BERND PAPE Asset Allocation, Multivariate Position Based Trading ...

ACTA WASAENSIA 77Iori (2002) comes even closer to a replication of the stylized facts of financial returnsby considering a superposition of a lattice based communication structure and idiosyncraticsignals, where the sum of both has to exceed an agent-specific threshold inorder to generate a trading order, with thresholds periodically adjusted proportional toprice changes. Iori’s model simultaneously generates uncorrelated returns with volatilityclustering, long memory in volatility, a positive cross-correlation between volatilityand trading volume, and power-law distributed returns with a realistic tail index.Kirman (1991) provides an exchange rate model, which combines an infection processinspired from the communication behaviour of tandem recruiting ants (Kirman 1993)with chartist-fundamentalist interaction of utility maximizing agents. Traders holdeither a chartist or a fundamentalist view of the exchange rate and meet at randomin discrete time. When two agents meet, the first is converted to the seconds viewwith a given probability (1 − δ). There is also a small probability of spontaneouschange in opinion in order to avoid absorbing states with all agents holding the sameview. SuchaninfectionprocessmaybedescribedasanergodicMarkovchainwithasymmetric bimodal limit distribution for small enough spontanoues conversion probability compared to the infection probability (1-δ), with maxima near the extremesof identical opinion of all agents. That is, the investment community spends most ofthe time holding either a chartist or a fundamentalist view of the exchange rate, withonly occasional shifts between both regimes. With chartists extrapolating the recentprice trend, fundamentalists expecting reversion to the fundamental price, and a priceequilibrium equiation derived from mean-variance utility maximization of both agents,prices are close to fundamental value when fundamentalists dominate, but follow bubblepaths under the chartist regime. The endogenous switching between both regimesinduced by the infection process above implies then a near unit-root process with clusteredvolatility. In a later extension (Kirman & Teyssière 2002), the model generatesalso long memory in volatility.It is an important advantage of formulating agent-based models as ergodic Markovchains with explicit limit distributions, that it allows for estimation of the underlyingparameters by comparison of the model implied return distribution with the returnsobserved in financial markets. This has been done for Kirman’s original model by Gilli