Time Series Properties from an Artificial Stock Market with a Walrasian Auctioneer

Abstract

This paper presents the results from an agent-based stock market with a Walrasian auctioneer (Walrasian adaptive simulation market, abbrev.: WASIM) based on the Santa Fe artificial stock market (SF-ASM, see e.g. [1], [2],[3],[4],[5]). The model is purposely simple in order to show that a parsimonious nonlinear framework with an equilibrium model can replicate typical stock market phenomena including phases of speculative bubbles and market crashes. As in the original SF-ASM, agents invest in a risky stock (with price p t and stochastic dividend d t ) or in a risk-free asset. One of the properties of SF-ASM is that the microscopic wealth of the agents has no influence on the macroscopic price of the risky asset (see [5]). Moreover, SF-ASM uses trading restrictions which can lead to a deviation from the underlying equilibrium model. Our simulation market uses a Walrasian auctioneer to overcome these shortcomings, i.e. the auctioneer builds a causality between wealth of each agent and the arising price function of the risky asset, and the auctioneer iterates toward the equilibrium. The Santa Fe artificial stock market has been criticized because the mutation operator for producing new trading rules is not bit-neutral (see [6]). That means with the original SF-ASM mutation operator the trading rules are generalized, which also could be interpreted as a special market design. However, using the original non bit-neutral mutation operator with fast learning agents there is a causality between the used technical trading rules and a deviation from an intrinsic value of the risky asset in SF-ASM. This causality gets lost when using a bit-neutral mutation operator. WASIM uses this bit-neutral mutation operator and presents a model in which high fluctuations and deviations occur due to extreme wealth concentrations. We introduce a Herfindahl index measuring these wealth concentrations and show reasons for arising of market monopolies. Instabilities diminish with introducing a Tobin tax which avoids that rich and influential agents emerge.