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

ACTA WASAENSIA 1251. α B ≤ 1,2.α(1 + √ 1+16ls) ≤ 4 for ls ≤ 3/2,αls ≤ 1 for ls ≥ 3/2,withl := t c /t fProof. See appendix A9.The above conditions for local stability of the fundamental equilibrium with respectto the regime-specific dynamics conform with intuition. Large strength of attractionparameters imply that small deviations from equilibrium trigger fast changes in thetrader populations, leading to fast price changesaswell. Largeholdingsofchartistsrelative to fundamentalists speed up price changes as was already mentioned in thediscussion of (5.3). Large discount factors have a similar effect in speeding up populationchanges by their inclusion into the transition rates between equity investors (5.9)through the fundamentalist utilities (5.6).5.2 Simulation StudyWe shall in the following simulate the artificial market defined by equations (5.3)and (5.14) along the same lines as in Lux & Marchesi (2000). That is, we consider anensemble of N = 500 traders with asynchronous updating of strategies approximated byfinite time increments of size ∆t =0.002 in the domain of attraction of the fundamentalequilibrium. In order to initialize the simulations both trading prices are set to theirfundamental value, while the numbers of chartists and fundamentalists in each stock areset to 62 and 63 respectively, close to their fundamental equilibrium value of 500/8 =Table 14. Parameter set used in the simulations.p f1 p f2 v v B α α B l = t c /t f s0 0 0.001 0.04 0.1 0.4 0.5 0.8