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arXiv2008

Modified Holder Exponents Approach to Prediction of the USA Stock Market Critical Points and Crashes

The paper is devoted to elaboration of a novel specific indicator based on the modified Holder exponents. This indicator has been used for forecasting critical points of financial time series and crashes of the USA stock market. The proposed approach is based on the hypothesis, which claims that before market critical points occur the dynamics of financial time series radically changes, namely time series become smoother. The approach has been tested on the stylized data and real USA stock market data. It has been shown that it is possible to forecast such critical points of financial time series as large upward and downward movements and trend changes. On this basis a new trading strategy has been elaborated and tested.

q-fin.ST↗

arXiv2008

Cross-correlations in Warsaw Stock Exchange

We study the inter-stock correlations for the largest companies listed on Warsaw Stock Exchange and included in the WIG20 index. Our results from the correlation matrix analysis indicate that the Polish stock market can be well described by a one factor model. We also show that the stock-stock correlations tend to increase with the time scale of returns and they approach a saturation level for the time scales of at least 200 min, i.e. an order of magnitude longer than in the case of some developed markets. We also show that the strength of correlations among the stocks crucially depends on their capitalization. These results combined with our earlier findings together suggest that now the Polish stock market situates itself somewhere between an emerging market phase and a mature market phase.

q-fin.ST↗

arXiv2008

Double Power Law Decay of the Persistence in Financial Markets

The persistence phenomenon is studied in the Japanese financial market by using a novel mapping of the time evolution of the values of shares quoted on the Nikkei Index onto Ising spins. The method is applied to historical end of day data from the Japanese stock market during 2002. By studying the time dependence of the spins, we find clear evidence for a double-power law decay of the proportion of shares that remain either above or below ` starting\rq\ values chosen at random. The results are consistent with a recent analysis of the data from the London FTSE100 market. The slopes of the power-laws are also in agreement. We estimate a long time persistence exponent for the underlying Japanese financial market to be 0.5.

q-fin.ST↗

arXiv2009

Modeling interaction of trading volume in financial dynamics

A dynamic herding model with interactions of trading volumes is introduced. At time $t$, an agent trades with a probability, which depends on the ratio of the total trading volume at time $t-1$ to its own trading volume at its last trade. The price return is determined by the volume imbalance and number of trades. The model successfully reproduces the power-law distributions of the trading volume, number of trades and price return, and their relations. Moreover, the generated time series are long-range correlated. We demonstrate that the results are rather robust, and do not depend on the particular form of the trading probability.

q-fin.TR↗

arXiv2008

Different fractal properties of positive and negative returns

We perform an analysis of fractal properties of the positive and the negative changes of the German DAX30 index separately using Multifractal Detrended Fluctuation Analysis (MFDFA). By calculating the singularity spectra $f(α)$ we show that returns of both signs reveal multiscaling. Curiously, these spectra display a significant difference in the scaling properties of returns with opposite sign. The negative price changes are ruled by stronger temporal correlations than the positive ones, what is manifested by larger values of the corresponding Hölder exponents. As regards the properties of dominant trends, a bear market is more persistent than the bull market irrespective of the sign of fluctuations.

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arXiv2008

Stock price jumps: news and volume play a minor role

In order to understand the origin of stock price jumps, we cross-correlate high-frequency time series of stock returns with different news feeds. We find that neither idiosyncratic news nor market wide news can explain the frequency and amplitude of price jumps. We find that the volatility patterns around jumps and around news are quite different: jumps are followed by increased volatility, whereas news tend on average to be followed by lower volatility levels. The shape of the volatility relaxation is also markedly different in the two cases. Finally, we provide direct evidence that large transaction volumes are_not_ responsible for large price jumps. We conjecture that most price jumps are induced by order flow fluctuations close to the point of vanishing liquidity.

q-fin.ST↗

arXiv2009

Heavy-Tailed Distribution of Cyber-Risks

With the development of the Internet, new kinds of massive epidemics, distributed attacks, virtual conflicts and criminality have emerged. We present a study of some striking statistical properties of cyber-risks that quantify the distribution and time evolution of information risks on the Internet, to understand their mechanisms, and create opportunities to mitigate, control, predict and insure them at a global scale. First, we report an exceptionnaly stable power-law tail distribution of personal identity losses per event, ${\rm Pr}({\rm ID loss} \geq V) \sim 1/V^b$, with $b =0.7 \pm 0.1$. This result is robust against a surprising strong non-stationary growth of ID losses culminating in July 2006 followed by a more stationary phase. Moreover, this distribution is identical for different types and sizes of targeted organizations. Since $b<1$, the cumulative number of all losses over all events up to time $t$ increases faster-than-linear with time according to $\mathbf{\simeq t^{1/b}}$, suggesting that privacy, characterized by personal identities, is necessarily becoming more and more insecure. We also show the existence of a size effect, such that the largest possible ID losses per event grow faster-than-linearly as $\sim S^{1.3}$ with the organization size $S$. The small value $b \simeq 0.7$ of the power law distribution of ID losses is explained by the interplay between Zipf's law and the size effect. We also infer that compromised entities exhibit basically the same probability to incur a small or large loss.

