Application of Elzaki Transform Method to Market Volatility Using the Black-Scholes Model

Black-Scholes Model (B-SM) simulates the dynamics of financial market and contains instruments such as options and puts which are major indices requiring solution. B-SM is known to estimate the correct prices of European Stock options and establish the theoretical foundation for Option pricing. Therefore, this paper evaluates the Black-Schole model in simulating the European call in a cash flow in the dependent drift and focuses on obtaining analytic and then approximate solution for the model. The work also examines Fokker Planck Equation (FPE) and extracts the link between FPE and B-SM for non equilibrium systems. The B-SM is then solved via the Elzaki transform method (ETM). The computational procedures were obtained using MAPLE 18 with the solution provided in the form of convergent series.

Research on the Dynamic Volatility Relationship between Chinese and U.S. Stock Markets Based on the DCC-GARCH Model under the Background of the COVID-19 Pandemic

This study utilizes the Dynamic Conditional Correlation-Generalized Autoregressive Conditional Heteroskedasticity (DCC-GARCH) model to investigate the dynamic relationship between Chinese and U.S. stock markets amid the COVID-19 pandemic. Initially, a univariate GARCH model is developed to derive residual sequences, which are then used to estimate the DCC model parameters. The research reveals a significant rise in the interconnection between the Chinese and U.S. stock markets during the pandemic. The S&P 500 index displayed higher sensitivity and greater volatility in response to the pandemic, whereas the CSI 300 index showed superior resilience and stability. Analysis and model estimation suggest that the market’s dependence on historical data has intensified and its sensitivity to recent shocks has heightened. Predictions from the model indicate increased market volatility during the pandemic. While the model is proficient in capturing market trends, there remains potential for enhancing the accuracy of specific volatility predictions. The study proposes recommendations for policymakers and investors, highlighting the importance of improved cooperation in international financial market regulation and investor education.

Optimal Quota-Share and Excess-of-Loss Reinsurance and Investment with Heston’s Stochastic Volatility Model

An optimal quota-share and excess-of-loss reinsurance and investment problem is studied for an insurer who is allowed to invest in a risk-free asset and a risky asset.Especially the price process of the risky asset is governed by Heston's stochastic volatility(SV)model.With the objective of maximizing the expected index utility of the terminal wealth of the insurance company,by using the classical tools of stochastic optimal control,the explicit expressions for optimal strategies and optimal value functions are derived.An interesting conclusion is found that it is better to buy one reinsurance than two under the assumption of this paper.Moreover,some numerical simulations and sensitivity analysis are provided.

Impact of trading hours extensions on foreign exchange volatility:intraday evidence from the Moscow exchange

Using transaction-level tick-by-tick data of same-and next-day settlement of the Russian Ruble versus the US Dollar exchange rate(RUB/USD)traded on the Moscow Exchange Market during the period 2005–2013,we analyze the impact of trading hours extensions on volatility.During the sample period,the Moscow Exchange extended trading hours three times for the same-day settlement and two times for the next-day settlement of the RUB/USD rate.To analyze the effect of the implementations,various measures of historical and realized volatility are calculated for 5-and 15-min intraday intervals spanning a period of three months both prior to and following trading hours extensions.Besides historical volatility measures,we also examine volume and spread.We apply an autoregressive moving average-autoregressive conditional heteroscedasticity(ARMA-GARCH)model utilizing realized volatility and a trade classification rule to estimate the probability of informed trading.The extensions of trading hours cause a significant increase in both volatility and volume for further analyzing the reasons behind volatility changes.Volatility changes mostly occur after the opening of the market.The length of the extension has a significant positive effect on realized volatility.The results indicate that informed trading increased substantially after the opening for the rate of same-day settlement,whereas this is not observed for next-day settlement.Although trading hours extensions raise opportunities for more transactions and liquidity in foreign exchange markets,they may also lead to higher volatility in the market.Furthermore,this distortion is more significant at opening and midday.A potential explanation for the increased volatility mostly at the opening is that the trading hours extension attracts informed traders rather than liquidity providers.

Do U.S.economic conditions at the state level predict the realized volatility of oil‑price returns?A quantile machine‑learning approach

Because the U.S.is a major player in the international oil market,it is interesting to study whether aggregate and state-level economic conditions can predict the subse-quent realized volatility of oil price returns.To address this research question,we frame our analysis in terms of variants of the popular heterogeneous autoregressive realized volatility(HAR-RV)model.To estimate the models,we use quantile-regression and quantile machine learning(Lasso)estimators.Our estimation results highlights the dif-ferential effects of economic conditions on the quantiles of the conditional distribution of realized volatility.Using weekly data for the period April 1987 to December 2021,we document evidence of predictability at a biweekly and monthly horizon.

