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Forschungskolloquium 2008

Forschungskolloquium 2008. Kommunikations-Netzwerk-Topologie und Marktverhalten 15. Februar 2008. von Oliver Hein. Contents. Frankfurt Artificial Stock Market Components Agent Types Auction Method Networks Network Topologies Network Centralization Measures Simulation Parameters

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Forschungskolloquium 2008

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  1. Forschungskolloquium 2008 Kommunikations-Netzwerk-Topologie und Marktverhalten 15. Februar 2008 von Oliver Hein

  2. Contents • Frankfurt Artificial Stock Market • Components • Agent Types • Auction Method • Networks • Network Topologies • Network Centralization Measures • Simulation • Parameters • Simulation Results: • Centralization against Volatility and Distortion • Agent Type Performance • Outlook

  3. 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.

  4. Frankfurt Artificial Stock Market (FASM) ver. 1.6

  5. Handelsablauf

  6. Kommunikationsnetzwerke Börse Meistausführungsprinzip Zufallsnetzwerk Scale-Free-Netzwerk Blau=kaufen, Rot=verkaufen

  7. 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

  8. 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 • μis 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.

  9. 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: • no neighbor with strategy no trading, wait • neighbor has strategy adopt and start trading • several neighbors with strategy adopt the best one and start trading

  10. Retail Agents (2) • 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

  11. Distribution of Agent Types Green=Retail Agents, Yellow=Fundamental Agents, Red=Trend Agents

  12. Double Auction Batch Limit Order Book Orders Possible Trade Volume The maximum possible trade volume defines the new price at 1019.

  13. NETWORKS

  14. Random Network Red=Retail Agents, Yellow=Fundamental Agents, Blue=Trend Agents

  15. Small-World Network Red=Retail Agents, Blue=Fundamental Agents, Yellow=Trend Agents

  16. Scale-Free Network Red=Retail Agents, Yellow=Fundamental Agents, Blue=Trend Agents

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

  18. 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. pjk(i) equals the probability that node i is on the path between node j and k sjk equals the amount of shortest paths between nodes j and k. 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). Freeman, L. C. (1978/79). "Centrality in Social Networks. Conceptual Clarification." Social Networks 1, p. 215-239.

  19. 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) between node i and j. Freeman, L. C. (1978/79). "Centrality in Social Networks. Conceptual Clarification." Social Networks 1, p. 215-239.

  20. Used Centralization Measures

  21. SIMULATIONS AND RESULTS

  22. Simulation Parameters

  23. Simulation Run withthe Small-World Network

  24. Simulation Run with theSmall-World Network

  25. Number of Agent Types with the Small-World Network

  26. DescriptiveStatistics(10 Runs per Network)

  27. Unit-Root andFatTail Properties(10 Runs per Network)

  28. Definition of Volatility and Distortion 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.

  29. Volatility and Agent Type Performance

  30. Volatility and Network Centralization (10 Runs per Network)

  31. Distortion and Network Centralization(10 Runs per Network)

  32. Agent Type Performance(10 Runs per Network)

  33. 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.

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