scholarly journals Application of fractal properties in studies of financial markets

2018 ◽  
Vol 170 ◽  
pp. 01074
Author(s):  
Sergey Erokhin ◽  
Olga Roshka
Keyword(s):  
Financial Markets ◽  
Financial Market ◽  
Hurst Exponent ◽  
Point Particle ◽  
Time Interval ◽  
Time Intervals ◽  
Fractal Properties ◽  
Self Similar ◽  
Fractional Differential ◽  
Us Dollar

When studying the financial markets, the currency quotations of the Russian ruble / US dollar pair are examined for fractality. It is demonstrated that the time series of the quotations under study has basic fractal properties. Hurst exponent is used here to confirm the hypothesis of fractality whereby Hausdorff dimension was calculated, which turned out to be a fraction. The state of flux graphs were compared with the solution graphs of the known fractional differential equation of a point particle random walk along a self-similar fractal set. The solution of such an equation is given using the Mittag-Leffler functions. The graphs of these solutions are compared with state of flux graphs for different time intervals. Hence, it is proved that the Russian financial market is fractal and these results will help to forecast market behavior for a specified time interval in the future.

scholarly journals SOME APPLICATION OF THE FOKKER-PLANCK EQUATION

Vestnik MGSU ◽  
2017 ◽  
pp. 809-821
Author(s):  
Victor Grigorevich Pirozhkov ◽  
Olga Olegovna Roshka ◽  
Temirkhan Sultanovich Aleroev
Keyword(s):  
Planck Equation ◽  
Point Particle ◽  
Foreign Exchange Rates ◽  
Currency Market ◽  
Fractal Properties ◽  
Preset Time ◽  
The Subject ◽  
Self Similar ◽  
Fractional Differential ◽  
Us Dollar

In this paper, we study the foreign exchange rates of a pair Russian ruble/US dollar on the subject of fractality. It has been shown that the time series studied quotes has the basic fractal properties. With the help of the Hurst exponent was calculated by the Hausdorff dimension, which was a fractional number that supports the hypothesis of fractality. Volatility charts were compared with charts of known solutions of the fractional differential equation wandering point particle in a self-similar fractal set. The solution of this equation is a function of Mittag-Leffler. It is shown that graphs of the Mittag-Leffler function repeat exactly the structure of graphs volatilities for different periods of time. The solution of such an equation is written out using the Mittag-Leffler functions. The graphs of these decisions are compared with the volatility charts for different time periods. It also clearly confirms that the Russian currency market is a fractal. Thus, these results will help in predicting market behavior in advance a preset time in the future, which is almost a valuable tool for working with Russian currency market.

Critical Value-Based Power Options Pricing Problems in Uncertain Financial Markets

2021 ◽  
pp. 2150002
Author(s):  
Guimin Yang ◽  
Yuanguo Zhu
Keyword(s):  
Financial Markets ◽  
Financial Market ◽  
Numerical Experiments ◽  
Critical Value ◽  
The Other ◽  
Options Pricing ◽  
Underlying Asset ◽  
Pricing Problems ◽  
Fractional Differential ◽  
The One

Compared with investing an ordinary options, investing the power options may possibly yield greater returns. On the one hand, the power option is the best choice for those who want to maximize the leverage of the underlying market movements. On the other hand, power options can also prevent the financial market changes caused by the sharp fluctuations of the underlying assets. In this paper, we investigate the power option pricing problem in which the price of the underlying asset follows the Ornstein–Uhlenbeck type of model involving an uncertain fractional differential equation. Based on critical value criterion, the pricing formulas of European power options are derived. Finally, some numerical experiments are performed to illustrate the results.

Fractal Properties of Financial Assets and Forcasting Financial Crisis

2018 ◽  
pp. 23-41 ◽  
Author(s):  
Inna Nekrasova ◽  
Oxana Karnaukhova ◽  
Oleg Sviridov
Keyword(s):  
Fractal Dimension ◽  
Financial Markets ◽  
Future Development ◽  
Small Time ◽  
Practical Significance ◽  
Financial Assets ◽  
Time Intervals ◽  
Price Fluctuations ◽  
Fractal Properties ◽  
Fractal Index

The chapter is aimed at identification of criteria to select financial assets for investment; observing price fluctuations at small time intervals (up to one week) as possible predictors of the future of a significant increase in the price fluctuations amplitude; determining a fractal dimension of the financial markets on the basis of R/S-analysis; constructing a fractal index indicator to identify a bifurcation point, which gives birth to a possibility of crisis phenomena in economy. Therefore, the practical significance of the chapter lies in the idea of equipping academics and practitioners with new methods and tools for analysis and forecasting future development and dynamics of the financial markets.

scholarly journals Behavior of financial markets efficiency during the financial market crisis: 2007 – 2009

