Log Returns Research Articles

Opinion dynamics in financial markets via random networks

We investigate financial market dynamics by introducing a heterogeneous agent-based opinion formation model. In this work, we organize individuals in a financial market according to their trading strategy, namely, whether they are noise traders or fundamentalists. The opinion of a local majority compels the market exchanging behavior of noise traders, whereas the global behavior of the market influences the decisions of fundamentalist agents. We introduce a noise parameter, q, to represent the level of anxiety and perceived uncertainty regarding market behavior, enabling the possibility of adrift financial action. We place individuals as nodes in an Erdös-Rényi random graph, where the links represent their social interactions. At any given time, individuals assume one of two possible opinion states ±1 regarding buying or selling an asset. The model exhibits fundamental qualitative and quantitative real-world market features such as the distribution of logarithmic returns with fat tails, clustered volatility, and the long-term correlation of returns. We use Student's t distributions to fit the histograms of logarithmic returns, showing a gradual shift from a leptokurtic to a mesokurtic regime depending on the fraction of fundamentalist agents. Furthermore, we compare our results with those concerning the distribution of the logarithmic returns of several real-world financial indices.

A study of stock returns based on ARMA-GARCH model: Taking the CSI 300 Index as an example

This paper selects the daily return data of CSI 300 index from January 2, 2014 to September 30, 2020 to study the characteristics of CSI 300 index return volatility. An ARMA(3,3) model was fitted to the daily log returns of the CSI 300 index using R software, and the ARCH effect was found to exist. The returns were then fitted with an ARMA(3,3)-GARCH(1,1) model, the model fitting effect was tested, and finally the short-term returns of the CSI 300 index were predicted. The results of the empirical analysis show that the CSI 300 index return series has characteristics such as non-normal distributivity, spikes and thick tails, and aggregation.

A Study on the Impact of Macro Uncertainty on the Volatility of China's Carbon Emissions Trading Market

This paper selects three carbon emissions trading prices in Tianjin, Guangzhou and Hubei for the period 2019-2021 as the samples and conducts a cross-sectional and longitudinal analysis of their volatility. The study shows that: (1) the price volatility and price level of carbon market in the three places differ significantly, and the difference between the highest and lowest price is significant; (2) the standard deviation of the logarithmic return of carbon trading pilot in the three places is large, and the riskiness of carbon trading is high. Based on this, this paper puts forward suggestions in four aspects: accelerating the improvement of basic system guarantee, accelerating the construction of national carbon market system, steadily promoting the construction of national carbon market, and establishing carbon market risk identification and prevention mechanism.

Pairwise and high-order dependencies in the cryptocurrency trading network

In this paper we analyse the effects of information flows in cryptocurrency markets. We first define a cryptocurrency trading network, i.e. the network made using cryptocurrencies as nodes and the Granger causality among their weekly log returns as links, later we analyse its evolution over time. In particular, with reference to years 2020 and 2021, we study the logarithmic US dollar price returns of the cryptocurrency trading network using both pairwise and high-order statistical dependencies, quantified by Granger causality and O-information, respectively. With reference to the former, we find that it shows peaks in correspondence of important events, like e.g., Covid-19 pandemic turbulence or occasional sudden prices rise. The corresponding network structure is rather stable, across weekly time windows in the period considered and the coins are the most influential nodes in the network. In the pairwise description of the network, stable coins seem to play a marginal role whereas, turning high-order dependencies, they appear in the highest number of synergistic information circuits, thus proving that they play a major role for high order effects. With reference to redundancy and synergy with the time evolution of the total transactions in US dollars, we find that their large volume in the first semester of 2021 seems to have triggered a transition in the cryptocurrency network toward a more complex dynamical landscape. Our results show that pairwise and high-order descriptions of complex financial systems provide complementary information for cryptocurrency analysis.