physics.soc-ph↗

arXiv2008

Feasibility of Portfolio Optimization under Coherent Risk Measures

It is shown that the axioms for coherent risk measures imply that whenever there is an asset in a portfolio that dominates the others in a given sample (which happens with finite probability even for large samples), then this portfolio cannot be optimized under any coherent measure on that sample, and the risk measure diverges to minus infinity. This instability was first discovered on the special example of Expected Shortfall which is used here both as an illustration and as a prompt for generalization.

q-fin.RM↗

arXiv2008

Quantitative analysis of privatization

In recent years, the economic policy of privatization, which is defined as the transfer of property or responsibility from public sector to private sector, is one of the global phenomenon that increases use of markets to allocate resources. One important motivation for privatization is to help develop factor and product markets, as well as security markets. Progress in privatization is correlated with improvements in perceived political and investment risk. Many emerging countries have gradually reduced their political risks during the course of sustained privatization. In fact, most risk resolution seems to take place as privatization proceeds to its later stage. Alternative benefits of privatization are improved risk sharing and increased liquidity and activity of the market. One of the main methods to develop privatization is entering a new stock to the markets for arising competition. However, attention to the capability of the markets to accept a new stock is substantial. Without considering the above statement, it is possible to reduce the market's efficiency. In other words, introduction of a new stock to the market usually decreases the stage of development and activity and increases the risk. Based on complexity theory, we quantify how the following factors: stage of development, activity, risk and investment horizons play roles in the privatization.

q-fin.GN↗

arXiv2008

Some Considerations on Six Degrees of Separation from A Theoretical Point of View

In this article we discuss six degrees of separation, which has been proposed by Milgram, from a theoretical point of view. Simply if one has $k$ friends, the number $N$ of indirect friends goes up to $\sim k^d$ in $d$ degrees of separation. So it would easily come up to population of whole world. That, however, is unacceptable. Mainly because of nonzero clustering coefficient $C$, $N$ does not become $\sim k^d$. In this article, we first discuss relations between six degrees of separation and the clustering coefficient in the small world network proposed by Watt and Strogatz\cite{Watt1},\cite{Watt2}. Especially, conditions that $(N)>$ (population of U.S.A or of the whole world) arises in the WS model is explored by theoretical and numerical points of view. Secondly we introduce an index that represents velocity of propagation to the number of friends and obtain an analytical formula for it as a function of $C$, $K$, which is an average degree over all nodes, and some parameter $P$ concerned with network topology. Finally the index is calculated numerically to study the relation between $C$, $K$ and $P$ and $N$.

physics.data-an↗

arXiv2008

The virtues and vices of equilibrium and the future of financial economics

The use of equilibrium models in economics springs from the desire for parsimonious models of economic phenomena that take human reasoning into account. This approach has been the cornerstone of modern economic theory. We explain why this is so, extolling the virtues of equilibrium theory; then we present a critique and describe why this approach is inherently limited, and why economics needs to move in new directions if it is to continue to make progress. We stress that this shouldn't be a question of dogma, but should be resolved empirically. There are situations where equilibrium models provide useful predictions and there are situations where they can never provide useful predictions. There are also many situations where the jury is still out, i.e., where so far they fail to provide a good description of the world, but where proper extensions might change this. Our goal is to convince the skeptics that equilibrium models can be useful, but also to make traditional economists more aware of the limitations of equilibrium models. We sketch some alternative approaches and discuss why they should play an important role in future research in economics.

q-fin.GN↗

arXiv2008

Can extremism guarantee pluralism?

Many models have been proposed to explain opinion formation in groups of individuals; most of these models study opinion propagation as the interaction between nodes/agents in a social network. Opinion formation is a complex process and a realistic model should also take into account the important feedbacks that the opinions of the agents have on the structure of the social networks and on the characteristics of the opinion dynamics. In this paper we will show that associating to different agents different kinds of interconnections and different interacting behaviours can lead to interesting scenarios, like the coexistence of several opinion clusters, namely pluralism. In our model agents have opinions uniformly and continuously distributed between two extremes. The social network is formed through a social aggregation mechanism including the segregation process of the extremists that results in many real communities. We show how this process affects the opinion dynamics in the whole society. In the opinion evolution we consider the different predisposition of single individuals to interact and to exchange opinion with each other; we associate to each individual a different tolerance threshold, depending on its own opinion: extremists are less willing to interact with individuals with strongly different opinions and to change significantly their ideas. A general result is obtained: when there is no interaction restriction, the opinion always converges to uniformity, but the same is happening whenever a strong segregation process of the extremists occurs. Only when extremists are forming clusters but these clusters keep interacting with the rest of the society, the survival of a wide opinion range is guaranteed.

