Hasil untuk "q-fin.ST"

A. H. Nzokem

The cryptocurrency market presents both significant investment opportunities and higher risks relative to traditional financial assets. This study examines the tail behavior of daily returns for two leading cryptocurrencies, Bitcoin and Ethereum, using seven-parameter estimates from prior research, which applied the Generalized Tempered Stable (GTS) distribution. Quantile-quantile (Q-Q) plots against the Normal distribution reveal that both assets exhibit heavy-tailed return distributions. However, Ethereum consistently shows a greater frequency of extreme values than would be expected under its Bitcoin-modeled counterpart, indicating more pronounced tail risk.

L. Ponta, A. Carbone

The Kullback-Leibler cluster entropy $\mathcal{D_{C}}[P \| Q] $ is evaluated for the empirical and model probability distributions $P$ and $Q$ of the clusters formed in the realized volatility time series of five assets (SP\&500, NASDAQ, DJIA, DAX, FTSEMIB). The Kullback-Leibler functional $\mathcal{D_{C}}[P \| Q] $ provides complementary perspectives about the stochastic volatility process compared to the Shannon functional $\mathcal{S_{C}}[P]$. While $\mathcal{D_{C}}[P \| Q] $ is maximum at the short time scales, $\mathcal{S_{C}}[P]$ is maximum at the large time scales leading to complementary optimization criteria tracing back respectively to the maximum and minimum relative entropy evolution principles. The realized volatility is modelled as a time-dependent fractional stochastic process characterized by power-law decaying distributions with positive correlation ($H>1/2$). As a case study, a multiperiod portfolio built on diversity indexes derived from the Kullback-Leibler entropy measure of the realized volatility. The portfolio is robust and exhibits better performances over the horizon periods. A comparison with the portfolio built either according to the uniform distribution or in the framework of the Markowitz theory is also reported.

Vygintas Gontis

Modeling financial markets based on empirical data poses challenges in selecting the most appropriate models. Despite the abundance of empirical data available, researchers often face difficulties in identifying the best-fitting model. Long-range memory and self-similarity estimators, commonly used for this purpose, can yield inconsistent parameter values, as they are tailored to specific time series models. In our previous work, we explored order disbalance time series from the broader perspective of fractional L'{e}vy stable motion, revealing a stable anti-correlation in the financial market order flow. However, a more detailed analysis of empirical data indicates the need for a more specific order flow model that incorporates the power-law distribution of limit order cancellation times. When considering a series in event time, the limit order cancellation times follow a discrete probability mass function derived from the Tsallis q-exponential distribution. The combination of power-law distributions for limit order volumes and cancellation times introduces a novel approach to modeling order disbalance in the financial markets. Moreover, this proposed model has the potential to serve as an example for modeling opinion dynamics in social systems. By tailoring the model to incorporate the unique statistical properties of financial market data, we can improve the accuracy of our predictions and gain deeper insights into the dynamics of these complex systems.

Yutong Chen, Paul Bilokon, Conan Hales et al.

Cryptocurrency market is known for exhibiting significantly higher volatility than traditional asset classes. Efficient and adequate risk calculation is vital for managing risk exposures in such market environments where extreme price fluctuations occur in short timeframes. The objective of this thesis is to build a real-time computation workflow that provides VaR estimates for non-linear portfolios of cryptocurrency derivatives. Many researchers have examined the predictive capabilities of time-series models within the context of cryptocurrencies. In this work, we applied three commonly used models - EMWA, GARCH and HAR - to capture and forecast volatility dynamics, in conjunction with delta-gamma-theta approach and Cornish-Fisher expansion to crypto derivatives, examining their performance from the perspectives of calculation efficiency and accuracy. We present a calculation workflow which harnesses the information embedded in high-frequency market data and the computation simplicity inherent in analytical estimation procedures. This workflow yields reasonably robust VaR estimates with calculation latencies on the order of milliseconds.

Lorenzo Mercuri, Andrea Perchiazzo, Edit Rroji

In this paper we introduce a new model named CARMA(p,q)-Hawkes process as the Hawkes model with exponential kernel implies a strictly decreasing behaviour of the autocorrelation function and empirically evidences reject the monotonicity assumption on the autocorrelation function. The proposed model is a Hawkes process where the intensity follows a Continuous Time Autoregressive Moving Average (CARMA) process and specifically is able to reproduce more realistic dependence structures. We also study the conditions of stationarity and positivity for the intensity and the strong mixing property for the increments. Furthermore we compute the likelihood, present a simulation method and discuss an estimation method based on the autocorrelation function. A simulation and estimation exercise highlights the main features of the CARMA(p,q)-Hawkes.

