Paolo Pellizzari

Fundamentalists clashing over the book: a study of order-driven stock markets

Abstract Agent-based models of market dynamics must strike a compromise between the structural assumptions that represent the trading mechanism and the behavioural assumptions that describe the rules by which traders make their decisions. We present a structurally detailed model of an order-driven stock market and show that a minimal set of behavioural assumptions suffices to generate a leptokurtic distribution of short-term log-returns. This result supports the conjecture that the emergence of some statistical properties of financial time series is due to the microstructure of stock markets.

Zero-Intelligence Trading Without Resampling

This paper studies the consequences of removing the resampling assumption from the zero-intelligence trading model in Gode and Sunder (1993). We obtain three results. First, individual rationality is no longer sufficient to attain allocative effciency in a continuous double auction; hence, the rules of the market matter. Second, the allocative effciency of the continuous double auction is higher than for other sequential protocols both with or without resampling. Third, compared to zero intelligence, the effect of learning on allocative effciency is sharply positive without resampling and mildly negative with resampling.

The Allocative Effectiveness of Market Protocols Under Intelligent Trading

We study the performance of four market protocols that lead to allocative efficiency: batch auction, continuous double auction, specialist dealership, and a hybrid of these last two. In a former study, we compared them with respect to several additional performance criteria under the assumption of zero intelligence. This paper analyzes three performance criteria under different ways to remove the assumption of zero intelligence. The following conclusions are robust. The number of wasteful transaction is minimized by the batch auction and the dealership. Moreover, the former minimizes price dispersion and the latter minimizes time to convergence.

A DYNAMIC ANALYSIS OF THE MICROSTRUCTURE OF MOVING AVERAGE RULES IN A DOUBLE AUCTION MARKET

Inspired by the theoretically oriented dynamic analysis of moving average rules in the model of Chiarella, He, and Hommes (CHH) [ Journal of Economic Dynamics and Control 30 (2006), 1729—1753], this paper conducts a dynamic analysis of a more realistic microstructure model of continuous double auctions in which the probability of heterogeneous agents trading is determined by the rules of either fundamentalists mean-reverting to the fundamental or chartists choosing moving average rules based on their relative performance. With such a realistic market microstructure, the model is able not only to obtain the results of the CHH model but also to characterize most of the stylized facts including volatility clustering, insignificant autocorrelations (ACs) of returns, and significant slowly decaying ACs of the absolute returns. The results seem to suggest that a comprehensive explanation of several statistical properties of returns is possible in a framework where both behavioral traits and realistic microstructure have a role.

Static hedging of multivariate derivatives by simulation

We propose an approximate static hedging procedure for multivariate derivatives. The hedging portfolio is composed of statically held simple univariate options, optimally weighted minimizing the variance of the difference between the target claim and the approximate replicating portfolio. The method uses simulated paths to estimate the weights of the hedging portfolio and is related to Monte Carlo control variates techniques. We report numerical results showing the performance of this static hedging procedure on bivariate options on the maximum of two assets and on 2- and 7-dimensional portfolio options. It is shown that, in the presence of transaction costs, Value at Risk and Expected Shortfall of the dynamically hedged positions can be higher than the ones obtained by a static hedge.

Facebook as an Academic Learning Platform: A Case Study in Mathematics

The paper discusses the impact of the use of Facebook as a supporting learning platform for a course in Mathematics at the undergraduate level. After the examination of some critical issues of Facebook in a learning framework, we analyze data on the usage the page (total reach and number of engaged users) and the results of a survey taken by 217 students. Their appreciation for Facebook in such a context is stark and improvements of qualitative aspects of academic performance are perceived. Studying a subset of data tagged with ID information, we also investigate the quantitative performance (i.e., grades) in connection with the level of Facebook activity and usefulness. We find some evidence of positive correlation of grades and several variables. This is at odds with other studies, where active users experienced poorer performance when the use of Facebook is not related to academic work.

