Equilibrium Return and Agents Survival in a Multiperiod Asset - PowerPoint PPT Presentation

Introduction LLS Simulations Trick Support of Simulations Conclusions Equilibrium Return and Agents’ Survival in a Multiperiod Asset Market: Analytic Support of a Simulation Model Mikhail Anufriev Pietro Dindo CeNDEF , Faculty of Economics and Business University of Amsterdam Complex Markets Meeting Marseille 05 October 2006 Mikhail Anufriev, Pietro Dindo CeNDEF , University of Amsterdam Equilibrium Return and Agents’ Survival in a Multiperiod Asset Market: Analytic Support of a Simulation Model

Introduction LLS Simulations Trick Support of Simulations Conclusions Idea of Microscopic Simulations and analytic challenge Microscopic Simulations Levy, Levy and Solomon (2000) Microscopic Simulation of Financial Markets: from investor behavior to market phenomena ◮ ...The great advantage of the MS methodology is that systems that do not yield analytical treatment can easily be studied. ◮ ...A disadvantage of the MS approach is that it is more difficult to reach general conclusions from simulations than from analytical results... Mikhail Anufriev, Pietro Dindo CeNDEF , University of Amsterdam Equilibrium Return and Agents’ Survival in a Multiperiod Asset Market: Analytic Support of a Simulation Model

Introduction LLS Simulations Trick Support of Simulations Conclusions Idea of Microscopic Simulations and analytic challenge Microscopic Simulations Levy, Levy and Solomon (2000) Microscopic Simulation of Financial Markets: from investor behavior to market phenomena ◮ ...The great advantage of the MS methodology is that systems that do not yield analytical treatment can easily be studied. ◮ ...A disadvantage of the MS approach is that it is more difficult to reach general conclusions from simulations than from analytical results... Mikhail Anufriev, Pietro Dindo CeNDEF , University of Amsterdam Equilibrium Return and Agents’ Survival in a Multiperiod Asset Market: Analytic Support of a Simulation Model

Introduction LLS Simulations Trick Support of Simulations Conclusions Idea of Microscopic Simulations and analytic challenge Microscopic Simulations Levy, Levy and Solomon (2000) Microscopic Simulation of Financial Markets: from investor behavior to market phenomena ◮ ...The great advantage of the MS methodology is that systems that do not yield analytical treatment can easily be studied. ◮ ...A disadvantage of the MS approach is that it is more difficult to reach general conclusions from simulations than from analytical results... Mikhail Anufriev, Pietro Dindo CeNDEF , University of Amsterdam Equilibrium Return and Agents’ Survival in a Multiperiod Asset Market: Analytic Support of a Simulation Model

Introduction LLS Simulations Trick Support of Simulations Conclusions Idea of Microscopic Simulations and analytic challenge Plan of the Talk ◮ Review of the LLS model and their results ◮ Levy, Levy and Solomon (1994, Economic Letters), Levy and Levy (1996, The Financial Analyst Journal), Zschischang and Lux (2001, Physica A) ◮ Trick allowing the analytical treatment of the model ◮ Anufriev, Bottazzi and Pancotto (2006, Journal of Economic Dynamics and Control), Anufriev and Bottazzi (2006, CeNDEF WP) ◮ Application of the trick to the LLS model ◮ Anufriev and Dindo (2006, Advances in Artificial Economics ) Mikhail Anufriev, Pietro Dindo CeNDEF , University of Amsterdam Equilibrium Return and Agents’ Survival in a Multiperiod Asset Market: Analytic Support of a Simulation Model

Introduction LLS Simulations Trick Support of Simulations Conclusions Idea of Microscopic Simulations and analytic challenge Plan of the Talk ◮ Review of the LLS model and their results ◮ Levy, Levy and Solomon (1994, Economic Letters), Levy and Levy (1996, The Financial Analyst Journal), Zschischang and Lux (2001, Physica A) ◮ Trick allowing the analytical treatment of the model ◮ Anufriev, Bottazzi and Pancotto (2006, Journal of Economic Dynamics and Control), Anufriev and Bottazzi (2006, CeNDEF WP) ◮ Application of the trick to the LLS model ◮ Anufriev and Dindo (2006, Advances in Artificial Economics ) Mikhail Anufriev, Pietro Dindo CeNDEF , University of Amsterdam Equilibrium Return and Agents’ Survival in a Multiperiod Asset Market: Analytic Support of a Simulation Model

Introduction LLS Simulations Trick Support of Simulations Conclusions Model of Levy, Levy and Solomon and its simulations LLS model ◮ N agents trade 2 assets in discrete time ◮ stock: price P t , dividend D t ◮ bond: price 1, interest rate r f ◮ max expected power utility with risk aversion γ ◮ ex post returns are used to predict next return h t + 1 = P t + 1 − 1 + D t + 1 P t P t ◮ each of past L returns can occur with equal probability 1 / L ◮ Walrasian market clearing Mikhail Anufriev, Pietro Dindo CeNDEF , University of Amsterdam Equilibrium Return and Agents’ Survival in a Multiperiod Asset Market: Analytic Support of a Simulation Model