Y. Chang, C. Lizardi, R. Shah

Momentum and mean reversion trading strategies have opposite characteristics. The former is generally better with trending assets, and the latter is generally better with mean reverting assets. Using the Hurst exponent, which classifies time series as trending or mean reverting, we attempt to trade with each strategy when it is advantageous to generate higher returns on average. We ultimately find that trading with the Hurst exponent can achieve higher returns, but it also comes at a higher risk. Finally, we consider limitations of our study and propose a method using Q-learning to improve our strategy and implementation of individual algorithms.

Stefan Bornholdt

Spin models of markets inspired by physics models of magnetism, as the Ising model, allow for the study of the collective dynamics of interacting agents in a market. The number of possible states has been mostly limited to two (buy or sell) or three options. However, herding effects of competing stocks and the collective dynamics of a whole market may escape our reach in the simplest models. Here I study a q-spin Potts model version of a simple Ising market model to represent the dynamics of a stock market index in a spin model. As a result, a self-organized gain-loss asymmetry in the time series of an index variable composed of stocks in this market is observed.

Jinho Lee, Raehyun Kim, Yookyung Koh et al.

We applied Deep Q-Network with a Convolutional Neural Network function approximator, which takes stock chart images as input, for making global stock market predictions. Our model not only yields profit in the stock market of the country where it was trained but generally yields profit in global stock markets. We trained our model only in the US market and tested it in 31 different countries over 12 years. The portfolios constructed based on our model's output generally yield about 0.1 to 1.0 percent return per transaction prior to transaction costs in 31 countries. The results show that there are some patterns on stock chart image, that tend to predict the same future stock price movements across global stock markets. Moreover, the results show that future stock prices can be predicted even if the training and testing procedures are done in different countries. Training procedure could be done in relatively large and liquid markets (e.g., USA) and tested in small markets. This result demonstrates that artificial intelligence based stock price forecasting models can be used in relatively small markets (emerging countries) even though they do not have a sufficient amount of data for training.

Alonso-Marroquin Fernando, Arias-Calluari Karina, Harre Michael et al.

We analyze the Standard & Poor's 500 stock market index from the last 22 years. The probability density function of price returns exhibits two well-distinguished regimes with self-similar structure: the first one displays strong super-diffusion together with short-time correlations, and the second one corresponds to weak super-diffusion with weak time correlations. Both regimes are well-described by q-Gaussian distributions. The porous media equation is used to derive the governing equation for these regimes, and the Black-Scholes diffusion coefficient is explicitly obtained from the governing equation.

Charles Shaw

This paper examines the time series properties of cryptocurrency assets, such as Bitcoin, using established econometric inference techniques, namely models of the GARCH family. The contribution of this study is twofold. I explore the time series properties of cryptocurrencies, a new type of financial asset on which there appears to be little or no literature. I suggest an improved econometric specification to that which has been recently proposed in Chu et al (2017), the first econometric study to examine the price dynamics of the most popular cryptocurrencies. Questions regarding the reliability of their study stem from the authors mis-diagnosing the distribution of GARCH innovations. Checks are performed on whether innovations are Gaussian or GED by using Kolmogorov type non-parametric tests and Khmaladze's martingale transformation. Null of gaussianity is strongly rejected for all GARCH(p,q) models, with $p,q \in \{1,\ldots,5 \}$, for all cryptocurrencies in sample. For tests of normality, I make use of the Gauss-Kronrod quadrature. Parameters of GARCH models are estimated with generalized error distribution innovations using maximum likelihood. For calculating P-values, the parametric bootstrap method is used. Arguing against Chu et al (2017), I show that there is a strong empirical argument against modelling innovations under some common assumptions.

Longfeng Zhao, Wei Li, Andrea Fenu et al.

