The IP also implies some principles of economics never before understood as joint implications of a single mathematical model Angle, b. That is, in the IP there is no divide between sociophysics and econophysics. If a student asks what sociology would be like if it were a mathematical science, consider that it might be like statistical mechanics in physics and that the Inequality Process might be a starting point.

There are short descriptions of the IP in Tim Liao, et al. Some economists, such as Lux, Univer-sity of Kiel Germany , have crossed the disciplinary divide between economics and econophysics to the enrichment of both.

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Sociologists have been invited by professors B. Chakrabarti and A. There is no difference in meaning between sociophysics as used today by statistical physicists and sociology as coined by Comte almost two centuries ago. For more information on how interdisciplinary physicists have incorporated the IP into their research since , do a search at www. References Angle, J.

Chatterjee and B. Chakrabarti Eds. Milan: Springer. Bernstein, R. Keith, B. Kleiber, C. New York: Wiley. Kotz, S. Abstract is online at meetings. Lenski, G. Power and Privilege. New York: McGraw-Hill. Liao, T.

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Thousand Oaks, CA: Sage. Lux, T. Chatterjee, S. Yarlagadda, and B. Join the discussion about this article at members. Then we compute the infinitesimal generator associated with the order book in a general setting, and link the price dynamics to the instantaneous state of the order book. In the last section, we prove the stationarity of the order book and give some hints about the behaviour of the price process in long time scales.

In the past years several Agents Based Models ABMs have been introduced to reproduce and interpret the main features of financial markets [ 7 , 14 ]. The ABMs go beyond simple differential equations with the aim of being able to address the complex phenomenology of a dynamics. The ABMs give the possibility to describe the intrinsic heterogeneity of the market which seems to be responsible for many of these SF [ 6 , 12 ]. The main SF are the fat tails for the fluctuations of price-returns, the arbitrage condition, which implies no correlations in the price returns, and the volatility clustering which implies long memory correlations for volatility.

I review in this paper 1 my findings on order driven market modeling. Following my previous works on robust agents based modeling in finance [ 1 — 3 , 5 ], I study specific characteristics of order book markets. By controlling the descriptive time scale of the dynamics involved, I show how market impact, linear by definition, and trading strategies lead to precise pictures for clarifying order book dynamics, consistent with what is observed empirically.

I then discuss more specifically the role of market impact in the created dynamics and structure of the book and the economic implications of my studies. The article is organized as follows. In Sect. I define in Sect. I focus the analysis on the dynamics and structures of the book in Sect.

## Econophysics of Stocks and other Markets - Proceedings of the Econophys-Kolkata II

I discuss the economic implications of the results and draw conclusions in the last sections. We present some simulation results on various mono- and multi-asset market making strategies. Starting with a zero-intelligence market, we gradually enhance the model by taking into account such properties as the autocorrelation of trade signs, or the existence of informed traders. We then use Monte Carlo simulations to study the effects of those properties on some elementary market making strategies. Finally, we present some possible improvements of the strategies. We And that when the trading rate becomes faster, the return variance per trade or the impact, as measured by the price variation in the direction of the trade, strongly increases.

We provide evidence that these properties persist at coarser time scales. We also show that the spread value is an increasing function of the activity. This suggests that order books are more likely empty when the trading rate is high. A tick size is the smallest increment of a security price. Tick size is typically regulated by the exchange where the security is traded and it may be modified either because the exchange enforces an overall tick size change or because the price of the security is too low or too high. There is an extensive literature, partially reviewed in Sect.

However, the role and the importance of tick size has not been yet fully understood, as testified, for example, by a recent document of the Committee of European Securities Regulators CESR [ 1 ]. Many statistical arbitrage strategies, such as pair trading or basket trading, are based on several assets.

Optimal execution routines should also take into account correlation between stocks when proceeding clients orders. However, not so much effort has been devoted to correlation modelling and only few empirical results are known about high frequency correlation. Depending on the time scale under consideration, a plausible candidate for modelling correlation should: at high frequency: reproduce the Epps effect [ 1 ], take into account lead-lag relationships between assets [ 2 ].

The goal of this note is to describe a model for ultra high frequency prices and durations, the model with uncertainty zones developed in [ 27 ]. We also give some results from [ 28 ] and [ 29 ] which show how it can be used in practice for statistical estimation or in order to hedge derivatives. Before introducing this model, we briefly recall the classical approaches of price modelling in the so-called microstructure noise literature. Assuming a particular price process, it was shown by Gatheral in [ 6 ], that a model that combines nonlinear price impact with exponential decay of market impact admits price manipulation, an undesirable feature that should lead to rejection of the model.

Subsequently, Alfonsi and Schied proved in [ 2 ] that their model of the order book which has nonlinear market impact and exponential resilience, is free of price manipulation.

## Arnab Chatterjee - Google Scholar Citations

In this paper, we show how these at-first-sight incompatible results are in reality perfectly compatible. A central problem of Quantitative Finance is that of formulating a probabilistic model of the time evolution of asset prices allowing reliable predictions on their future volatility. As in several natural phenomena, the predictions of such a model must be compared with the data of a single process realization in our records.

In order to give statistical significance to such a comparison, assumptions of stationarity for some quantities extracted from the single historical time series, like the distribution of the returns over a given time interval, cannot be avoided. Such assumptions entail the risk of masking or misrepresenting non-stationarities of the underlying process, and of giving an incorrect account of its correlations.

The statistics of this ensemble allows to propose and test an adequate model of the stochastic process driving the exchange rate. This turns out to be a non-Markovian, self-similar process with non-stationary returns. The empirical ensemble correlators are in agreement with the predictions of this model, which is constructed on the basis of the time-inhomogeneous, anomalous scaling obeyed by the return distribution. Two Arrow-Pratt measures of risk aversion indicate attitudes of the individuals towards risk.

In the theory of finance often these measures are assumed to be constant. Using certain intuitively reasonable conditions, this paper develops axiomatic characterizations of the utility functions for which the Arrow-Pratt measures are constant. There are empirical evidences regrading the Pareto tail of the income distribution and the expenditure distribution. We formulate a simple economic framework to study the relation between them.

We explain the Pareto tails in both the distributions with a Cobb-Douglas felicity function to describe the preferences of agents. Moreover, the Indian data suggest a thicker Pareto tail for the expenditure distribution in comparison to the income distribution.

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With a uniform distribution of taste parameters for various goods, we identify a process that can give rise to this empirical phenomenon. We also verify our observation with appropriate simulation results. We consider a general class of two agent allocation problems and identify the complete class of first best rules.