Scaling properties in financial fluctuations are reviewed from the standpoint of statistical physics. We firstly show theoretically that the balance of demand and supply enhances fluctuations due to the underlying phase transition mechanism. By analyzing tick data of yen-dollar exchange rates we confirm two fractal properties: 1 The distribution of rate change in a fixed ticks is approximated by a symmetric stretched exponential function for a wide range of time intervals; 2 the interval time distribution of trades nearly follows a power law. Empirical fractal properties in companies financial data, such as distributions and fluctuations in assets and incomes are discussed with a simple model. The importance of methods and theories for phase transitions is discussed.
In light of micro-scale inefficiencies induced by the high degree of fragmentation of the Bitcoin trading landscape, we utilize a granular data set comprised of orderbook and trades data from the most liquid Bitcoin markets, in order to understand the price formation process at sub-1 second time scales. To achieve this goal, we construct a set of features that encapsulate relevant microstructural information over short lookback windows. These features are subsequently leveraged first to generate a leader-lagger network that quantifies how markets impact one another, and then to train linear models capable of explaining between 10% and 37% of total variation in $500$ms future returns (depending on which market is the prediction target). The results are then compared with those of various PnL calculations that take trading realities, such as transaction costs, into account. The PnL calculations are based on natural $textit{taker}$ strategies (meaning they employ market orders) that we associate to each model. Our findings emphasize the role of a markets fee regime in determining its propensity to being a leader or a lagger, as well as the profitability of our taker strategy. Taking our analysis further, we also derive a natural $textit{maker}$ strategy (i.e., one that uses only passive limit orders), which, due to the difficulties associated with backtesting maker strategies, we test in a real-world live trading experiment, in which we turned over 1.5 million USD in notional volume. Lending additional confidence to our models, and by extension to the features they are based on, the results indicate a significant improvement over a naive benchmark strategy, which we also deploy in a live trading environment with real capital, for the sake of comparison.
Using an exhaustive list of Japanese bankruptcy in 1997, we discover a Zipf law for the distribution of total liabilities of bankrupted firms in high debt range. The life-time of these bankrupted firms has exponential distribution in correlation with entry rate of new firms. We also show that the debt and size are highly correlated, so the Zipf law holds consistently with that for size distribution. In attempt to understand ``physics of bankruptcy, we show that a model of debtor-creditor dynamics of firms and a bank, recently proposed by economists, can reproduce these phenomenological findings.
We introduce an irreversible discrete multiplicative process that undergoes Bose-Einstein condensation as a generic model of competition. New players with different abilities successively join the game and compete for limited resources. A players future gain is proportional to its ability and its current gain. The theory provides three principles for this type of competition: competitive exclusion, punctuated equilibria, and a critical condition for the distribution of the players abilities necessary for the dominance and the evolution. We apply this theory to genetics, ecology and economy.
We investigate the wealth evolution in a system of agents that exchange wealth through a disordered network in presence of an additive stochastic Gaussian noise. We show that the resulting wealth distribution is shaped by the degree distribution of the underlying network and in particular we verify that scale free networks generate distributions with power-law tails in the high-income region. Numerical simulations of wealth exchanges performed on two different kind of networks show the inner relation between the wealth distribution and the network properties and confirm the agreement with a self-consistent solution. We show that empirical data for the income distribution in Australia are qualitatively well described by our theoretical predictions.
We study a self-reflexive DSGE model with heterogeneous households, aimed at characterising the impact of economic recessions on the different strata of the society. Our framework allows to analyse the combined effect of income inequalities and confidence feedback mediated by heterogeneous social networks. By varying the parameters of the model, we find different crisis typologies: loss of confidence may propagate mostly within high income households, or mostly within low income households, with a rather sharp crossover between the two. We find that crises are more severe for segregated networks (where confidence feedback is essentially mediated between agents of the same social class), for which cascading contagion effects are stronger. For the same reason, larger income inequalities tend to reduce, in our model, the probability of global crises. Finally, we are able to reproduce a perhaps counter-intuitive empirical finding: in countries with higher Gini coefficients, the consumption of the lowest income households tends to drop less than that of the highest incomes in crisis times.