physics.soc-ph↗

arXiv2008

Integration I(d) of Nonstationary Time Series: Stationary and nonstationary increments

The method of cointegration in regression analysis is based on an assumption of stationary increments. Stationary increments with fixed time lag are called integration I(d). A class of regression models where cointegration works was identified by Granger and yields the ergodic behavior required for equilibrium expectations in standard economics. Detrended finance market returns are martingales, and martingales do not satisfy regression equations. We extend the standard discussion to discover the class of detrended processes beyond standard regression models that satisfy integration I(d). In the language of econometrics, the models of interest are unit root models, meaning martingales. Typical martingales do not have stationary increments, and those that do generally do not admit ergodicity. Our analysis leads us to comment on the lack of equilibrium observed earlier between FX rates and relative price levels.

physics.soc-ph↗

arXiv2008

Crime and punishment in scientific research

Typical arguments against scientific misconduct generally fail to support current policies on research fraud: they may not prove wrong what is usually considered research misconduct and they tend to make wrong things that are not normally seen as scientific fraud, in particular honest errors. I also point out that sanctions are not consistent with the reasons why scientific fraud is supposed to be wrong either. Moreover honestly seeking truth should not be contrived as a moral rule -- it is instead a necessary condition for work to qualify as scientific. Keywords: cheating; ethics; fabrication; falsification; integrity; plagiarism; research fraud; scientific misconduct.

physics.soc-ph↗

arXiv2008

ARCH and GARCH Models vs. Martingale Volatility of Finance Market Returns

ARCH and GARCH models assume either i.i.d. or (what economists lable as) white noise as is usual in regression analysis while assuming memory in a conditional mean square fluctuation with stationary increments. We will show that ARCH/GARCH is inconsistent with uncorrelated increments, violating the i.i.d. and white assumptions and finance data and the efficient market hypothesis as well.

q-fin.ST↗

arXiv2008

Sensitivity of complex networks measurements

Complex networks obtained from the real-world networks are often characterized by incompleteness and noise, consequences of limited sampling as well as artifacts in the acquisition process. Because the characterization, analysis and modeling of complex systems underlain by complex networks are critically affected by the quality of the respective initial structures, it becomes imperative to devise methodologies for identifying and quantifying the effect of such sampling problems on the characterization of complex networks. Given that several measurements need to be applied in order to achieve a comprehensive characterization of complex networks, it is important to investigate the effect of incompleteness and noise on such quantifications. In this article we report such a study, involving 8 different measurements applied on 6 different complex networks models. We evaluate the sensitiveness of the measurements to perturbations in the topology of the network considering the relative entropy. Three particularly important types of progressive perturbations to the network are considered: edge suppression, addition and rewiring. The conclusions have important practical consequences including the fact that scale-free structures are more robust to perturbations. The measurements allowing the best balance of stability (smaller sensitivity to perturbations) and discriminability (separation between different network topologies) were also identified.

physics.soc-ph↗

arXiv2008

A note on wealth in a volatile economy

I show that if the capital accumulation dynamics is stochastic a new term, in addition to that given by accounting prices, has to be introduced in order to derive a correct estimate of the genuine wealth of an economy. In a simple model with multiplicative accumulation dynamics I show that: 1) the value function is always a decreasing function of volatility 2) the accounting prices are affected by volatility 3) the new term always gives a negative contribution to wealth changes. I discuss results for models with constant elasticity utility functions. When the elasticity of marginal utility is larger than one, accounting prices increase with volatility whereas when it is less than one accounting prices decrease with volatility. These conclusions are not altered when adopting optimal saving rates.

q-fin.GN↗

arXiv2008

A Theory for Market Impact: How Order Flow Affects Stock Price

It is known that the impact of transactions on stock price (market impact) is a concave function of the size of the order, but there exists little quantitative theory that suggests why this is so. I develop a quantitative theory for the market impact of hidden orders (orders that reflect the true intention of buying and selling) that matches the empirically measured result and that reproduces some of the non-trivial and universal properties of stock returns (returns are percent changes in stock price). The theory is based on a simple premise, that the stock market can be modeled in a mechanical way - as a device that translates order flow into an uncorrelated price stream. Given that order flow is highly autocorrelated, this premise requires that market impact (1) depends on past order flow and (2) is asymmetric for buying and selling. I derive the specific form for the dependence in (1) by assuming that current liquidity responds to information about all currently active hidden orders (liquidity is a measure of the price response to a transaction of a given size). This produces an equation that suggests market impact should scale logarithmically with total order size. Using data from the London Stock Exchange I empirically measure market impact and show that the result matches the theory. Also using empirical data, I qualitatively specify the asymmetry of (2). Putting all results together, I form a model for market impact that reproduces three universal properties of stock returns - that returns are uncorrelated, that returns are distributed with a power law tail, and that the magnitude of returns is highly autocorrelated (also known as clustered volatility).

q-fin.ST↗