How Does COVID-19 Affect the Volatility Spillover Between the Exchange Rate and the Export-oriented Businesses in Iran?

This study concentrates on examining the volatility spillover effects between the exchange rate (IRR to USD) and the leading export-oriented industries (i.e., petrochemical, basic metals and minerals) in Tehran Stock Exchange before and after the COVID-19 pandemic. Using DCC- and asymmetric DCC-GARCH approaches, the data sample (from 15 December 2018 to 24 April 2021) has been partitioned into two sub-samples: before and after the official announcement of COVID-19 outbreak. The results demonstrate that from the pre- to post-COVID-19 periods, first, the average returns of all industries have sharply fallen; second, the volatility of all variables has been significantly augmented in different horizons; third, for all industries, not only has the fractal market hypothesis approved in both separated periods, but also analysing the values of the fractional difference parameter, together with the outcomes of GARCH models, supports in the higher-risk post-COVID-19 period, wherein the effects of exogenous shocks last longer than their impacts in the alternative lower-risk period. Furthermore, our investigations demonstrate that the asymmetric spillover (based on the ADCC-GARCH models) in both pre- and post-COVID-19 periods are confirmed in all three industries, except for minerals after the novel coronavirus.Ultimately, the results not only corroborate the increase in the volatility spillover effects right after the COVID-19 but also substantiate that the exchange rate contributes most of the spillover effects into the petrochemical and minerals industries, which have been almost twice as much as those of the basic metals.

A Review of the Fractal Market Hypothesis for Trading and Market Price Prediction

This paper provides a review of the Fractal Market Hypothesis (FMH) focusing on financial times series analysis. In order to put the FMH into a broader perspective, the Random Walk and Efficient Market Hypotheses are considered together with the basic principles of fractal geometry. After exploring the historical developments associated with different financial hypotheses, an overview of the basic mathematical modelling is provided. The principal goal of this paper is to consider the intrinsic scaling properties that are characteristic for each hypothesis. In regard to the FMH, it is explained why a financial time series can be taken to be characterised by a 1/t1−1/γ scaling law, where γ>0 is the Lévy index, which is able to quantify the likelihood of extreme changes in price differences occurring (or otherwise). In this context, the paper explores how the Lévy index, coupled with other metrics, such as the Lyapunov Exponent and the Volatility, can be combined to provide long-term forecasts. Using these forecasts as a quantification for risk assessment, short-term price predictions are considered using a machine learning approach to evolve a nonlinear formula that simulates price values. A short case study is presented which reports on the use of this approach to forecast Bitcoin exchange rate values.

Efficient or Fractal Market Hypothesis? A Stock Indexes Modelling Using Geometric Brownian Motion and Geometric Fractional Brownian Motion

In this article, we propose a test of the dynamics of stock market indexes typical of the US and EU capital markets in order to determine which of the two fundamental hypotheses, efficient market hypothesis (EMH) or fractal market hypothesis (FMH), best describes market behavior. The article’s major goal is to show how to appropriately model return distributions for financial market indexes, specifically which geometric Brownian motion (GBM) and geometric fractional Brownian motion (GFBM) dynamic equations best define the evolution of the S&P 500 and Stoxx Europe 600 stock indexes. Daily stock index data were acquired from the Thomson Reuters Eikon database during a ten-year period, from January 2011 to December 2020. The main contribution of this work is determining whether these markets are efficient (as defined by the EMH), in which case the appropriate stock indexes dynamic equation is the GBM, or fractal (as described by the FMH), in which case the appropriate stock indexes dynamic equation is the GFBM. In this paper, we consider two methods for calculating the Hurst exponent: the rescaled range method (RS) and the periodogram method (PE). To determine which of the dynamics (GBM, GFBM) is more appropriate, we employed the mean absolute percentage error (MAPE) method. The simulation results demonstrate that the GFBM is better suited for forecasting stock market indexes than the GBM when the analyzed markets display fractality. However, while these findings cannot be generalized, they are verisimilar.

Efficient Market Hypothesis and Fractal Market Hypothesis: evidence from Russian stock exchange

This paper presents the results of the study of the fulfillment of the key conditions and prerequisites of the hypotheses of the efficiency and fractality of price behavior in financial markets for the period 1997–2021. Its relevance is due to the high volatility of the Russian stock market and its imperfections, which lead to significant price deviations. On the example of the analysis of the dynamics of the MOEX stock index, the method of testing the dynamics of prices on large arrays of real data with the use of statistical data processing methods and modern information technologies is demonstrated. The article concludes that the nature of the Russian market as a whole has a fractal character. At the same time, the assumptions underlying the hypothesis of information efficiency of the market are not fulfilled.