The properties of q-dependent cross-correlation matrices of stock market have been analyzed by using the random matrix theory and complex network. The correlation structures of the fluctuations at different magnitudes have unique properties. The cross-correlations among small fluctuations are much stronger than those among large fluctuations. The large and small fluctuations are dominated by different groups of stocks. We use complex network representation to study these q-dependent matrices and discover some new identities. By utilizing those q-dependent correlation-based networks, we are able to construct some portfolio by those most independent stocks which consistently perform the best. The optimal multifractal order for portfolio optimization is approximately $q=2$. These results have deepened our understanding about the collective behaviors of the complex financial system.

Adil Yilmaz, Gazanfer Unal

Fractionally integrated generalized autoregressive conditional heteroskedasticity (FIGARCH) arises in modeling of financial time series. FIGARCH is essentially governed by a system of nonlinear stochastic difference equations ${u_t}$ = ${z_t}$ $(1-\sum\limits_{j=1}^q β_j L^j)σ_{t}^2 = ω+(1-\sum\limits_{j=1}^q β_j L^j - (\sum\limits_{k=1}^p \varphi_k L^k) (1-L)^d) u_t^2$, where $ω\in$ R, and $β_j\in$ R are constant parameters, $\{u_t\}_{{t\in}^+}$ and $\{σ_t\}_{{t\in}^+}$ are the discrete time real valued stochastic processes which represent FIGARCH (p,d,q) and stochastic volatility, respectively. Moreover, L is the backward shift operator, i.e. $L^d u_t \equiv u_{t-d}$ (d is the fractional differencing parameter 0$<$d$<$1). In this work, we have studied the chaoticity properties of FIGARCH (p,d,q) processes by computing mutual information, correlation dimensions, FNNs (False Nearest Neighbour), the Lyapunov exponents, and for both the stochastic difference equation given above and for the financial time series. We have observed that maximal Lyapunov exponents are negative, therefore, it can be suggested that FIGARCH (p,d,q) is not deterministic chaotic process.

V. Kandiah, H. Escaith, D. L. Shepelyansky

Using the new data from the OECD-WTO world network of economic activities we construct the Google matrix $G$ of this directed network and perform its detailed analysis. The network contains 58 countries and 37 activity sectors for years 1995, 2000, 2005, 2008, 2009. The construction of $G$, based on Markov chain transitions, treats all countries on equal democratic grounds while the contribution of activity sectors is proportional to their exchange monetary volume. The Google matrix analysis allows to obtain reliable ranking of countries and activity sectors and to determine the sensitivity of CheiRank-PageRank commercial balance of countries in respect to price variations and labor cost in various countries. We demonstrate that the developed approach takes into account multiplicity of network links with economy interactions between countries and activity sectors thus being more efficient compared to the usual export-import analysis. Our results highlight the striking increase of the influence of German economic activity on other countries during the period 1995 to 2009 while the influence of Eurozone decreases during the same period. We compare our results with the similar analysis of the world trade network from the UN COMTRADE database. We argue that the knowledge of network structure allows to analyze the effects of economic influence and contagion propagation over the world economy.

Zhi-Qiang Jiang, Askery A. Canabarro, Boris Podobnik et al.

Being able to forcast extreme volatility is a central issue in financial risk management. We present a large volatility predicting method based on the distribution of recurrence intervals between volatilities exceeding a certain threshold $Q$ for a fixed expected recurrence time $τ_Q$. We find that the recurrence intervals are well approximated by the $q$-exponential distribution for all stocks and all $τ_Q$ values. Thus a analytical formula for determining the hazard probability $W(Δt |t)$ that a volatility above $Q$ will occur within a short interval $Δt$ if the last volatility exceeding $Q$ happened $t$ periods ago can be directly derived from the $q$-exponential distribution, which is found to be in good agreement with the empirical hazard probability from real stock data. Using these results, we adopt a decision-making algorithm for triggering the alarm of the occurrence of the next volatility above $Q$ based on the hazard probability. Using a "receiver operator characteristic" (ROC) analysis, we find that this predicting method efficiently forecasts the occurrance of large volatility events in real stock data. Our analysis may help us better understand reoccurring large volatilities and more accurately quantify financial risks in stock markets.

