Order-Book’s dynamics: Stigler model

In this thesis, are analized and simulated the Order-Book’s dynamics, reproduced through Stigler model and a modification brought to it (the presence of some strategic agents) searching for confirmation with the empirical data on the waiting times. After having shown the main features of the orders stored in the Order-Book and the results of the study of their trend (the variation of prices, waiting times and volatility), Stigler model, based on the zero-intelligence, is presented. With the hypothesis of lack of agents’ strategy, it’s observed the presence of the competitive window (inside of it orders are executed always at different prices, outside they accumulate). The values of the limits of the competitive window are obtained through a mathematical formulation and simulations of the model. There’s equivalence between the values obtained through the two different methods Waiting times of the orders generated by the simulation of the model have been analyzed and an equivalence has been found with the power law distribution of the empirical data. A modification as been brought to the model: the presence of strategic agents in the market, called “Market Makers”. They put their orders on the best sell/buy orders in the stock. Through simulations it’s been observed the progressive closure of the competitive window, which is complete when the rate of Market Makers is 0.5. Moreover the price is fixed when the rate is 0.5 (in the middle of the price interval) or higher (not in a precise value) and waiting times do not find equivalence with empirical data in their distribution.