Stock Prediction Analysis and Risk Conduction Path Research Based on EMD-LSTM Model

Stock market, government bond market and corporate bond market are important components of my country's financial market. It is of great significance to study stock market price fluctuations and their forecasting methods, and to reveal the risk transmission path between them. The first part of this paper mainly studies the construction of the index price prediction model, and makes a comprehensive comparison of the high-frequency fluctuation characteristics, long-term trend characteristics and average trend characteristics of the EMD decomposition results of the Shanghai Composite Index, the SSE Government Bond Index, and the SSE Corporate Bond Index. The LSTM prediction model and the EMD-LSTM prediction model were established for the three sequences respectively, and the prediction effects of the models were comprehensively compared by calculating the RMSE and MAPE of the predicted values of the test set. The results show that after the introduction of the EMD method, the prediction effects of the SSE Composite Index and the SSE Corporate Bond Index prediction model have been greatly improved, but the prediction effect of the SSE Government Bond Index prediction model is far inferior to that of the LSTM model. The second part of this paper mainly studies the financial market risk analysis and transmission path. First, the fluctuation risk analysis and stationarity analysis of the logarithmic return series of the three index price series are carried out. The yield series are stable. Then, the LSTM models based on different training data predict three index price series and compare the prediction results to study the similarity of the price fluctuation mechanism of the three financial markets. The results show that the price fluctuation mechanism of the stock market is similar to that of the corporate bond market, and the price fluctuation mechanism of the government bond market is more similar to the corporate bond market than the stock market. The paper conducts E-G cointegration test on three logarithmic return series that have been tested for stationarity to study the long-term equilibrium relationship between the three markets and finds that there is a cointegration relationship between the SSE Composite Index and the SSE Government Bond Index, as well as the SSE Government Bond Index and the SSE Corporate Bond Index. Finally, the Granger causality test is carried out between the sequences with cointegration relationship, and the result shows that the risk transmission mechanism between the national debt market and the corporate bond market is strong, while the risk transmission mechanism between the stock market and the bond market is weak.

Preference heterogeneity in Bitcoin and its forks' network

This study investigates the transmission channel of information diffusion in the network of Bitcoin and its six forks using daily closing prices from the start of trading for each one to September 24, 2021. In particular, the price series are stationarized for further analysis by converting them to log returns. We find the following: (i) the Bitcoin market has the central authority of information flow because of its large market size and high liquidity, and (ii) the Bitcoin Gold and Bitcoin Diamond markets collaborate in information dissemination and intermediary role despite their small market size and low liquidity. Using the scaling and Hurst exponents, we explain the roles of Bitcoin, Bitcoin Gold, and Bitcoin Diamond in the network of forks. The potential externality emerges from a highly liquid market and spreads through efficient markets in terms of price fairness, resulting in considerable information share in the cryptocurrency market. Our findings suggest that the forks' network evolves for preference heterogeneity rather than for a single dominant entity with market leadership in the network.

A comparative analysis of the volatility nature of cryptocurrency and JSE market

Despite the rapid growth of developing markets, aided by globalization, comparative studies of cryptocurrency and stock market volatility have focused on the developed markets and neglected developing ones. In this regard, this study compares cryptocurrency volatility with that of the Johannesburg Stock Exchange (JSE), a developing market. GARCH-type models are applied to daily log returns of Bitcoin, Ethereum, and the FTSE/JSE 4O in two ways. Firstly, the models are applied directly; secondly, structural breaks are tested and accounted for in the models. The sample period was from September 18, 2017, to May 27, 2021. The results show higher volatility and higher volatility persistence in cryptocurrency than in the JSE market. They also show that persistence is overestimated for cryptocurrencies when structural breaks are not accounted for. The opposite was true for the JSE.Moreover, the two cryptocurrencies were found to have close to identical volatility plots that differ from that of the JSE. High volatility periods of cryptocurrency also did not coincide with that of JSE and those of JSE did not coincide with the cryptocurrency ones. There is also evidence of an inverse leverage effect in cryptocurrency, which opposes the normal leverage effect of the JSE market.

Volatility models for stylized facts of high‐frequency financial data

This article introduces novel volatility diffusion models to account for the stylized facts of high‐frequency financial data such as volatility clustering, intraday U‐shape, and leverage effect. For example, the daily integrated volatility of the proposed volatility process has a realized GARCH structure with an asymmetric effect on log returns. To further explain the heavy‐tailedness of the financial data, we assume that the log returns have a finite th moment for . Then, we propose a Huber regression estimator that has an optimal convergence rate of . We also discuss how to adjust bias coming from Huber loss and show its asymptotic properties.

