Quantitative Finance

Empirical investor networks (EIN) proposed by \cite{Ozsoylev-Walden-Yavuz-Bildik-2014-RFS} are assumed to capture the information spreading path among investors. Here, we perform a comparative analysis between the EIN and the cellphone communication networks (CN) to test whether EIN is an information exchanging network from the perspective of the layer structures of ego networks. We employ two clustering algorithms ( k -means algorithm and H/T break algorithm) to detect the layer structures for each node in both networks. We find that the nodes in both networks can be clustered into two groups, one that has a layer structure similar to the theoretical Dunbar Circle corresponding to that the alters in ego networks exhibit a four-layer hierarchical structure with the cumulative number of 5, 15, 50 and 150 from the inner layer to the outer layer, and the other one having an additional inner layer with about 2 alters compared with the Dunbar Circle. We also find that the scale ratios, which are estimated based on the unique parameters in the theoretical model of layer structures \citep{Tamarit-Cuesta-Dunbar-Sanchez-2018-PNAS}, conform to a log-normal distribution for both networks. Our results not only deepen our understanding on the topological structures of EIN, but also provide empirical evidence of the channels of information diffusion among investors.

The attack intensity of distributed denial of service (DDoS) attacks is increasing every year. Botnets based on internet of things (IOT) devices are now being used to conduct DDoS attacks. The estimation of direct and indirect economic damages caused by these attacks is a complex problem. One of the indirect damage of a DDoS attack can be on the market value of the victim firm. In this article we analyze the impact of 45 different DDoS attack announcements on victim's stock prices. We find that previous studies have a mixed conclusion on the impact of DDoS attack announcements on the victim's stock price. Hence, in this article we evaluate this impact using three different approaches and compare the results. In the first approach, we use the assume the cumulative abnormal returns to be normally distributed and test the hypothesis that a DDoS attack announcement has no impact on the victim's stock price. In the latter two methods, we do not assume a distribution and use the empirical distribution of cumulative abnormal returns to test the hypothesis. We find that the assumption of cumulative abnormal returns being normally distributed leads to overestimation/underestimation of the impact. Finally, we analyze the impact of DDoS attack announcement on victim's stock price in each of the 45 cases and present our results.

We consider shared listings on two South African equity exchanges: the Johannesburg Stock Exchange (JSE) and the A2X Exchange. A2X is an alternative exchange that provides for both shared listings and new listings within the financial market ecosystem of South Africa. From a science perspective it provides the opportunity to compare markets trading similar shares, in a similar regulatory and economic environment, but with vastly different liquidity, costs and business models. A2X currently has competitive settlement and transaction pricing when compared to the JSE, but the JSE has deeper liquidity. In pursuit of an empirical understanding of how these differences relate to their respective price response dynamics, we compare the distributions and auto-correlations of returns on different time scales; we compare price impact and master curves; and we compare the cost of trading on each exchange. This allows us to empirically compare the two markets. We find that various stylised facts become similar as the measurement or sampling time scale increase. However, the same securities can have vastly different price responses irrespective of time scales. This is not surprising given the different liquidity and order-book resilience. Here we demonstrate that direct costs dominate the cost of trading, and the importance of competitively positioning cost ceilings. Universality is crucial for being able to meaningfully compare cross-exchange price responses, but in the case of A2X, it has yet to emerge in a meaningful way due to the infancy of the exchange -- making meaningful comparisons difficult.

Cross-correlations in fluctuations of the daily exchange rates within the basket of the 100 highest-capitalization cryptocurrencies over the period October 1, 2015, through March 31, 2019, are studied. The corresponding dynamics predominantly involve one leading eigenvalue of the correlation matrix, while the others largely coincide with those of Wishart random matrices. However, the magnitude of the principal eigenvalue, and thus the degree of collectivity, strongly depends on which cryptocurrency is used as a base. It is largest when the base is the most peripheral cryptocurrency; when more significant ones are taken into consideration, its magnitude systematically decreases, nevertheless preserving a sizable gap with respect to the random bulk, which in turn indicates that the organization of correlations becomes more heterogeneous. This finding provides a criterion for recognizing which currencies or cryptocurrencies play a dominant role in the global crypto-market. The present study shows that over the period under consideration, the Bitcoin (BTC) predominates, hallmarking exchange rate dynamics at least as influential as the US dollar. The BTC started dominating around the year 2017, while further cryptocurrencies, like the Ethereum (ETH) and even Ripple (XRP), assumed similar trends. At the same time, the USD, an original value determinant for the cryptocurrency market, became increasingly disconnected, its related characteristics eventually approaching those of a fictitious currency. These results are strong indicators of incipient independence of the global cryptocurrency market, delineating a self-contained trade resembling the Forex.

