Detection of power-law behavior and studies of scaling exponents uncover the characteristics of complexity in many real world phenomena. The complexity of financial markets has always presented challenging issues and provided interesting findings, such as the inverse cubic law in the tails of stock price fluctuation distributions. Motivated by the rise of novel digital assets based on blockchain technology, we study the distributions of cryptocurrency price fluctuations. We consider Bitcoin returns over various time intervals and from multiple digital exchanges, in order to investigate the existence of universal scaling behavior in the tails, and ascertain whether the scaling exponent supports the presence of a finite second moment. We provide empirical evidence on slowly decaying tails in the distributions of returns over multiple time intervals and different exchanges, corresponding to a power-law. We estimate the scaling exponent and find an asymptotic power-law behavior with 2 < α < 2.5 suggesting that Bitcoin returns, in addition to being more volatile, also exhibit heavier tails than stocks, which are known to be around 3. Our results also imply the existence of a finite second moment, thus providing a fundamental basis for the usage of standard financial theories and covariance-based techniques in risk management and portfolio optimization scenarios.

In complex systems, statistical dependencies between individual components are often considered one of the key mechanisms which drive the system dynamics observed on a macroscopic level. In this paper, we study cross-sectional time-lagged dependencies in financial markets, quantified by nonparametric measures from information theory, and estimate directed temporal dependency networks in financial markets. We examine the emergence of strongly connected feedback components in the estimated networks, and hypothesize that the existence of information feedback in financial networks induces strong spatiotemporal spillover effects and thus indicates systemic risk. We obtain empirical results by applying our methodology on stock market and real estate data, and demonstrate that the estimated networks exhibit strongly connected components around periods of high volatility in the markets. To further study this phenomenon, we construct a systemic risk indicator based on the proposed approach, and show that it can be used to predict future market distress. Results from both the stock market and real estate data suggest that our approach can be useful in obtaining early-warning signals for crashes in financial markets.

Much research has been conducted arguing that tipping points at which complex systems experience phase transitions are difficult to identify. [1,2,3,4,5,6,7] To test the existence of tipping points in financial markets, based on the alternating offer strategic model we propose a network of bargaining agents [8,9,10,11,12,13,14] who mutually either cooperate or compete, [18,15,16,17] where the feedback mechanism [19,20] between trading and price dynamics is driven by an external "hidden" variable R that quantifies the degree of market overpricing. Due to the feedback mechanism, R fluctuates and oscillates over time, and thus periods when the market is underpriced and overpriced occur repeatedly. As the market becomes overpriced, bubbles are created that ultimately burst in a market crash. The probability that the index will drop in the next year exhibits a strong hysteresis behavior from which we calculate the tipping point. The probability distribution function of R has a bimodal shape characteristic of small systems near the tipping point. By examining the S&P500 index we illustrate the applicability of the model and demonstate that the financial data exhibits a hysteresis and a tipping point that agree with the model predictions. We report a cointegration between the returns of the S&P 500 index and its intrinsic value.

Market making is the process whereby a market participant, called a market maker, simultaneously and repeatedly posts limit orders on both sides of the limit order book of a security in order to both provide liquidity and generate profit. Optimal market making entails dynamic adjustment of bid and ask prices in response to the market maker’s current inventory level and market conditions with the goal of maximizing a risk-adjusted return measure. This problem is naturally framed as a Markov decision process, a discrete-time stochastic (inventory) control process. Reinforcement learning, a class of techniques based on learning from observations and used for solving Markov decision processes, lends itself particularly well to it. Recent years have seen a very strong uptick in the popularity of such techniques in the field, fueled in part by a series of successes of deep reinforcement learning in other domains. The primary goal of this paper is to provide a comprehensive and up-to-date overview of the current state-of-the-art applications of (deep) reinforcement learning focused on optimal market making. The analysis indicated that reinforcement learning techniques provide superior performance in terms of the risk-adjusted return over more standard market making strategies, typically derived from analytical models.

Unsupervised learning methods have been increasingly used for detecting latent factors in high-dimensional time series, with many applications, especially in financial risk modelling. Most latent factor models assume that the factors are pervasive and affect all of the time series. However, some factors may affect only certain assets in financial markets, due to their clustering within countries, asset classes, or sector classifications. In this paper we consider high-dimensional financial time series with pervasive and cluster-specific latent factors, and propose a clustering and latent factor estimation method. We also develop a model selection algorithm, based on the spectral properties of asset correlation matrices and asset graphs. A simulation study with known data generating processes demonstrates that the proposed method outperforms other clustering methods and provides estimates with a high degree of accuracy. Moreover, the model selection procedure is also shown to provide stable and accurate estimates for the number of clusters and latent factors. We apply the proposed methods to datasets of asset returns from global financial markets using a backtesting approach. The results demonstrate that the clustering approach and estimated latent factors yield relevant information, improve risk modelling and reduce volatility in optimal minimum variance portfolios.INDEX TERMS Latent factor models, High-dimensional data analysis, Financial risk modelling.