Mateusz Denys, Tomasz Gubiec, Ryszard Kutner

We proposed the agent-based model of financial markets where agents (or traders) are represented by three-state spins located on the plane lattice or social network. The spin variable represents only the individual opinion (advice) that each trader gives to his nearest neighbors. In the model the agents can be considered as cunning. For instance, although agent having currently a maximal value of the spin advises his nearest neighbors to buy some stocks he, perfidiously, will sell some stocks in the next Monte Carlo step or will occupy a neutral position. In general, the trader has three possibilities: he can buy some stocks if his opinion change within a single time step is positive, sell some stocks if this change is negative, or remain inactive if his opinion is unchanged. The predictions of our model, found by simulations, well agree with the empirical universal distribution of interoccurrence times between daily losses below negative thresholds following the Tsallis q-exponential.

Yuri A. Katz

We present the qGaussian generalization of the Merton framework, which takes into account slow fluctuations of the volatility of the firms market value of financial assets. The minimal version of the model depends on the Tsallis entropic parameter q and the generalized distance to default. The empirical foundation and implications of the model are illustrated by the study of 645 North American industrial firms during the financial crisis, 2006 - 2012. All defaulters in the sample have exceptionally large, corresponding to unusually fat-tailed unconditional distributions of log-asset-returns. Using Receiver Operating Characteristic curves, we demonstrate the high forecasting power of the model in prediction of 1-year defaults. Our study suggests that the level of complexity of the realized time series, quantified by q, should be taken into account to improve valuations of default risk.

Il Gu Yi, Gabjin Oh, Beom Jun Kim

We apply a simple trading strategy for various time series of real and artificial stock prices to understand the origin of fractality observed in the resulting profit landscapes. The strategy contains only two parameters $p$ and $q$, and the sell (buy) decision is made when the log return is larger (smaller) than $p$ ($-q$). We discretize the unit square $(p, q) \in [0, 1] \times [0, 1]$ into the $N \times N$ square grid and the profit $Π(p, q)$ is calculated at the center of each cell. We confirm the previous finding that local maxima in profit landscapes are scattered in a fractal-like fashion: The number M of local maxima follows the power-law form $M \sim N^{a}$, but the scaling exponent $a$ is found to differ for different time series. From comparisons of real and artificial stock prices, we find that the fat-tailed return distribution is closely related to the exponent $a \approx 1.6$ observed for real stock markets. We suggest that the fractality of profit landscape characterized by $a \approx 1.6$ can be a useful measure to validate time series model for stock prices.

Andreas Gronlund, Il Gu Yi, Beom Jun Kim

We investigate the structure of the profit landscape obtained from the most basic, fluctuation based, trading strategy applied for the daily stock price data. The strategy is parameterized by only two variables, p and q. Stocks are sold and bought if the log return is bigger than p and less than -q, respectively. Repetition of this simple strategy for a long time gives the profit defined in the underlying two-dimensional parameter space of p and q. It is revealed that the local maxima in the profit landscape are spread in the form of a fractal structure. The fractal structure implies that successful strategies are not localized to any region of the profit landscape and are neither spaced evenly throughout the profit landscape, which makes the optimization notoriously hard and hypersensitive for partial or limited information. The concrete implication of this property is demonstrated by showing that optimization of one stock for future values or other stocks renders worse profit than a strategy that ignores fluctuations, i.e., a long-term buy-and-hold strategy.

Juan C. Ferrero

The analysis of the USA 2001 income distribution shows that it can be described by at least two main components, which obey the generalized Tsallis statistics with different values of the q parameter. Theoretical calculations using the gas kinetics model with a distributed saving propensity factor and two ensembles reproduce the empirical data and provide further information on the structure of the distribution, which shows a clear stratification. This stratification is amenable to different interpretations, which are analyzed. The distribution function is invariant with the average individual income, which implies that the inequity of the distribution cannot be modified by increasing the total income.

Fei Ren, Wei-Xing Zhou

We investigate the probability distributions of the recurrence intervals $τ$ between consecutive 1-min returns above a positive threshold $q>0$ or below a negative threshold $q<0$ of two indices and 20 individual stocks in China's stock market. The distributions of recurrence intervals for positive and negative thresholds are symmetric, and display power-law tails tested by three goodness-of-fit measures including the Kolmogorov-Smirnov (KS) statistic, the weighted KS statistic and the Cramér-von Mises criterion. Both long-term and shot-term memory effects are observed in the recurrence intervals for positive and negative thresholds $q$. We further apply the recurrence interval analysis to the risk estimation for the Chinese stock markets based on the probability $W_q(Δ{t},t)$, Value-at-Risk (VaR) analysis and VaR analysis conditioned on preceding recurrence intervals.