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

70 ACTA WASAENSIAIn the following we shall take a brief look at some microscopic mdels of heterogenousinteracting agents, which bear some relation to the model to be developed in section5, in that they aim to explain the statistical properties of financial time series fromsome kind of fundamentalist chartist interation or mimetic contagion, and that at leastsome qualitative results can be deduced by means of analytical methods. This is only asmall subset of the literature on the dynamically evolving field of heterogenoeus agentmodels, which has already grown too large to be comprehensively reviewed here. Formore extensive reviews on such models refer to Tesfatsion & Judd (2006), in particularchapters 8 and 9.4.2.1 Fundamentalist Chartist InteractionThe first quantitative model of fundamentalist chartist interaction is due to Zeeman(1974) in an effort to model bubbles and crashes in a stock market. Zeeman describesthe stock market in terms of a stock index and the excess demand for stocks by fundamentalistand chartists. He shows that purely qualitative assumptions about theinterplay of these three variables suffice to explain cycles of bull and bear markets ormarket crashes depending upon the proportion of the market held by chartists. Thebasic mechanism for generating such dynamic behaviour of the stock market is thesame as in nowadays’ models: A stochastic disturbance of the equilibrium price generatesself-accelerating excess demand by chartists, until the price is sufficiently far awayfrom equilibrium to be corrected by fundamentalists.Beja & Goldman (1980) provide the first explicit formalization of trading demand bychartist and fundamentalists and show that a large excess demand by chartists relativeto fundamentalists may destabilize an otherwise stable price equilibrium. The excessdemand D f t by fundamentalists is formalized asD f t = a(p f (t) − p(t)), a > 0, (4.3)where p f (t) andp(t) denote the exogenously generated fundamental price and theendogeneously determined trading price, respectively, and the coefficient a measuresthe relative impact of fundamental demand upon price movements.