Carbon Futures Trading and Short-Term Price Prediction: An Analysis Using the Fractal Market Hypothesis and Evolutionary Computing

This paper presents trend prediction results based on backtesting of the European Union Emissions Trading Scheme futures market. This is based on the Intercontinental Exchange from 2005 to 2019. An alternative trend prediction strategy is taken that is predicated on an application of the Fractal Market Hypothesis (FMH) in order to develop an indicator that is predictive of short term future behaviour. To achieve this, we consider that a change in the polarity of the Lyapunov-to-Volatility Ratio precedes an associated change in the trend of the European Union Allowances (EUAs) price signal. The application of the FMH in this case is demonstrated to provide a useful tool in order to assess the likelihood of the market becoming bear or bull dominant, thereby helping to inform carbon trading investment decisions. Under specific conditions, Evolutionary Computing methods are utilised in order to optimise specific trading execution points within a trend and improve the potential profitability of trading returns. Although the approach may well be of value for general energy commodity futures trading (and indeed the wider financial and commodity derivative markets), this paper presents the application of an investment indicator for EUA carbon futures risk modelling and investment trend analysis only.

Empirical Research on the effectiveness of national pilot carbon trading market based on carbon price time series

We will promote the establishment of a unified national carbon market, effectively control and gradually reduce carbon emissions, and contribute to the reduction of carbon emissions, it is of great significance to promote the economic transformation to green and low-carbon. Based on the time series of carbon price, this paper conducts exploratory research on the effectiveness of the carbon trading market in eight pilot regions, uses the fractal market hypothesis, adopts the re-rating difference analysis method, takes the effective carbon price of each pilot every day as the research variable, and empirically analyzes the effectiveness of the pilot carbon market.

Efficiency of Price Movements in Futures Markets

We study behaviour in the E-mini S&P (ES) commodity futures data market to test for violation of the efficient market hypothesis (EMH), and test for market inefficiency. We demonstrate that, on long timescales, a single scaling determines dynamics. ES returns behave in a more general manner than random walks. We find that deviations from the EMH, and the associated heavy-tailed distributions, are more common than expected, and price returns can be fitted with an alpha-stable Lévy distribution. Our results indicate that while the ES futures market operates close to the state predicted by the EMH, the observed transient deviations from this state fail to have a statistical origin consistent with a purely random geometric Brownian motion, and are better described by the fractal market hypothesis.

Multifractal Analysis of African Stock Markets During the 2007–2008 US Crisis

In this paper, we examine the effects of subprime crisis on the largest African stock markets (South Africa, Nigeria, Egypt, and Morocco) by testing the fractal market hypothesis. We use a rolling window Multifractal Detrended Fluctuation Analysis, and find decline in local Hurst exponent and an increase in short-term trading activity for all considered stock markets during the global financial crisis. We furthermore investigate the interrelationships of African and the American stock markets using multi-scale contagion test. Findings suggest that the cross-correlation of African stock markets increases with American markets becoming higher during the crisis sub-period. However, the presence of contagion or interdependence effects are country and time horizon-dependent. Implications of the results are discussed.

Econophysics and Fractional Calculus: Einstein’s Evolution Equation, the Fractal Market Hypothesis, Trend Analysis and Future Price Prediction

This paper examines a range of results that can be derived from Einstein’s evolution equation focusing on the effect of introducing a Lévy distribution into the evolution equation. In this context, we examine the derivation (derived exclusively from the evolution equation) of the classical and fractional diffusion equations, the classical and generalised Kolmogorov–Feller equations, the evolution of self-affine stochastic fields through the fractional diffusion equation, the fractional Poisson equation (for the time independent case), and, a derivation of the Lyapunov exponent and volatility. In this way, we provide a collection of results (which includes the derivation of certain fractional partial differential equations) that are fundamental to the stochastic modelling associated with elastic scattering problems obtained under a unifying theme, i.e., Einstein’s evolution equation. This includes an analysis of stochastic fields governed by a symmetric (zero-mean) Gaussian distribution, a Lévy distribution characterised by the Lévy index γ ∈ [ 0 , 2 ] and the derivation of two impulse response functions for each case. The relationship between non-Gaussian distributions and fractional calculus is examined and applications to financial forecasting under the fractal market hypothesis considered, the reader being provided with example software functions (written in MATLAB) so that the results presented may be reproduced and/or further investigated.