Exploring Financial Instability Through Agent-based Modeling Part 1: Background and Early Models

Transcription

1 Blake LeBaron International Business School Brandeis University blebaron Mini course CIGI-INET: False Dichotomies Exploring Financial Instability Through Agent-based Modeling Part 1: Background and Early Models

2 Course Road Map What Are Agent-based Models? Agent-based Financial Markets Features of Financial Time Series Design Questions A Representative Simple Model Course Road Map LeBaron CIGI/INET November / 38

3 Main goals and philosophy Basic modeling tools LeBaron CIGI/INET November / 38

4 Main goals and philosophy Basic modeling tools Short guide to literature LeBaron CIGI/INET November / 38

5 Main goals and philosophy Basic modeling tools Short guide to literature Contributions to understanding financial market dynamics LeBaron CIGI/INET November / 38

6 Main goals and philosophy Basic modeling tools Short guide to literature Contributions to understanding financial market dynamics Macro economic connections LeBaron CIGI/INET November / 38

7 Where are we going? Part 1: What are agent-based models? Simple models from finance LeBaron CIGI/INET November / 38

8 Where are we going? Part 1: What are agent-based models? Simple models from finance Part 2: Adaptation and time series Heterogeneous gain learning LeBaron CIGI/INET November / 38

9 Where are we going? Part 1: What are agent-based models? Simple models from finance Part 2: Adaptation and time series Heterogeneous gain learning Part 3: Current directions in agent design and applications Empirical validation Instability and macro connections LeBaron CIGI/INET November / 38

10 Overview: Part 1 Course Road Map What Are Agent-based Models? Agent-based Financial Markets Features of Financial Time Series Design Questions A Representative Simple Model LeBaron CIGI/INET November / 38

11 Course Road Map What Are Agent-based Models? Agent-based Financial Markets Features of Financial Time Series Design Questions A Representative Simple Model What Are Agent-based Models? LeBaron CIGI/INET November / 38

12 What are agent-based models? Individual, autonomous agents LeBaron CIGI/INET November / 38

13 What are agent-based models? Individual, autonomous agents Distributions matter LeBaron CIGI/INET November / 38

14 What are agent-based models? Individual, autonomous agents Distributions matter Endogenous heterogeneity LeBaron CIGI/INET November / 38

15 What are agent-based models? Individual, autonomous agents Distributions matter Endogenous heterogeneity Computational? LeBaron CIGI/INET November / 38

16 Where are they used? Economics Finance Marketing LeBaron CIGI/INET November / 38

17 Where are they used? Economics Finance Marketing Sociology Political Science Biology LeBaron CIGI/INET November / 38

18 Where are they used? Economics Finance Marketing Sociology Political Science Biology Applications Public policy Business Military LeBaron CIGI/INET November / 38

19 Simple model philosophy Axelrod (1984) Epstein and Axtell (1997) Miller and Page (2007) Schelling (1978) LeBaron CIGI/INET November / 38

20 Major resources in economics Handbook: Leigh Tesfatsion and Kenneth L. Judd, editors. Handbook of Computational Economics: Agent-based computational economics. North-Holland, Amsterdam, 2006 LeBaron CIGI/INET November / 38

21 Major resources in economics Handbook: Leigh Tesfatsion and Kenneth L. Judd, editors. Handbook of Computational Economics: Agent-based computational economics. North-Holland, Amsterdam, 2006 ACE website: LeBaron CIGI/INET November / 38

22 Useful features for economic models Endogenous coordination Small independent, individual shocks large macro shocks LeBaron CIGI/INET November / 38

23 Why simple finance models? Understand financial price dynamics Simpler agent behavior Connections to macro LeBaron CIGI/INET November / 38

24 Why simple finance models? Understand financial price dynamics Simpler agent behavior Connections to macro Modeling: E t (P t+1 ) > P t LeBaron CIGI/INET November / 38

25 Course Road Map What Are Agent-based Models? Agent-based Financial Markets Features of Financial Time Series Design Questions A Representative Simple Model Agent-based Financial Markets LeBaron CIGI/INET November / 38

26 Agent-based financial market goals 1.Replicate interesting time series features LeBaron CIGI/INET November / 38

27 Agent-based financial market goals 1.Replicate interesting time series features 2.Understand adaptive behavior and market ecology LeBaron CIGI/INET November / 38

