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My research work has covered different areas in physics, applied mathematics, biology, finance and economics. My contributions are in the area of disordered systems and non-equilibrium statistical mechanics as well as in financial time series analysis and its implications to option pricing and hedging. I also contributed to the development of an approach to complexity in financial markets and economic networks derived from the tools of statistical mechanics and non-linear dynamics. In the following I will discuss only some of my research contributions, focusing on the work of more interdisciplinary nature.

The objective of my MSc thesis was the realization of a superconducting neuromagnetic sensor based on a rf-SQUID device. We measured spontaneous and evoked magnetic cerebral activity on healthy and epileptic subjects. This work was of experimental nature. During my PhD studies my research interested have shifted toward more theoretical matters mainly in the area of statistical mechanics of complex systems. One of the main trends of statistical physics in the last two decades has been the emergence of new concepts and techniques to study the co-operative behaviour of disordered and frustrated systems and provide the means for their fruitful application. Complexity theory involves the study of worlds whose microscopic constituents, often heterogeneous, all react and adapt to each other generating aggregate behaviour which is difficult to predict and very different from individual behaviour. My research has developed in this broad area, and my interests have shifted over the years from applications to protein folding and spin glass models, to pattern formation, and more recently to finance and economics. These apparently different topics all relate in some way to the collective behaviour of heterogeneous agents, where “agents” can be as diverse as amino-acids in a protein, spins, particle of sands or human beings. Proteins have been my first encounter with the fascinating world of complex system. Proteins are very elegant and multifunctional entities, large and complex on the scale of their fundamental constituents, but very simple if regarded on the scale of the structures they eventually constitute. Folding is one of the essential and most interesting features of proteins. Biologically active proteins are in a folded state: a globular state with a precise shape, characteristic of the given protein. One or a very few allowed folded states characterise a given, biologically active, protein. The given sequence of amino-acids, which eventually constitutes the working protein, is coded in the RNA but there is no space in the RNA for explicit coding of the 3-dimensional structure, which must be determined from the interaction laws of the constituent amino-acids. Folding is a complex and quite mysterious procedure. The time scales involved in the problem are very different: folding times vary considerably, but the time scale is much longer than that needed for a steepest descent to a simple minimum, and too short for an exhaustive search of the configuration space. The aim of my work has been to try and understand which are the relevant mechanisms used by nature in the process of folding. Physicists are used to approaches based on the idea of universality: relevant mechanisms are often independent of the details of the interaction laws, and just depend on very general features of the problem. Protein folding is an exquisite candidate to such an approach. It is clear that real proteins are the products of natural evolution and they are not random sequences of random interacting amino-acids. It is however extremely interesting to understand which properties proteins share with generic random heteropolymers, and on the contrary which of their properties are selected by natural evolution. In collaboration with G. Parisi and E. Marinari we formulated a model based on spin glass theory and investigated, using Monte Carlo simulations, the thermodynamic behaviour of a linear heteropolymer in which the interactions between different monomers contain a quenched (i.e. time independent) random component. We showed the existence, along with the usual coil and globule phases, of a new folded phase, characterised by long relaxation times and by the existence of few stable states. We also studied the dynamics of the heteropolymeric chain relaxing toward a new equilibrium configuration after the action of an external perturbation, a matter which had been studied experimentally. We built a numerical experiment close to the experimental conditions by starting from a chain thermalized at a given temperature and abruptly decreasing its temperature. Since the perturbation was small the system was only allowed to change in similar quasi-states and not to have a transition to a completely different state. We found good evidence that the non exponential decay observed in the experiments is not generated from the visiting of different minima with different underlying time scales (as suggested by others), but from the fact that the dynamics in a single minimum is itself nonexponential. Our work had an important impact in the area of protein folding and has triggered a large body of subsequent research. Protein folding is still an active line of research with important applications for drug design.

The work on protein folding naturally brought me to study other types of spin glass models as well like the RFIM and the XY model, during my stay as a Marie Curie post-doctoral fellow at the CEA-Saclay in Paris. My interest for patterns formation started with some work on phase separation. Phase separating systems, initially prepared in a state of equilibrium, and perturbed by modifying a control parameter such as the temperature, restore stability by evolving towards a different equilibrium state determined by the final value of the controlling field. Such evolution can be very slow and is often characterised by nonuniform, complex structures both in space and time. Pattern formation has been the main subject of my research during my stay in Barcelona as a postdoctoral fellow of the TMR research network. I worked in collaboration with experimental groups and we proposed a phenomenological model to describe the dynamics of fingering patterns observed in quasi-two-dimensional electro-deposition experiments. We also investigated the temporal evolution of water-sand interface driven by gravity.

In the last six years my research has mainly focus on applications of methods of statistical mechanics and applied probability to finance and economics. Traditional economic theory considers humans as rational, self-interested agents. Macro variables such as prices, supply and demand are derived from the behaviour of a hypothetical representative agent who takes calculated decisions to maximise personal benefit or profit. In reality, however, peoples’ decisions are often idiosyncratic, influenced by perceptions, beliefs and emotions. The traditional representative agent approach ignores important characteristics of real markets: the interaction between market participants and the heterogeneity and evolution of their characteristics. Furthermore, in a real market agents are not only price takers but also price makers. Market supply and demand depend on the strategies adopted by the agents which in turn affect the evolution of prices. Agents may use as input their observations of past price movements, feedback mechanisms giving rise to subtle interdependencies between prices and strategies. An important contribution of my research has been to develop simple models of market mechanism and agents’ behaviour, capable of reproducing the rich phenomenology observed in real markets, as a matter of fundamental importance for identifying the relevant mechanisms that affect price fluctuations. The well functioning of financial markets is essential for governments’ economic and financial policies, and for the society. Panics, crashes and systemic failure in financial markets can have dramatic consequences for the stability of the economy as a whole. Any policy recommendation not taking market sentiments into consideration, underestimate what financial practitioners believe to be an important source of price changes. Likewise, any governmental acting not taking into account the globally interconnected nature of the economy, will most likely misestimate its complex effects on the economic fabric. Understanding and controlling stability and efficiency is a crucial public policy objective both when designing trading platforms and payment, clearing and settlement infrastructures. Understanding how market design may affect stability and efficiency of markets is of fundamentals importance to achieve a better financial integration. Practitioners and regulators are very interested in financial stability issues and it is often the new and challenging problems that they raise, that stimulate the progress of theoretical models.