Volatility Dynamics of Non-Linear Volatile Time Series and Analysis of Information Flow: Evidence from Cryptocurrency Data.

This paper aims to empirically examine long memory and bi-directional information flow between estimated volatilities of highly volatile time series datasets of five cryptocurrencies. We propose the employment of Garman and Klass (GK), Parkinson’s, Rogers and Satchell (RS), and Garman and Klass-Yang and Zhang (GK-YZ), and Open-High-Low-Close (OHLC) volatility estimators to estimate cryptocurrencies’ volatilities. The study applies methods such as mutual information, transfer entropy (TE), effective transfer entropy (ETE), and Rényi transfer entropy (RTE) to quantify the information flow between estimated volatilities. Additionally, Hurst exponent computations examine the existence of long memory in log returns and OHLC volatilities based on simple R/S, corrected R/S, empirical, corrected empirical, and theoretical methods. Our results confirm the long-run dependence and non-linear behavior of all cryptocurrency’s log returns and volatilities. In our analysis, TE and ETE estimates are statistically significant for all OHLC estimates. We report the highest information flow from BTC to LTC volatility (RS). Similarly, BNB and XRP share the most prominent information flow between volatilities estimated by GK, Parkinson’s, and GK-YZ. The study presents the practicable addition of OHLC volatility estimators for quantifying the information flow and provides an additional choice to compare with other volatility estimators, such as stochastic volatility models.

Calendar anomalies in commodity markets for natural resources: Evidence from India

The study investigates the existence of wide range of fifteen calendar anomalies in daily log returns of seven metal futures (aluminium, copper, gold, lead, nickel, silver, zinc) and two energy-based futures (crude oil and natural gas) quoted on Multi-Commodity Exchange (MCX) of India. Using daily closing prices of all selected commodity futures over the period from 2008 to 2018, evidences have been found for the presence of calendar anomalies in commodity market. However, we have also found disappearance of calendar anomalies in the recent years. The results of the study have important implications for the various market participants in commodity markets.

The Term Structure of Equity Risk Premia: Levered Noise and New Estimates

Abstract Levered noise occurs when no-arbitrage replication hedges fundamentals but amplifies price errors. Motivated by our theory, we use widely-available end-of-day OptionMetrics data to improve accuracy of synthetic dividend strip prices and provide longer samples than prior studies. Term structure point estimates are approximately flat in simple returns (88 bp/month vs. 87 bp/month for short-term dividends vs. index), and upward-sloping in measurement-error-robust logarithmic returns (43 bp/month vs. 77 bp/month). These results from prominent index options show the importance of diagnosing noise in no-arbitrage prices. Prior conclusions of an average downward slope in the equity term structure are not robust.

Comparison Analysis of Arima and Z-test for Forecasting the Maximum Return Based on the Pair Trading Strategy

The stock market trends are of great challenge. Even some of the mutual market's strategies, such as traditional pair trading strategy may still be risky and are likely to suffer an unbearable loss due to an unreasonable stop mechanism. In this paper, a novel approach of pair trading strategy – using the logarithmic return to generate pairs and those deviations to construct trading signals. In addition, two methods that ARIMA and Z-TEST used to construct trading signals are compared according to their corresponding cumulative returns. In part one, the ARIMA model has been used to identify whether there is a constant predictive power and how trading signals should be generated to obtain the highest returns. Therefore, a stationary test has been done, and an optimal threshold has been selected. In part two, the Z-test has been used to distribute the preceding data, and the best threshold to construct trading signals has been found in the same mechanism with that process of ARIMA. As a result, the Z-test method shows a better return than that of the ARIMA model, which could be caused by a more stable forecasting accuracy from the distribution. To conclude, this novel approach is efficacious to lower the risks from unanticipated extreme cases and unwise designs on stopping signals. Furthermore, the Z-test method for signals construction is more stable and profitable than the ARIMA. The research greatly maximizes profits in stock markets by selecting the best model and an optimal threshold that models should be applied.

