Stock price fluctuations and the mimetic behaviors of traders

Abstract

We give a stochastic microscopic modelling of stock markets driven by continuous double auction. If we take into account the mimetic behavior of traders, when they place limit order, our virtual markets shows the power-law tail of the distribution of returns with the exponent outside the Levy stable region, the short memory of returns and the long memory of volatilities. The Hurst exponent of our model is asymptotically 1/2. An explanation is also given for the profile of the autocorrelation function, which is responsible for the value of the Hurst exponent.

Simple stochastic order-book model of swarm behavior in continuous double auction

“…Figure 3 shows that the standard deviation of the price gap for the time scale is proportional to the one-half power of the time scale for each model. This is similar to the results obtained from past experimental studies [1] [11], which reported that slow diffusion occurred over a short time scale, where the Hurst exponent was below 0.5, and approached a value of 0.5 at a longer time scale. The data derived from the current simulations, however, exhibited an absence of slow diffusion over short time scales.…”

When organisations and ecosystems interact: toward a law of requisite fractality in firms

“…Consequently economies operate at or near the critical state. This shows up in the things like the price of cotton and many other economic realities described by Mandelbrot and Hudson (2004), consumer product sales (Moss, 2002;Sornette et al, 2004), entrepreneurial responses and results leading to different sized firms , and stock-market price volatilities (Zhou and Sornette, 2002, Sornette and Zhou, 2006, Jondeau et al, 2007Maskawa, 2007;Calvet and Fisher, 2008;Du and Ning, 2008;Eom et al, 2008;Kumar and Deo, 2009;Sornette and Woodard, 2009;Yan et al, 2010;McKelvey and Salmador Sanchez, 2011;Yalamova, 2011a, 2011b;Yalamova and McKelvey, 2011) -all of which show PL signatures. The parallel to sand avalanches is clear: from gravity to supply/demand; from irregular sand grains to irregular consumer and managerial decision processes and outcomes, from biological SOC to firms' and stock market SOC, the results are similar: PL shaped avalanches vs. PL shaped economic events and changes.…”

Correlation of coming limit price with order book in stock markets

“…It is a simplification of the actual way of traders to select a limit order. In the paper [10], traders are assumed to be mimetic, and prefer the limit price which has a large stock of limit orders, when they place limit orders. Incorporating this tendency of coming limit price into the microscopic model of stock market, the author reproduces the price fluctuation with the more real statistics depending on the parameter of the model.…”