28 Agent-based financial market goals 1.Replicate interesting time series features 2.Understand adaptive behavior and market ecology 3.More realistic modeling platform LeBaron CIGI/INET November / 38

29 Useful finance surveys Chiarella et al. (2009) Carl Chiarella, Roberto Dieci, and Xue-Zhong He. Heterogeneity, market mechanisms, and asset price dynamics. In T. Hens and K. R. Schenk-Hoppe, editors, Handbook of Financial Markets: Dynamics and Evolution, pages Elsevier, USA, 2009 Hommes and Wagener (2009) Cars H. Hommes and Florian Wagener. Complex evolutionary systems in behavioral finance. In Thorsten Hens and Klaus Reiner Schenk-Hoppe, editors, Handbook of Financial Markets: Dynamics and Evolution, pages North-Holland, 2009 LeBaron (2006) B. LeBaron. Agent-based computational finance. In Leigh Tesfatsion and Kenneth L. Judd, editors, Handbook of Computational Economics, pages Elsevier, 2006 Lux (2009) Thomas Lux. Stochastic behavioral asset pricing models and the stylized facts. In Thorsten Hens and Klaus Reiner Schenk-Hoppe, editors, Handbook of Financial Markets: Dynamics and Evolution, pages North-Holland, 2009 LeBaron CIGI/INET November / 38

30 Key features Interacting agents and/or strategies Endogenous price time series Endogenous heterogeneity Self-contained learning: Learning prices learning... LeBaron CIGI/INET November / 38

31 Time series and populations Time series features Strategy populations LeBaron CIGI/INET November / 38

32 Course Road Map What Are Agent-based Models? Agent-based Financial Markets Features of Financial Time Series Design Questions A Representative Simple Model Features of Financial Time Series LeBaron CIGI/INET November / 38

33 Financial empirical summary Short term Uncorrelated returns Volatility persistence Leptokurtic (fat tailed) return distributions LeBaron CIGI/INET November / 38

34 Financial empirical summary Short term Uncorrelated returns Volatility persistence Leptokurtic (fat tailed) return distributions Long term Volatility persistence Return predictability Fundamental mean reversion Momentum (return persistence) Risk and return relationships Consumption and returns LeBaron CIGI/INET November / 38

35 Course Road Map What Are Agent-based Models? Agent-based Financial Markets Features of Financial Time Series Design Questions A Representative Simple Model Design Questions LeBaron CIGI/INET November / 38

36 Design questions Price determination Learning and adaptation Past data/learning gain Information representations Preferences LeBaron CIGI/INET November / 38

37 Very short history of agent-based finance Multi-agent (many/open) Computational learning algorithms Interesting and rich evolutionary dynamics Difficult to analyze LeBaron CIGI/INET November / 38

38 Very short history of agent-based finance Multi-agent (many/open) Computational learning algorithms Interesting and rich evolutionary dynamics Difficult to analyze Simple (few agent models) Relatively easy to analyze Simpler dynamics LeBaron CIGI/INET November / 38

39 Very short history of agent-based finance Multi-agent (many/open) Computational learning algorithms Interesting and rich evolutionary dynamics Difficult to analyze Simple (few agent models) Relatively easy to analyze Simpler dynamics Hybrid models (in between) LeBaron CIGI/INET November / 38

40 Examples of many type Arthur et al. (1997) Chen and Yeh (2002) Tay and Linn (2001) LeBaron (2001) LeBaron CIGI/INET November / 38

41 Many (open) type philosophy Idealized features New strategies/types/firms appear to take advantage of environment Realistic Problems How well can you build open ended systems? Need to put in some assumptions/structure LeBaron CIGI/INET November / 38

42 Few type philosophy Small (sometimes 2) set of strategies Often fixed parameters Analytic results Tractable dynamics LeBaron CIGI/INET November / 38

43 Two types Trend following, adaptive expectations E i,t (P t+1 ) = P t +g(p t P t 1 ) g > 0 (1) LeBaron CIGI/INET November / 38