Do Rare Earths and Energy Commodities Drive Volatility Transmission in Sustainable Financial Markets? Evidence from China, Australia, and the US

The high volatility and energy usage of rare earths have raised sustainable and financial concerns for environmentalists and sustainable investors. Therefore, this paper aims to investigate time-varying volatility transmission among rare earths elements, energy commodities, and sustainable financial markets. The sample covers global and major financial markets, i.e., US, China, and Australia. Using daily log returns from 2018 to 2022, the paper considers the dynamic Time Varying Parameter-Vector Autoregression (TVP-VAR) connectedness approach to gauge the time-varying features of volatility spillovers. The findings of total spillovers index reveal weak connectedness among markets during the sampled period. US and China rare earth markets were net volatility transmitters, whereas the Dow Jones Australia Sustainability Index (ASI), China Sustainability Index (CSI), Dow Jones Sustainability World Index (SWI), and MVIS Global Rare Earth Index (MVISGREI) were net recipients. Moreover, energy commodities i.e., WTI Crude Oil, Gasoline, and Natural Gas were net volatility transmitters, while ASI, CSI, and SWI were major volatility recipients. The weak financial contagion effect and connectedness across financial markets uncovers possible diversification opportunities. However, the US sustainable financial market is persistently not affected by these volatility spillovers. Policymakers need to establish strict regulations to protect sustainable financial markets in China and Australia.

The Persistence of Volatility in Nifty 50

The market participants trade in the Nifty index to mitigate the risk, as trading in Nifty leads to wealth and exposes the market participants to external shocks. Normally, market participants disfavor volatility as it is a serious concern. So, volatility measures the magnitude of the information’s impact on any index or stock. The unpredictability of external shock toward the market was a cause for concern because it had adverse effects on the market. The index values worldwide had been substantially sensitive to the external stock. With several factors contributing to the stock market’s performance, distilling volatility is impossible. In addition, the COVID-19 pandemic was the starlight in fuelling the unpredictability in the security markets. The study empirically investigated the impact of events (shocks) on the Nifty 50 index. To achieve our objective, we applied the GARCH model for estimating the volatility of daily returns of the closing price of the Nifty 50 index from January 1, 2019 to December 15, 2021. A total of 732 observations were sourced from the NSE website and transformed into natural log returns for volatility pattern analysis. The findings revealed that the Indian secondary market had experienced unanticipated volatility during the study period. The shock was strong even when the positive information arrived. The existing negative information had a stronger hold over the market movement.

A new hybrid machine learning model for predicting the bitcoin (BTC-USD) price

Several machine learning techniques and hybrid architectures for predicting bitcoin price movement have been presented in the past. Our paper proposes a hybrid model encompassing classification and regression models for predicting bitcoin prices. Our analysis found that the automated feature interactions learner (deep cross networks) error performance using a plethora of technical indicators, including crypto-specific technical indicator difficulty ribbon compression and control variables such as Metcalfe’s value of bitcoin, number of unique active addresses, bitcoin network hash rate, and S&P 500 log returns, in a hybrid architecture is better than the single-stage architecture. The hybrid model predicted a 100% directional hit rate and maintained steady volatility in returns for the out-of-sample period. Our paper concludes that in terms of risk (Sharpe ratio 1.03) and profitability (260% and 82%), the hybrid model’s bitcoin futures strategy performed better than the deep cross network regression and buy-and-hold benchmark strategies.

A comparison of the operation of China's carbon trading market and energy market and their spillover effects

This study measures the liquidity and volatility of the operation of the carbon trading and energy markets using liquidity ratio indicators and log return indicators. It adopts China's carbon trading and energy markets as the research objects, and evaluates the mean spillover effects and volatility spillover effects between the two using the vector autoregression (VAR) model and the BEKK-MGARCH model. The findings indicate that: (1) The liquidity of China's carbon trading market is better than that of the energy market. The average liquidity ratio of the Hubei and Shenzhen carbon trading markets is much lower than that of the coal market, 43016.131. It may be attributed to the fact that China's carbon trading market is currently small and easy to regulate. (2) The volatility of both the Chinese carbon trading market and energy market is small, and the absolute values of the mean log return rate are close to 0. It could be because China's carbon trading market is mainly distributed through free quota allocation, while the energy market has been mature and stable for many years. (3) There is a spillover effect between the carbon trading and energy markets in some parts of China, but the direction and degree of spillover effect vary, which may be due to differences in the economic development level, energy consumption structure, and environmental policies of each pilot carbon trading region. (4) The spillover effect between the two markets is stronger, perhaps due to China's current model of using coal as the main fuel.