Introduction LLS Simulations Trick Support of Simulations Conclusions Model of Levy, Levy and Solomon and its simulations LLS model ◮ N agents trade 2 assets in discrete time ◮ stock: price P t , dividend D t ◮ bond: price 1, interest rate r f ◮ max expected power utility with risk aversion γ ◮ ex post returns are used to predict next return h t + 1 = P t + 1 − 1 + D t + 1 P t P t ◮ each of past L returns can occur with equal probability 1 / L ◮ Walrasian market clearing Mikhail Anufriev, Pietro Dindo CeNDEF , University of Amsterdam Equilibrium Return and Agents’ Survival in a Multiperiod Asset Market: Analytic Support of a Simulation Model

Introduction LLS Simulations Trick Support of Simulations Conclusions Model of Levy, Levy and Solomon and its simulations LLS model ◮ N agents trade 2 assets in discrete time ◮ stock: price P t , dividend D t ◮ bond: price 1, interest rate r f ◮ max expected power utility with risk aversion γ ◮ ex post returns are used to predict next return h t + 1 = P t + 1 − 1 + D t + 1 = r t + 1 + y t + 1 P t P t ◮ each of past L returns can occur with equal probability 1 / L ◮ Walrasian market clearing Mikhail Anufriev, Pietro Dindo CeNDEF , University of Amsterdam Equilibrium Return and Agents’ Survival in a Multiperiod Asset Market: Analytic Support of a Simulation Model

Introduction LLS Simulations Trick Support of Simulations Conclusions Model of Levy, Levy and Solomon and its simulations Important features of the LLS model ◮ share of investor’s wealth invested to the risky asset is independent of his wealth ◮ price and wealth are determined simultaneously and endogenously ⇓ ◮ “natural” dynamics is constant price growth Mikhail Anufriev, Pietro Dindo CeNDEF , University of Amsterdam Equilibrium Return and Agents’ Survival in a Multiperiod Asset Market: Analytic Support of a Simulation Model

Introduction LLS Simulations Trick Support of Simulations Conclusions Model of Levy, Levy and Solomon and its simulations Important features of the LLS model ◮ share of investor’s wealth invested to the risky asset is independent of his wealth ◮ price and wealth are determined simultaneously and endogenously ⇓ ◮ “natural” dynamics is constant price growth Mikhail Anufriev, Pietro Dindo CeNDEF , University of Amsterdam Equilibrium Return and Agents’ Survival in a Multiperiod Asset Market: Analytic Support of a Simulation Model

Introduction LLS Simulations Trick Support of Simulations Conclusions Model of Levy, Levy and Solomon and its simulations LL: Price with homogeneous investors L = 15 for all investors, γ = 1 Mikhail Anufriev, Pietro Dindo CeNDEF , University of Amsterdam Equilibrium Return and Agents’ Survival in a Multiperiod Asset Market: Analytic Support of a Simulation Model

Introduction LLS Simulations Trick Support of Simulations Conclusions Model of Levy, Levy and Solomon and its simulations LL: Price with heterogeneous investors 0 < L < 30 for half of investors, γ = 1 Mikhail Anufriev, Pietro Dindo CeNDEF , University of Amsterdam Equilibrium Return and Agents’ Survival in a Multiperiod Asset Market: Analytic Support of a Simulation Model

Introduction LLS Simulations Trick Support of Simulations Conclusions Model of Levy, Levy and Solomon and its simulations LPS: Survival of investors with high memory span three groups: ( L , γ ) = ( 256 , 1 ) , ( 141 , 1 ) , ( 10 , 1 ) Mikhail Anufriev, Pietro Dindo CeNDEF , University of Amsterdam Equilibrium Return and Agents’ Survival in a Multiperiod Asset Market: Analytic Support of a Simulation Model

Introduction LLS Simulations Trick Support of Simulations Conclusions Model of Levy, Levy and Solomon and its simulations ZL: Sensitivity to initial conditions three groups: ( L , γ ) = ( 256 , 1 ) , ( 141 , 1 ) , ( 10 , 1 ) Mikhail Anufriev, Pietro Dindo CeNDEF , University of Amsterdam Equilibrium Return and Agents’ Survival in a Multiperiod Asset Market: Analytic Support of a Simulation Model

Introduction LLS Simulations Trick Support of Simulations Conclusions Model of Levy, Levy and Solomon and its simulations ZL: Interplay of memory span L and risk aversion γ ( 256 , 0 . 4 ) , ( 141 , 0 . 6 ) , ( 10 , 0 . 4 ) and ( 256 , 0 . 6 ) , ( 141 , 0 . 4 ) , ( 10 , 0 . 4 ) Mikhail Anufriev, Pietro Dindo CeNDEF , University of Amsterdam Equilibrium Return and Agents’ Survival in a Multiperiod Asset Market: Analytic Support of a Simulation Model