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Financial time series exhibit non-trivial and intriguing statistical features which are not easy to model and to explain. Intermittent behaviour, volatility clustering (amplitudes of successive price movements are persistent, but not necessarily their signs), heavy tailed increments, and subtle dependence structures are important factors, crucial for assessing risks in financial markets and pricing tailored risk-management products. Furthermore the analysis of financial time series shows that the asymptotic behavior of the probability distribution of stock market returns is consistent with a power law decay at relatively short time scales while the shape of the Gaussian is recovered for monthly returns. This change of behaviour generates multiscaling in the moments of absolute returns. Anomalous scaling, or multiscaling, has also been detected in the autocorrelations of absolute returns for various market indices and currencies.

I proposed a model with heterogeneous interacting traders which can explain some of the stylized facts of stock market returns. In the model synchronization effects, which generate large fluctuations in returns, can arise purely from communication and imitation among traders. This imitative behaviour can spread through the system generating avalanches of different sizes in trading volumes. Traders buy from or sell to a market maker who, at the end of every trading period, adjusts the stock prices according to the relative demand and supply and the overall trading volume. The key element in the model is the introduction of a trade friction which, by responding to price movements, creates a feedback mechanism on future trading and generates volatility clustering. The model reproduces the empirically observed positive cross-correlation between volatility and trading volume. Scaling and multiscaling analysis performed on the simulated data is in good quantitative agreement with the empirical results.

Improvements in information technology and organization/deregulation of exchanges has led to a growing interest in the way financial markets are structured. In quote-driven systems, competing market makers supply liquidity by quoting bid and ask prices and the number of shares at which they are willing to trade. Investors demand liquidity through the submission of market orders. In order-driven markets investors can, but are not obliged to, submit limit orders. Orders are stored in the exchange’s book and executed in the sequence they arrive to the market. A transaction occurs when a trader hits the quote on the opposite side of the market. Transactions are executed using time priority at a given price and price priority across prices. Thus an electronic trading mechanism is comparable to a continuous auction system with automatic order matching and anonymous traders interacting via computer screens. In collaboration with C. Chiarella, we introduced an order-driven market model with heterogenous agents trading via a central orders matching mechanism.

Traders set bids and asks and post market or limit orders according to exogenously fixed rules. We investigate how different trading strategies, fundamentalst, chartist and random, may affect the dynamics of price, bid-ask spreads, trading volume and volatility. We also analyze how some features of market design, such as tick size and order lifetime, affect market liquidity. The model is able to reproduce many of the complex phenomena observed in real stock markets. G. Iori and C. Chiarella A Simulation Analysis of the Microstructure of Double Auction Markets, to be published in Quantitative Finance, Vol. 2, no. 5 (2002). In collaboration with Marcus G. Daniels, J. Doyne Farmer and Eric Smith, we develop a microscopic statistical model of the limit order book under random order flow, using simulation, dimensional analysis, and an analytic treatment based on a master equation. We make testable predictions of the price diffusion rate, the depth of stored demand vs. price, the bid-ask spread, and the price impact function, and show that even under completely random order flow the process of storing supply and demand induces anomalous diffusion and temporal structure in prices.

While the pros and cons of dealer versus order driven markets have been extensively discussed in the economic literature, as well as the impact of different trading strategies, and of the rate of order arrival on the dynamics of prices and spreads, the desirability of limit order trading, from the point of view of investors, has not received much attention in the literature.
In collaboration with Mihalis Zervos and Francisco Padilla we we investigate, by using analytical techniques and numerical Monte Carlo simulations, how, under different scenarios for the underlying asset price process, traders can optimize a limit order strategies.