1 Indirect Estimation of the Parameters of Agent Based Models of Financial Markets Peter Winker Manfred Gilli

2 Outline Background Information. Background Information. Introduction. Introduction. Method. Method. Result. Result. Conclusion of the Paper. Conclusion of the Paper. Further Improvement. Further Improvement.

3 Standard Models Assumptions Assumptions Agents are fully rational. Agents are fully rational. Markets are efficient. Markets are efficient.

4 Rational Behaviour Agent is rational if Agent is rational if He is aware of his alternatives. He is aware of his alternatives. Form expectations about any unknowns. Form expectations about any unknowns. Has clear preferences. Has clear preferences. Chooses his action deliberately after some process of optimization. Chooses his action deliberately after some process of optimization. Taking into account their knowledge or expectations of other decision makers’ behaviour. Taking into account their knowledge or expectations of other decision makers’ behaviour.

5 Efficient Market Hypothesis All market participants receive and act on all relevant information as soon as it is available. All market participants receive and act on all relevant information as soon as it is available. Perfect information within the market. Perfect information within the market. Cannot “beat the market”. Cannot “beat the market”.

6 Agent Based Models Agents to be heterogenous. Agents to be heterogenous. Agents with limited rational behaviour. Agents with limited rational behaviour. Market does not need to be efficient. Market does not need to be efficient. Interaction between agents. Interaction between agents.

7 Parameters Not directly observable. Not directly observable. Compare with empirical data. Compare with empirical data. DM/US-$ exchange rate. DM/US-$ exchange rate.

8 Characteristic of DM/US-$ Daily Returns DM/US-$

9 Characteristic of DM/US-$ Excess kurtosis. Excess kurtosis. Volatility varies over time. Volatility varies over time. AR(1) process with ARCH(1) effect. AR(1) process with ARCH(1) effect. where where

10 Model (Kirman 1990) Two prevalent views of the world. Two prevalent views of the world. Each agent holds one view. Each agent holds one view. N agents. N agents. State: number of agents, k, for first view. State: number of agents, k, for first view. Two agents, A and B, meet at random. Two agents, A and B, meet at random. P(A ’ s view → B ’ s view) =. P(A ’ s view → B ’ s view) =. P(A changed his view independently) =. P(A changed his view independently) =.

11 Model (Kirman 1990) If, large shares of first type of agents and second type of agents, respectively, with high probability. If, large shares of first type of agents and second type of agents, respectively, with high probability.

12 Fundamentalist / Chartists There are two types of agents: There are two types of agents: Fundamentalist: Fundamentalist: Chartist: Chartist:

13 Advantages Complicated non-stationary dynamics. Complicated non-stationary dynamics. Non-fundamentalist behaviour. Non-fundamentalist behaviour.

14 Simulation Objective function. Objective function. estimated ARCH(1)-effect. estimated ARCH(1)-effect. empirical kurtosis. empirical kurtosis. and mean values from 1000 simulations. and mean values from 1000 simulations. First and last 10% results deleted. First and last 10% results deleted.

15 Monte Carlo Simulation 200 Monte Carlo simulation

16 Monte Carlo Simulation Monte Carlo simulation

17 Monte Carlo Simulation Monte Carlo simulation

18 Threshold Accepting Initial:Choose threshold sequence Initial:Choose threshold sequence, set, set and generate an initial. Step 1:Choose some. Step 1:Choose some. Step 2:Calculate. Step 2:Calculate. Step 3:If, set. Step 3:If, set. Step 4:If, set and go to 1. Step 4:If, set and go to 1. Otherwise, output.

19 Simulation

20 Simulation

21 Result Optimal values are and Optimal values are and, market is better characterized by switching moods of the investors than by assuming that the mix of fundamentalists and chartists remains rather stable over time., market is better characterized by switching moods of the investors than by assuming that the mix of fundamentalists and chartists remains rather stable over time.

22 Conclusion Agent based models can replicate empirical data of the financial markets. Agent based models can replicate empirical data of the financial markets. Parameters may be difficult to estimate. Parameters may be difficult to estimate. Indirect method can be used. Indirect method can be used. Optimization heuristic may need to be used. Optimization heuristic may need to be used.

23 Further Improvement First and last 10% simulation results removed. Too much? First and last 10% simulation results removed. Too much? Number of parameters to be estimated. Number of parameters to be estimated. Only two types of agents? Only two types of agents?

24 Reference Fama, E.F. 1970, “Efficient capital markets: a review of theory and empirical work”, Journal of Finance, V25, Issue 2, p Fama, E.F. 1970, “Efficient capital markets: a review of theory and empirical work”, Journal of Finance, V25, Issue 2, p Gilli, M., Winker, P. 2003, “A global optimization heuristic for estimating agent based models”, Computational Statistics & Data Analysis, 42, p Gilli, M., Winker, P. 2003, “A global optimization heuristic for estimating agent based models”, Computational Statistics & Data Analysis, 42, p Kirman, A. 1990, “Epidemics of opinion and speculative bubbles in financial markets”, in Taylor M.P.(eds), Money and financial markets, Basil Blackwell Ltd, Oxford, p Kirman, A. 1990, “Epidemics of opinion and speculative bubbles in financial markets”, in Taylor M.P.(eds), Money and financial markets, Basil Blackwell Ltd, Oxford, p Tsay, R.S. 2002, Analysis of financial time series, John Wiley & Sons, Inc. Tsay, R.S. 2002, Analysis of financial time series, John Wiley & Sons, Inc. Winker, P. 2001, “Application of the optimization heuristic threshold accepting in statistics”. Winker, P. 2001, “Application of the optimization heuristic threshold accepting in statistics”.