No association between the degree of liver steatosis and early signs of vasculopathy in T2DM

Non alcoholic fatty liver disease (NAFLD) is both an independent and an associated risk factor for cardiovascular (CV) disease in the general population [1]. Whereas the association between NAFLD, and early signs of vasculopathy, such as an increased intima-media thickness (IMT) and a decreased flow-mediated vasodilation (FMD), has been reported in the general population, such an association in type 2 diabetes mellitus (T2DM) is controversial. In T2DM patients with NAFLD FMD was decreased [2], whereas IMT was not different, with respect to patients without liver steatosis [3]. Should a (causative) relationship between hepatic steatosis and early signs of vasculopathy exists, the degree of liver fat should be associated with a worse endothelial function and morphology. However, despite the bulk of data generated on this complex association, insufficient reports exist on T2DM. To this aim, we measured the extent of liver fat, average IMT, the presence and type of carotid plaques, and FMD, in sixty consecutive T2DM patients largely affected by features of the MS. Liver steatosis, IMT, and presence and types of carotid plaques, were evaluated by ultrasonography (using an HDI 5000 Philips Medical Systems apparatus, Bothell, WA, USA), with a broad-band width phased array transducer (2e5 MHz). Steatosis was divided into four classes following the traditional US classification (class 0: absence; classes 1e3: increasing degrees, of steatosis) [4]. IMT was assessed using standard procedures [5]. FMD was evaluated in 45 patients using an internationally validated approach [6]. Only six patients were current smokers, and seven had a positive history for CV disease (five for ischemic heart disease, and two for cerebrovascular disease). No subject was positive for hepatitis C virus infection. The overall prevalence of steatosis was 88% (34% mild, 34% moderate e 20% severe). Average IMT was 0.88 0.03 mm (Mean SE), significantly greater (p < 0.0001) than the mean value of a healthy, ageand sex matched population at our Institution (0.72 0.03 mm). Fifty-eight percent of patients had carotid plaques. Average FMD in the patients (5.02 0.81%) was lower (p < 0.001) than the normal values of healthy, ageand sex matched individuals from our Institution (6.56 0.60%).

The Simplicity of Optimal Trading in Order Book Markets

A traders execution strategy has a large effect on his profits. Identifying an optimal strategy, however, is often frustrated by the complexity of market microstructures. We analyse an order book based continuous double auction market under two different models of traders behaviour. In the first case actions only depend on a linear combination of the best bid and ask. In the second model traders adopt the Markov perfect equilibrium strategies of the trading game. Both models are analytically intractable and so optimal strategies are identified by the use of numerical techniques. Using the Markov model we show that, beyond the best quotes, additional information has little effect on either the behaviour of traders or the dynamics of the market. The remarkable similarity of the results obtained by the linear model indicates that the optimal strategy may be reasonably approximated by a linear function. We conclude that whilst the order book market and strategy space of traders are potentially very large and complex, optimal strategies may be relatively simple and based on a minimal information set.

Trade-In Programs in the Context of Technological Innovation with Herding

We study optimal pricing strategies and consequent market shares’ dynamics in a transition from an old and established technology to a new one. We simulate an agent-based model, in which a large population of possible buyers decide whether to adopt or not depending on prices, private signals and herding behavior. The firm, on its part, sets prices to maximize revenues. We show that trade-in programs, in practice comparable to very aggressive discounts, are supported by a rational attitude.

Time-dependent trading strategies in a continuous double auction

We model a continuous double auction with heterogenous agents and compute approximate optimal trading strategies using evolution strategies. Agents privately know their values and costs and have a limited time to transact. We focus on equilibrium strategies that are developed taking into account the number of traders that submitted orders previously, as well as the number of who will submit subsequently. We find that it is optimal to place increasingly aggressive orders, according to a roughly linear schedule, and test the resulting equilibrium for robustness and accuracy.