VARIANCE GAMMA MODEL AND ITS DEVELOPMENT FOR STOCKS CALL OPTION PRICES ESTIMATION

One of the developments in the options market is the formation of various pricing models for an option to help the buyer determine the fairness of the price. Black-Scholes model uses the assumption that the log return price of stocks is normally distributed, while in reality, the real-world price couldn’t fit into that assumption. To be able to obtain an option price calculation that considers skewness and kurtosis in the stock price data, there are many alternative methods, namely Black-Scholes with Gram-Charlier expansion and Variance Gamma models. As a development of the Variance Gamma model, there are also several methods that are able to reduce the simulations variance generated by the Variance Gamma model, namely Antithetic Variate Variance Gamma model and the Importance Sampling Variance Gamma method. For the results, the Importance Sampling Variance Gamma model and the Antithetic Variate Variance Gamma model are really able to reduce the resulting simulations variance so that it can produce more accurate option prices with market prices compared to the Variance Gamma model. In the end, all Variance Gamma models are able to produce a call option price that is more in line with the market price than all Black Scholes models.

Prediction on the Price of Technology Stock and COVID-19 Based on Multiple Linear Regression

The outbreak of COVID-19 hit the world economy. Represented as an ownership share in the company, stock is one of the most common financial products and economic indicator. However, the stock market is known as being volatile, which makes it hard to predict. Many factors may affect the stock market, e.g., interest rate, trade wars, political scandals, and widespread pandemic such as COVID-19. While stock prediction is extremely challenging, the passage uses multiple linear regression model to predict the price of three technology stock: Apple, Amazon, and Google. The author builds the linear model based on the 5 factors of stock price, including VR (Volume Variation Index), WR (Williams Overbought/Oversold index), ATR (Average True Range), TRIX (Triple Exponential Average) and Log Return of the Close. From the website, yahoo finance, the author obtained the raw data of these three technology companies in recent five years. Compared the final linear regression model with the real adjusted closing price of the stock, there is a clear difference between them. Additionally, the passage finds that TRIX, ATR and Log Return of the Close have larger influence on the predicted closing price as they have larger coefficient. According to the regression model, one can predict the price of the stock in the future. Based on the predicted stock price, it is feasible to investigate the future influence of COVID-19 on the technology price. These results shed light on guiding further exploration of impact of COVID-19 on the stock market.

Probability Density of Lognormal Fractional SABR Model

Instantaneous volatility of logarithmic return in the lognormal fractional SABR model is driven by the exponentiation of a correlated fractional Brownian motion. Due to the mixed nature of driving Brownian and fractional Brownian motions, probability density for such a model is less studied in the literature. We show in this paper a bridge representation for the joint density of the lognormal fractional SABR model in a Fourier space. Evaluating the bridge representation along a properly chosen deterministic path yields a small time asymptotic expansion to the leading order for the probability density of the fractional SABR model. A direct generalization of the representation of joint density often leads to a heuristic derivation of the large deviations principle for joint density in a small time. Approximation of implied volatility is readily obtained by applying the Laplace asymptotic formula to the call or put prices and comparing coefficients.

Forecasting Crude Oil Prices with Major S&P 500 Stock Prices: Deep Learning, Gaussian Process, and Vine Copula

This paper introduces methodologies in forecasting oil prices (Brent and WTI) with multivariate time series of major S&P 500 stock prices using Gaussian process modeling, deep learning, and vine copula regression. We also apply Bayesian variable selection and nonlinear principal component analysis (NLPCA) for data dimension reduction. With a reduced number of important covariates, we also forecast oil prices (Brent and WTI) with multivariate time series of major S&P 500 stock prices using Gaussian process modeling, deep learning, and vine copula regression. To apply real data to the proposed methods, we select monthly log returns of 2 oil prices and 74 large-cap, major S&P 500 stock prices across the period of February 2001–October 2019. We conclude that vine copula regression with NLPCA is superior overall to other proposed methods in terms of the measures of prediction errors.