The Waiting-Time Distribution of Trading Activity in a Double Auction Artificial Financial Market

Summary In this paper, the statistical properties of high-frequency data are investigated by means of computational experiments performed with the Genoa Artificial Stock Market (Raberto et al. 2001, 2003, 2004). In the market model, heterogeneous agents trade one risky asset in exchange for cash. Agents have zero intelligence and issue random limit or market orders depending on their budget constraints. The price is cleared by means of a limit order book. The order generation is modelled with a renewal process where the distribution of waiting times between two consecutive orders is a Weibull distribution. This hypothesis is based on recent empirical investigation made on high-frequency financial data (Mainardi et al. 2000, Raberto et al. 2002, Scalas et al. 2003). We investigate how the statistical properties of prices and of waiting times between transactions are affected by the particular renewal process chosen for orders. Results point out that the mechanism of the limit order book is able to recover fat tails in the distribution of price returns without ad-hoc behavioral assumptions regarding agents; moreover, the kurtosis of the return distribution depends also on the renewal process chosen for orders. As regarding the renewal process underlying trades, in the case of exponentially distributed order waiting times, also trade waiting times are exponentially distributed. Conversely, if order waiting times follow a Weibull, the same does not hold for trade waiting times.