We propose a novel approach that allows to calculate Hilbert transform based complex correlation for unevenly spaced data. This method is especially suitable for high frequency trading data, which are of a particular interest in finance. Its most important feature is the ability to take into account lead-lag relations on different scales, without knowing them in advance. We also present results obtained with this approach while working on Tokyo Stock Exchange intraday quotations. We show that individual sectors and subsectors tend to form important market components which may follow each other with small but significant delays. These components may be recognized by analysing eigenvectors of complex correlation matrix for Nikkei 225 stocks. Interestingly, sectorial components are also found in eigenvectors corresponding to the bulk eigenvalues, traditionally treated as noise.

We present a brief overview of random matrix theory (RMT) with the objectives of highlighting the computational results and applications in financial markets as complex systems. An oft-encountered problem in computational finance is the choice of an appropriate epoch over which the empirical cross-correlation return matrix is computed. A long epoch would smoothen the fluctuations in the return time series and suffers from non-stationarity, whereas a short epoch results in noisy fluctuations in the return time series and the correlation matrices turn out to be highly singular. An effective method to tackle this issue is the use of the power mapping, where a non-linear distortion is applied to a short epoch correlation matrix. The value of distortion parameter controls the noise-suppression. The distortion also removes the degeneracy of zero eigenvalues. Depending on the correlation structures, interesting properties of the eigenvalue spectra are found. We simulate different correlated Wishart matrices to compare the results with empirical return matrices computed using the S&P 500 (USA) market data for the period 1985-2016. We also briefly review two recent applications of RMT in financial stock markets: (i) Identification of "market states" and long-term precursor to a critical state; (ii) Characterization of catastrophic instabilities (market crashes).

Social systems are characterized by an enormous network of connections and factors that can influence the structure and dynamics of these systems. All financial markets, including the cryptocurrency market, belong to the economical sphere of human activity that seems to be the most interrelated and complex. The cryptocurrency market complexity can be studied from different perspectives. First, the dynamics of the cryptocurrency exchange rates to other cryptocurrencies and fiat currencies can be studied and quantified by means of multifractal formalism. Second, coupling and decoupling of the cryptocurrencies and the conventional assets can be investigated with the advanced cross-correlation analyses based on fractal analysis. Third, an internal structure of the cryptocurrency market can also be a subject of analysis that exploits, for example, a network representation of the market. We approach this subject from all three perspectives based on data recorded between January 2019 and June 2020. This period includes the Covid-19 pandemic and we pay particular attention to this event and investigate how strong its impact on the structure and dynamics of the market was. Besides, the studied data covers a few other significant events like double bull and bear phases in 2019. We show that, throughout the considered interval, the exchange rate returns were multifractal with intermittent signatures of bifractality that can be associated with the most volatile periods of the market dynamics like a bull market onset in April 2019 and the Covid-19 outburst in March 2020. The topology of a minimal spanning tree representation of the market also used to alter during these events from a distributed type without any dominant node to a highly centralized type with a dominating hub of USDT. However, the MST topology during the pandemic differs in some details from other volatile periods.

The popularity of deep reinforcement learning (DRL) methods in economics have been exponentially increased. DRL through a wide range of capabilities from reinforcement learning (RL) and deep learning (DL) for handling sophisticated dynamic business environments offers vast opportunities. DRL is characterized by scalability with the potential to be applied to high-dimensional problems in conjunction with noisy and nonlinear patterns of economic data. In this work, we first consider a brief review of DL, RL, and deep RL methods in diverse applications in economics providing an in-depth insight into the state of the art. Furthermore, the architecture of DRL applied to economic applications is investigated in order to highlight the complexity, robustness, accuracy, performance, computational tasks, risk constraints, and profitability. The survey results indicate that DRL can provide better performance and higher accuracy as compared to the traditional algorithms while facing real economic problems at the presence of risk parameters and the ever-increasing uncertainties.

In quantitative finance, it is often necessary to analyze the distribution of the sum of specific functions of observed values at discrete points of an underlying process. Examples include the probability density function, the hedging error, the Asian option, and statistical hypothesis testing. We propose a method to calculate such a distribution, utilizing a recursive method, and examine it using various examples. The results of the numerical experiment show that our proposed method has high accuracy.

We explore the effect of past market movements on the instantaneous correlations between assets within the futures market. Quantifying this effect is of interest to estimate and manage the risk associated to portfolios of futures in a non-stationary context. We apply and extend a previously reported method called the Principal Regression Analysis (PRA) to a universe of 84 futures contracts between 2009 and 2019 . We show that the past up (resp. down) 10 day trends of a novel predictor -- the eigen-factor -- tend to reduce (resp. increase) instantaneous correlations. We then carry out a multifactor PRA on sectorial predictors corresponding to the four futures sectors (indexes, commodities, bonds and currencies), and show that the effect of past market movements on the future variations of the instantaneous correlations can be decomposed into two significant components. The first component is due to the market movements within the index sector, while the second component is due to the market movements within the bonds sector.