This document summarizes research on modeling speculative bubbles using agent-based computational economics. It describes a simple model of a financial market with two types of artificial agents - zero-intelligence agents and agents that evaluate risk endogenously. Through experiments varying model parameters like risk sensitivity and pricing strategies, the researchers were able to generate speculative bubble-like behavior, including sustained price increases and occasional crashes. The work aims to provide a simple model for studying market efficiency and the boundary between speculation and efficiency.

1. Computational Finance 2004 Artificial Agents and Speculative Bubbles Y. Semet , S. Gelly, M. Schoenauer, M. Sebag Optimization & Machine Learning Group INRIA Futurs Orsay, France

2. Roadmap Agent-based Computational Economics (ACE) A financial asset trading problem: speculative bubbles A simple model studied in two contexts: Exogenous risk, ZI, finite time horizon; Endogenous risk with elementary strategy. A set of conditions for the appearance of speculative bubbles

3. Background European Project: DREAM (Distributed Evolutionary Algorithms…) Social and Economic problems are interesting to AI: high frequency data, distributed interactions, stochasticity, cognition and rationality, emergent computation. Market efficiency: simple models for a critical debate.

4. Previous Works Gode & Sunder, 93: Rationality and market efficiency Tool: « Zero-Intelligence » traders Conclusions: aggregate rationality The Santa Fe Artificial Stock Market, 96 Complexity and inductive reasonning Tool: Genetic Algorithms Conclusions: a hint on the efficiency/speculation boundary

5. Our market Double Auctions, Cleared Book Convention 1 financial asset 2 kinds of Agents: ZI and Agents are randomly endowed with cash & shares

6. Auction Algorithm

7. ZI-Agents, Exogenous Risk Risk set by given external function Simulates decreasing hope for dividend collecting Finite time horizon

8. Evaluating Risk Endogenously Risk is high when: P is far above F P is going down Weights = control A smoothing sigmoïd r(i,t): risk at time t for agent i p(t): asset price a, v, w: controlling weights F: fundamental value

9. Choosing a strategy… 1 1 1 Buy Idle Sell 0 Exuberance Buy Idle Sell 0 Comfort Buy Idle Sell 0 Panic Exuberance Comfort Panic  R 0 R 0 0 1 r(i,t)

10. Making an offer Anchoring effect: offers are uniformly distributed around previous price. In most cases: An asymetric possibility for the panic mode:

11. A glimpse on the GUI Code in JAVA Large number of control parameters An even larger number of time series Visualization is a critical issue for ACE experimetns

12. Experiments Value Tuning + Heterogenization Many cross dependencies Reminder: w, alpha, R0, F, Pricing policy. Typical values:… Around 1 minute of computation time, grows very quickly with # of agents

13. Linear risk ; Time horizon=500 p(t) Buy & Sell r(t)

14. Endogenous risk: default behavior (efficiency) p(t) r(t) Buy & Sell Exuberance Comfort Panic

15. At t=250, F becomes 75 p(t) r(t) Buy & Sell Exuberance Comfort Panic

16. Bubbles w/o krach ; R0 in [0.4;0.6] p(t) Close-up Buy & Sell Exuberance Comfort Panic

17. Bubbles w/o krach ; R0 in [0.4;0.8] p(t) Buy & Sell Exuberance Comfort Panic

18. Influence of fool factor 1.05 1.1 1.2 1.0

19. Introducing asymetry p t-1 -5% in panic vs p t-1 +/- 1% comfort/exb. bubbly behavior (R0 in [0.4;0.6]) p(t) Close-up Buy & Sell Exuberance Comfort Panic

20. Bubbly behavior (R0 in [0.4;0.8]) p(t) Close-up Buy & Sell Exuberance Comfort Panic

21. Conclusions Speculative bubbles in two contexts With exogenous risk Endogenous risk in conjunction with: High sensitivity to recent trends Biased heterogeneity Asymetric pricing strategy Future work: a Game Theory take Contact: semet@lri.fr