2014 ◽  
Vol 11 (2) ◽  
pp. 473-487 ◽  
Author(s):  
Ronald Henry Mynhardt ◽  
Alexey Plastun ◽  
Inna Makarenko
Keyword(s):  
Financial Markets ◽  
Market Efficiency ◽  
Financial Market ◽  
Hurst Exponent ◽  
Developed Countries ◽  
Market Analysis ◽  
Financial Market Crisis ◽  
Financial Market Analysis

This paper examines the behavior of financial markets efficiency during the recent financial market crisis. Using the Hurst exponent as a criterion of market efficiency we show that level of market efficiency is different for pre-crisis and crisis periods. We also classify financial markets of different countries by the level of their efficiency and reaffirm that financial markets of developed countries are more efficient than the developing ones. Based on Ukrainian financial market analysis we show the reasons of inefficiency of financial markets and provide some recommendations on their solution and thus improving the efficiency.

scholarly journals THE IMPACT OF CORONAVIRUS ON FINANCIAL MARKETS OF DEVELOPED COUNTRIES

2021 ◽  
pp. 25-33
Author(s):  
Mehjbeen
Keyword(s):  
Financial Markets ◽  
Financial Market ◽  
Capital Market ◽  
Financial Stability ◽  
Money Market ◽  
World Health ◽  
Future Research ◽  
Time Interval ◽  
Study Results ◽  
The Impact

According to the World Health Organization, tens of millions of confirmed cases and hundreds of thousands of confirmed deaths have been registered worldwide. COVID-19, a kind of coronavirus, has emerged as one of the most serious dangers to the global economy and financial markets in human history. The Covid-19 virus's introduction has caused a global reduction in economic activity, perhaps posing new dangers to financial stability. This study aims to look into and reveal the effect of coronavirus on two financial markets. Ten advanced countries' capital market and money market data with the time interval from March 2020 to November 2020 has been used in this study. Six indices of these financial market Shares, Mutual Funds, Treasury Bills, Certificates of Deposits, Bonds, and Mortgages worked as samples. The research has been conducted on advanced nations USA, Norway, Canada, Germany, Ireland, Sweden, Singapore, Netherlands, Australia, and Switzerland. Panel Regression Analysis, Spearman's rank correlation, and ANOVA are used to estimate the study results. The scholar constructs a weekly panel data of COVID- 19 confirmed cases and financial market indices. The second purpose is to calculate the Risk on the six chosen indices of these markets. COVAR methodology is used to measure the risks among capital market and money markets indices. Interestingly, this research noticed that all financial markets impacted by the coronavirus while the capital market has recorded maximum fluctuations and the stock market show minimum volatility. The final results give a detailed understanding of financial market indices. It will support future research on other money and Capital markets indices and investors after the Coronavirus period. KEYWORDS: Coronavirus, Financial Markets, COVAR, COVID-19 Confirmed Cases. Capital Market. Money Market, Developed economies,

scholarly journals Multiplicative Stochastic Model of the Time Interval between Trades in Financial Markets

2002 ◽  
Vol 7 (1) ◽  
pp. 43-54 ◽  
Author(s):  
V. Gontis
Keyword(s):  
Stochastic Model ◽  
Financial Markets ◽  
Financial Market ◽  
Stock Price ◽  
Price Change ◽  
Time Interval ◽  
Power Law Distribution ◽  
Physical Systems ◽  
Long Range Correlations ◽  
Consistent Model

Stock price change in financial market occurs through transactions, in analogy with diffusion in stochastic physical systems. The analysis of price changes in real markets shows that long-range correlations of price fluctuations largely depend on the number of transactions. We introduce the multiplicative stochastic model of time interval between trades and analyze spectral density and correlations of the number of transactions. The model reproduces spectral properties of the real markets and explains the mechanism of power law distribution of trading activity. Our study provides an evidence that statistical properties of financial markets are enclosed in the statistics of the time interval between trades. Multiplicative stochastic diffusion may serve as a consistent model for this statistics.

scholarly journals INFLUENCE OF CALCULATION ACCURACY OF TRAFFIC SELF-SIMILARITY EXPONENT ON A QUALITY OF SERVICE CHARACTERISTICS

2020 ◽  
Vol 1 (1) ◽  
pp. 88-94
Author(s):  
A.G. Lozhkovskyi ◽  
V.A. Turchyn ◽  
V.S. Andriiaka ◽  
Keyword(s):  
Quality Of Service ◽  
Hurst Exponent ◽  
Accurate Determination ◽  
Similarity Coefficient ◽  
Time Interval ◽  
Self Similarity ◽  
Service Characteristics ◽  
Self Similar

