Transcript Indirect Estimation of the Parameters of Agent Based Models of

Indirect Estimation of the
Parameters of Agent Based
Models of Financial Markets
Peter Winker
Manfred Gilli
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Outline
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Background Information.
Introduction.
Method.
Result.
Conclusion of the Paper.
Further Improvement.
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Standard Models
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Assumptions
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Agents are fully rational.
Markets are efficient.
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Rational Behaviour
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Agent is rational if
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He is aware of his alternatives.
Form expectations about any unknowns.
Has clear preferences.
Chooses his action deliberately after some
process of optimization.
Taking into account their knowledge or
expectations of other decision makers’
behaviour.
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Efficient Market Hypothesis
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All market participants receive and act on
all relevant information as soon as it is
available.
Perfect information within the market.
Cannot “beat the market”.
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Agent Based Models
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Agents to be heterogenous.
Agents with limited rational behaviour.
Market does not need to be efficient.
Interaction between agents.
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Parameters
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Not directly observable.
Compare with empirical data.
DM/US-$ exchange rate.
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Characteristic of DM/US-$
Daily Returns DM/US-$
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Characteristic of DM/US-$
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Excess kurtosis.
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 E X  X
Volatility varies over time.
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AR(1) process with ARCH(1) effect.
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rt   0  1rt 1   t where V  t    0   1 t 1
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Model (Kirman 1990)
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Two prevalent views of the world.
Each agent holds one view.
N agents.
State: number of agents, k, for first view.
Two agents, A and B, meet at random.
P(A’s view → B’s view) = 1   .
P(A changed his view independently) =  .
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Model (Kirman 1990)
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N k
Pk , k  1 
N
k
Pk , k  1 
N
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k 
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  1    N  1
N k
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  1    N  1 
1
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N 1
If
, large shares of first type of
agents and second type of agents,
respectively, with high probability.
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Fundamentalist / Chartists
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There are two types of agents:
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Fundamentalist:
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Chartist:
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E f S t 1   v S  S t
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E St 1   St  St 1
c
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Advantages
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Complicated non-stationary dynamics.
Non-fundamentalist behaviour.
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Simulation
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Objective function.
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f  k d  k demp   1  1emp
1
estimated ARCH(1)-effect.
k d emp empirical kurtosis.
k d and  1 mean values from 1000
simulations.
emp
First and last 10% results deleted.
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Monte Carlo Simulation
200 Monte Carlo simulation
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Monte Carlo Simulation
10000 Monte Carlo simulation
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Monte Carlo Simulation
10000 Monte Carlo simulation
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Threshold Accepting
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Initial: Choose threshold sequence
Ti , i  0,, I max , set i  0
c
and generate an initial x .
n
c
Step 1: Choose some x  N x .
n
c
Step 2: Calculate f  f x   f x  .
c
n
Step 3: If f  Ti , set x  x .
Step 4: If i  I max , set i  i  1 and go to 1.
c
Otherwise, output x .
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 
Simulation
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Simulation
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Result
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Optimal values are   0.0008571 and
  0.3250
1
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N  1 , 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.
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Conclusion
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Agent based models can replicate
empirical data of the financial markets.
Parameters may be difficult to estimate.
Indirect method can be used.
Optimization heuristic may need to be
used.
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Further Improvement
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First and last 10% simulation results
removed. Too much?
Number of parameters to be estimated.
Only two types of agents?
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Reference
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Fama, E.F. 1970, “Efficient capital markets: a review of theory and empirical
work”, Journal of Finance, V25, Issue 2, p383-417.
Gilli, M., Winker, P. 2003, “A global optimization heuristic for estimating
agent based models”, Computational Statistics & Data Analysis, 42, p299312.
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, p354-368.
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Tsay, R.S. 2002, Analysis of financial time series, John Wiley & Sons, Inc.
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Winker, P. 2001, “Application of the optimization heuristic threshold
accepting in statistics”.
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