - 90 days 20 - 40 days 10 days

Order volumes of trend agents Order volumes of fundamental agentsdeviation from

signalorder volume in

sharesdeviation from

signalorder volume in

shares0% − 2% 2 0% − 2% 12% − 5% 5 2% − 4% 3

5% − 10% 15 4% − 7% 510% − ∞ 80 7% − ∞ 20


Simulation Run withthe Small-World Network

Volume

0 500 1000 1500 2000 2500 30000

500

1000

1500

2000

2500

3000

Log Returns

0 500 1000 1500 2000 2500 3000-0,10-0,08-0,06-0,04-0,020,000,020,040,06

Price and Inner Value

0 500 1000 1500 2000 2500 3000

800

900

1000

1100

1200

Price Inner Value


Simulation Run with theSmall-World Network

Autocorrelation of Absolute Returns

0 30 60 90 120 150-0,2

-0,1

0,0

0,1

0,2

0,3

0,4

Autokorrelation of Returns

0 30 60 90 120 150-0,2

-0,1

0,0

0,1

0,2

0,3

0,4

Annualized Moving Average Volatility

0 500 1000 1500 2000 2500 30000,04

0,06

0,08

0,10

0,12

0,14

Distribution of Returns (log scale)

-0,10 -0,05 0,00 0,05 0,100,1

1

10

100

1000


Number of Agent Types with the Small-World Network

Number of Retail Agents

0 500 1000 1500 2000 2500 3000

0

100

200

300

400

500

Number of Fundamental and Trend Agents

0 500 1000 1500 2000 2500 3000

0

100

200

300

400

500

Fundamental AgentsTrend Agents


Descriptive Statistics(10 Runs per Network)

A. Descriptive Statistics of Daily Log-YieldsRandom Small-World Scale-Free 1 Scale-Free 2

Mean 0% 0% 0% 0%

Standard Deviation 0.74% 0.78% 0.83% 0.91%

Skewness -0.54 -0.21 -0.56 -0.96

Min. -5.32% -7.45% -8.48% -13.22%

Max. 5.63% 5.26% 5.60% 7.35%


Unit-Root and Fat Tail Properties(10 Runs per Network)

B. Unit-RootRandom Small-World Scale-Free 1 Scale-Free 2

Augmented-Dickey-Fuller (ADF) Test:

1% level: -3.43 -3.43 -3.43 -3.43

5% level: -2.86 -2.86 -2.86 -2.86

10% level: -2.56 -2.56 -2.56 -2.56

ADF -16.45 -16.60 -14.46 -14.57

C. Fat Tail PropertyRandom Small-World Scale-Free 1 Scale-Free 2

Kurtosis 10.95 8.18 11.36 14.70

Hill-Estimator (5% tail) 5.4 5.2 4.9 4.8


Definition of Volatility and Distortion

21 1

2

100/

T

t t tt

volatility P P PT

2

100/

Tf f

t t tt

distortion P P PT

T = trading days (3,000), P = Price, Pf = inner value

Westerhoff, F. (2003). "Heterogeneous Traders and the Tobin tax." Journal of Evolutionary Economics 13, p. 53-70.


Volatility and Agent Type Performance

D. Volatility, Distortion and Volume (average for 10 runs)Random Small-World Scale-Free 1 Scale-Free 2

Volatility 10.95 8.18 11.36 14.70

Distortion 4.9 4.9 5.2 5.4

Volume (shares) 443,375 568,299 691,699 1,133,726

E. Agent Type Performance (average for 10 runs)Random Small-World Scale-Free 1 Scale-Free 2

Fundamental 10.53% 13.57% 17.14% 34.91%

Trend -11.39% -15.03% -18.93% -19.12%

Retail -6.60% -8.07% -11.36% -22.65%


Volatility and Network Centralization (10 Runs per Network)

Vo

latil

ity

40

50

60

70

80

90

Network Types

random small-world scale-free 1 scale-free 2

Ne

two

rk C

en

tra

liza

tion

0,0

0,2

0,4

0,6

0,8

VolatilityBetweeness CentralizationCloseness CentralizationDegree Centralization


Distortion and Network Centralization(10 Runs per Network)

Dis

tort

ion

2

3

4

5

Network Types

random small-world scale-free 1 scale-free 2

Ne

two

rk C

en

tral

iza

tion

0,0

0,2

0,4

0,6

0,8

DistortionBetweeness CentralizationCloseness CentralizationDegree Centralization


Agent Type Performance(10 Runs per Network)

We

alth

ch

an

ge

in %

-20

0

20

40

Fundamental Agents Trend Agents Retail Agents

Random

Small-World

Scale-Free 1

Scale-Free 2


Outlook

• A cooperation with the Sparkasse Gifhorn-Wolfsburg is in preparation, to find more empirical evidence about the behavior of retail investors.

• The model parameters are analyzed for their sensitivity and if

some may be endogenous.

• An analytical solution of the simulation model is still needed.

• Dynamic communication networks might be an interesting extension.

oliver hein, goethe university, frankfurt, financial agent-based computational economics (finace)...

Documents

financial agent

goethe university

sell order slide

limit p t

buy order limit p f

trading strategy

higher order volumes

netzwerkzufallsnetzwerk