The quality of service (QoS) characteristics in any telecommunication system depend on its scheme, requirements servicing rules and, to the greatest extent, on the type of traffic generated by the system requirements flow. In packet communication networks, a mathematical model of self-similar traffic is used, where the time interval between packets is described by Pareto or Weibull distributions. With an increase in the degree of self-similarity of packet traffic, the QoS characteristics in the system significantly deteriorate compared to servicing, for example, Poisson traffic. But for such traffic there is no reliable methodology for calculating the characteristics of the quality of service. The degree of self­similarity of traffic is determined by the Hurst exponent H or the coefficient of self-similarity. The method of increasing the accuracy of calculating the quality of service characteristics in a packet communication network with self-similar traffic due to a more accurate determination of the self-similarity coefficient or Hurst exponent depending on the parameters of the probability function of the distribution of the time interval between packets is analyzed. For self-similar traffic, the accuracy of new formulas for calculating the traffic self-similarity coefficient based on the shape parameter of the probability distribution has been verified. After a more accurate determination of the Hurst exponent, the average value of the number of packets in the system is calculated using the Norros formula, and then, from the approximation of the distribution function of the system states, the probability of waiting for packet service is calculated. With increasing accuracy of calculating the Hurst exponent, the accuracy of calculating the very characteristics of the quality of service also increases. Simulation confirmed the higher accuracy of these methods for calculating QoS characteristics in a system with self-similar traffic. Moreover, the differences in simulation and calculation results do not exceed 3 ... 5%.

METABOLIC STUDIES WITH 131I-LABELED THYROXINE. II.

1963 ◽  
Vol 44 (3) ◽  
pp. 475-480 ◽  
Author(s):  
R. Grinberg
Keyword(s):  
Spinal Cord ◽  
Central Nervous System ◽  
Nervous System ◽  
Optic Nerve ◽  
Pituitary Gland ◽  
Time Interval ◽  
Time Intervals ◽  
Pituitary Glands ◽  
The Central Nervous System ◽  
Tentative Explanation

ABSTRACT Radiologically thyroidectomized female Swiss mice were injected intraperitoneally with 131I-labeled thyroxine (T4*), and were studied at time intervals of 30 minutes and 4, 28, 48 and 72 hours after injection, 10 mice for each time interval. The organs of the central nervous system and the pituitary glands were chromatographed, and likewise serum from the same animal. The chromatographic studies revealed a compound with the same mobility as 131I-labeled triiodothyronine in the organs of the CNS and in the pituitary gland, but this compound was not present in the serum. In most of the chromatographic studies, the peaks for I, T4 and T3 coincided with those for the standards. In several instances, however, such an exact coincidence was lacking. A tentative explanation for the presence of T3* in the pituitary gland following the injection of T4* is a deiodinating system in the pituitary gland or else the capacity of the pituitary gland to concentrate T3* formed in other organs. The presence of T3* is apparently a characteristic of most of the CNS (brain, midbrain, medulla and spinal cord); but in the case of the optic nerve, the compound is not present under the conditions of this study.

Caputo fractional differential equations with non-instantaneous impulses and strict stability by Lyapunov functions

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5217-5239 ◽  
Author(s):  
Ravi Agarwal ◽  
Snehana Hristova ◽  
Donal O’Regan
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Time Intervals ◽  
Dini Derivative ◽  
Comparison Results ◽  
Strict Stability ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential

In this paper the statement of initial value problems for fractional differential equations with noninstantaneous impulses is given. These equations are adequate models for phenomena that are characterized by impulsive actions starting at arbitrary fixed points and remaining active on finite time intervals. Strict stability properties of fractional differential equations with non-instantaneous impulses by the Lyapunov approach is studied. An appropriate definition (based on the Caputo fractional Dini derivative of a function) for the derivative of Lyapunov functions among the Caputo fractional differential equations with non-instantaneous impulses is presented. Comparison results using this definition and scalar fractional differential equations with non-instantaneous impulses are presented and sufficient conditions for strict stability and uniform strict stability are given. Examples are given to illustrate the theory.

scholarly journals Valuing Peace: The Effects of Financial Market Exposure on Votes and Political Attitudes

Econometrica ◽  
2019 ◽  
Vol 87 (5) ◽  
pp. 1561-1588 ◽  
Author(s):  
Saumitra Jha ◽  
Moses Shayo
Keyword(s):  
Financial Markets ◽  
Financial Market ◽  
Political Attitudes ◽  
Peace Process ◽  
Superior Performance ◽  
Financial Assets ◽  
Material Incentive ◽  
Nonfinancial Information ◽  
Political Messages ◽  
Economic Risks

Can participation in financial markets lead individuals to reevaluate the costs of conflict, change their political attitudes, and even their votes? Prior to the 2015 Israeli elections, we randomly assigned Palestinian and Israeli financial assets to likely voters and incentivized them to actively trade for up to 7 weeks. No political messages or nonfinancial information were included. The treatment systematically shifted vote choices toward parties more supportive of the peace process. This effect is not due to a direct material incentive to vote a particular way. Rather, the treatment reduces opposition to concessions for peace and changes awareness of the broader economic risks of conflict. While participants who were assigned Palestinian assets are more likely to associate their assets' performance with peace, they are less engaged in the experiment. Combined with the superior performance of Israeli stocks during the study period, the ultimate effects of Israeli and Palestinian assets are similar.

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