One of the contribution of this line of research has been the analysis of the mechanisms that lead to large fluctuations in financial markets. My work has shown that the co-ordination of traders’ strategies, either directly through imitation or herding or mediated by the market (for example by following chartist trading rules) is one of the main responsible of the insurgence of high levels of volatility and of slowly decaying volatility autocorrelations (a phenomenon called volatility clustering). In a sequence of papers I developed a dealer market microstructure model that provides a possible explanation of a number of empirical features observed in empirical data, namely anomalous scaling, or multiscaling, of the moments of price returns, volatility clustering, leverage effect and volume-volatility correlation. In collaboration with Doyne Farmer and his group at the Santa Fe Institute we have developed 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. In this paper 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. In another paper in collaboration with Carl Chiarella we investigate how different trading strategies, fundamentalist, chartist and random, may affect the dynamics of price, bid-ask spreads, trading volume and volatility, order book and order flows in order driven markets where traders can submit both market orders and limit orders. We also analyse how some features of market design, such as tick size and order lifetime, affect market liquidity.

Another interesting line of my research has addresses the role of the interbank market on the stability of the banking systems. Because of inter-locking exposures, whether through equity, debt or participation in a common payments system, these systems are susceptible to crises to spread from one institution to another. Such spread, if it occurs, can lead to a ‘systemic failure’, i.e. a large-scale crisis affecting the entire system. An important ingredient affecting the stability of these systems is the connectivity patterns generated by agents’ multilateral exposures. We show that in heterogeneous banking systems (banks may differ in size or risk aversion coefficients) the nature of the emerging connectivity pattern leads to higher instabilities as the scope of the inter-bank lending market increases. In analogy to epidemiology models on scale free networks successful immunisation strategies can be developed only by taking advantage of the non homogeneous connectivity properties of the network. In this contest, ”too connected to fail” should replace the ”’too big to fail” criteria normally employed by regulators. Using techniques from random networks analysis, we have empirically analyzed the network of exchanges in the overnight Italian interbank market, in order to investigate its topological properties and financial fragility. This work has been funded by the EPSRC research grant Complexity in Economics.

Clearing and settlement are the processes by which securities market transactions are finalised, so that securities are transferred from the seller to the buyer and payments from the buyer to the seller. The European Central Bank has awarded me with a Lamfalussy Fellowship for the year 2003 to pursue research in this direction. In this project I compared securities settlement gross and netting architectures and study settlement risk arising from exogenous operational delays. I focused on settlement failures in the two architectures as functions of the length of the settlement interval under different market conditions. While settlement failures are nonmonotonically related to the length of settlement cycles under both architectures, there is no clear cut ranking of which architecture delivers greater stability. Fads and fashions are another interesting example of how a large set of heterogeneous agents, each one acting according to his own set of allowed strategies, and normally with finite foresight, generate emergent collective behaviour. I studied the role of asymmetric interactions in the consumption behaviour of a network of heterogeneous agents. Direct interactions among economic agents, are meant to capture how the decision of each individual is influenced by the choice of others in his reference group. In the literature, attention has mainly focused on the case of positive, pairwise symmetric, spillovers, i.e. the case where the payoff of a particular action increases when others behave similarly. We assumed instead that the interactions among agents are uniquely specified by their “social distance” and that the consumption decision is driven by peering, distinction and aspiration effects. I had already studied the role of asymmetric interaction in SK spin systems and this work builds from this previous experience. We analysed the long-time behaviour of the system which, given the asymmetric nature of the interactions, can either converge into a fixed point or a periodic attractor. We discussed the role of symmetric versus asymmetric contributions to the utility function of agents, as well as that of idiosyncratic preferences, costs and memory in the consumption decision of the agents and show that the model can reproduce a wide range of consumption behaviour, from consumption cycles and consumption waves, to the sudden emergence of trends and fashion or stable niche products. This work has attracted considerable interest particularly for its potentially important application in marketing.

While I was a Marie Curie fellow in Paris I came across the financial mathematics problem of option pricing and hedging. The well known and widely used Black-Scholes option pricing theory has two remarkable features: the hedging strategy eliminates risk entirely, and the option price does not depend on the average return of the underlying. This has led to a general framework for derivative pricing, where the absence of arbitrage opportunities leads to the existence of a ‘risk-neutral probability measure’ over which the relevant average should be taken to obtain the price of derivative. However, in most models of stock fluctuations (except for continuous time Brownian motion and binomial) risk in option trading cannot be eliminated. The natural framework for pricing in this case is the risk minimisation approach, where the optimal trading strategy is determined such that the chosen measure of risk is minimised. In collaboration with J.P. Bouchaud and D.Sornette we proposed a method for option pricing and hedging that makes use of historical probability distributions. This work, being among the first to suggest the use of L ́evy processes to model the dynamics of the underlying stock price, has had a ma jor impact both among academics and practitioners and elicited a very positive review article by Barry Riley, appeared on the Financial Times on 17 April 1996.