44 Two types Trend following, adaptive expectations E i,t (P t+1 ) = P t +g(p t P t 1 ) g > 0 (1) Fundamental/mean reverting E i,t (P t+1 ) = P f,t +ν(p t P f,t ) 0 ν 1 (2) P f,t = Fundamental value (3) LeBaron CIGI/INET November / 38

45 Two types Trend following, adaptive expectations E i,t (P t+1 ) = P t +g(p t P t 1 ) g > 0 (1) Fundamental/mean reverting E i,t (P t+1 ) = P f,t +ν(p t P f,t ) 0 ν 1 (2) P f,t = Fundamental value (3) Building block for interesting dynamics LeBaron CIGI/INET November / 38

46 Two type models: Ancient history Zeeman (1974) Catastrophe theory Frankel and Froot (1988) U.S. dollar behavior in the 80 s Kirman (1991) Ants and contagion LeBaron CIGI/INET November / 38

47 Few type models: Core approaches Brock and Hommes (1998) Chiarella and He (2001) Day and Huang (1990) De Grauwe and Grimaldi (2006) Farmer and Joshi (2002) Levy et al. (1994) Lux and Marchesi (1999) Westerhoff and Reitz (2003) LeBaron CIGI/INET November / 38

48 Course Road Map What Are Agent-based Models? Agent-based Financial Markets Features of Financial Time Series Design Questions A Representative Simple Model A Representative Simple Model LeBaron CIGI/INET November / 38

49 Quick model structure Gaunersdorfer and Hommes (2007) Trend following traders Fundamental traders Market clearing Adaptive populations ==== Andrea Gaunersdorfer and Cars Hommes. A nonlinear structural model for volatility clustering. In A. Kirman and G. Teyssiere, editors, Micro Economic Models for Long Memory in Economics, pages Springer-Verlag, 2007 LeBaron CIGI/INET November / 38

50 Quick model structure E F (P t+1 ) = P +ν(p t P ) 0 ν 1 E T (P t+1 ) = P t +g(p t P t 1 ) g > 0 P t+1 = 1 1+r ((1 n t)e F (P t+1 )+n t E T (P t+1 ))+ȳ LeBaron CIGI/INET November / 38

51 Quick model structure E F (P t+1 ) = P +ν(p t P ) 0 ν 1 E T (P t+1 ) = P t +g(p t P t 1 ) g > 0 P t+1 = 1 1+r ((1 n t)e F (P t+1 )+n t E T (P t+1 ))+ȳ z T t = ET (P t+1 )+ȳ (1+r)P t γσ 2 z F t = EF (P t+1 )+ȳ (1+r)P t γσ 2 LeBaron CIGI/INET November / 38

52 Quick model structure R t = P t +y t (1+r)P t 1 y t = ȳ +δ t u T t = R t z R t 1 +ηu T t 1 u F t = R t z F t 1 +ηu F t 1 LeBaron CIGI/INET November / 38

53 Quick model structure R t = P t +y t (1+r)P t 1 y t = ȳ +δ t u T t = R t z R t 1 +ηu T t 1 u F t = R t z F t 1 +ηu F t 1 ñ t = e βut t e βut t +e βuf t n t = ñ t e (P t P ) 2 /α LeBaron CIGI/INET November / 38

54 Prices and returns in GH (no noise) Price Trend followers(fraction) LeBaron CIGI/INET November / 38

55 Adding noise to pricing E F (P t+1 ) = P +ν(p t P ) 0 ν 1 E T (P t+1 ) = P t +g(p t P t 1 ) g > 0 P t+1 = 1 1+r ((1 n t)e F (P t+1 )+n t E T (P t+1 ))+ȳ +ǫ t+1 LeBaron CIGI/INET November / 38

56 Prices and returns in GH (noise) Price Return LeBaron CIGI/INET November / 38

57 Prices and trend fractions (n t ) in GH (noise) Price Trend followers(fraction) LeBaron CIGI/INET November / 38

58 Few type summary Can get basic price dynamics Two strategies as core dynamic Other models similar Requires noise for realistic prices Generates large, erratic swings in strategy fractions LeBaron CIGI/INET November / 38

59 Overview: Part 1 Course Road Map What Are Agent-based Models? Agent-based Financial Markets Features of Financial Time Series Design Questions A Representative Simple Model LeBaron CIGI/INET November / 38