An Improved Whale Optimization Algorithm for Global Optimization and Realized Volatility Prediction

The original whale optimization algorithm(WOA)has a low initial population quality and tends to converge to local optimal solutions.To address these challenges,this paper introduces an improved whale optimization algorithm called OLCHWOA,incorporating a chaos mechanism and an opposition-based learning strategy.This algorithm introduces chaotic initialization and opposition-based initialization operators during the population initialization phase,thereby enhancing the quality of the initial whale population.Additionally,including an elite opposition-based learning operator significantly improves the algorithm’s global search capabilities during iterations.The work and contributions of this paper are primarily reflected in two aspects.Firstly,an improved whale algorithm with enhanced development capabilities and a wide range of application scenarios is proposed.Secondly,the proposed OLCHWOA is used to optimize the hyperparameters of the Long Short-Term Memory(LSTM)networks.Subsequently,a prediction model for Realized Volatility(RV)based on OLCHWOA-LSTM is proposed to optimize hyperparameters automatically.To evaluate the performance of OLCHWOA,a series of comparative experiments were conducted using a variety of advanced algorithms.These experiments included 38 standard test functions from CEC2013 and CEC2019 and three constrained engineering design problems.The experimental results show that OLCHWOA ranks first in accuracy and stability under the same maximum fitness function calls budget.Additionally,the China Securities Index 300(CSI 300)dataset is used to evaluate the effectiveness of the proposed OLCHWOA-LSTM model in predicting RV.The comparison results with the other eight models show that the proposed model has the highest accuracy and goodness of fit in predicting RV.This further confirms that OLCHWOA effectively addresses real-world optimization problems.

Did weekly economic index and volatility index impact US food sales during the first year of the pandemic?

We explore the impacts of economic and financial dislocations caused by COVID-19 pandemic shocks on food sales in the United States from January 2020 to January 2021.We use the US weekly economic index(WEI)to measure economic dislocations and the Chicago Board Options Exchange volatility index(VIX)to capture the broader stock market dislocations.We validate the NARDL model by testing a battery of models using the autoregressive distributed lags(ARDL)methodology(ARDL,NARDL,and QARDL specifications).Our study postulates that an increase in WEI has a significant negative long-term effect on food sales,whereas a decrease in WEI has no statistically significant(long-run)effect.Thus,policy responses that ignore asymmetric effects and hidden cointegration may fail to promote food security during pandemics.

The predictive power of Bitcoin prices for the realized volatility of US stock sector returns

This paper is motivated by Bitcoin’s rapid ascension into mainstream finance and recent evidence of a strong relationship between Bitcoin and US stock markets.It is also motivated by a lack of empirical studies on whether Bitcoin prices contain useful information for the volatility of US stock returns,particularly at the sectoral level of data.We specifically assess Bitcoin prices’ability to predict the volatility of US composite and sectoral stock indices using both in-sample and out-of-sample analyses over multiple forecast horizons,based on daily data from November 22,2017,to December,30,2021.The findings show that Bitcoin prices have significant predictive power for US stock volatility,with an inverse relationship between Bitcoin prices and stock sector volatility.Regardless of the stock sectors or number of forecast horizons,the model that includes Bitcoin prices consistently outperforms the benchmark historical average model.These findings are independent of the volatility measure used.Using Bitcoin prices as a predictor yields higher economic gains.These findings emphasize the importance and utility of tracking Bitcoin prices when forecasting the volatility of US stock sectors,which is important for practitioners and policymakers.

Forecasting Stock Volatility Using Wavelet-based Exponential Generalized Autoregressive Conditional Heteroscedasticity Methods

In this study,we proposed a new model to improve the accuracy of fore-casting the stock market volatility pattern.The hypothesized model was validated empirically using a data set collected from the Saudi Arabia stock Exchange(Tada-wul).The data is the daily closed price index data from August 2011 to December 2019 with 2027 observations.The proposed forecasting model combines the best maximum overlapping discrete wavelet transform(MODWT)function(Bl14)and exponential generalized autoregressive conditional heteroscedasticity(EGARCH)model.The results show the model's ability to analyze stock market data,highlight important events that contain the most volatile data,and improve forecast accuracy.The results were compared from a number of mathematical mod-els,which are the non-linear spectral model,autoregressive integrated moving aver-age(ARIMA)model and EGARCH model.The performance of the forecasting model will be evaluated based on some of error functions such as Mean absolute percentage error(MAPE),Mean absolute scaled error(MASE)and Root means squared error(RMSE).

Applications of nonferrous metal price volatility to prediction of China's stock market

The aim of the present work is to examine whether the price volatility of nonferrous metal futures can be used to predict the aggregate stock market returns in China. During a sample period from January of 2004 to December of 2011, empirical results show that the price volatility of basic nonferrous metals is a good predictor of value-weighted stock portfolio at various horizons in both in-sample and out-of-sample regressions. The predictive power of metal copper volatility is greater than that of aluminum. The results are robust to alternative measurements of variables and econometric approaches. After controlling several well-known macro pricing variables, the predictive power of copper volatility declines but remains statistically significant. Since the predictability exists only during our sample period, we conjecture that the stock market predictability by metal price volatility is partly driven by commodity financialization.

基于Volatility的内存信息调查方法研究

随着反取证技术的发展,调查人员越来越难于在磁盘介质中寻找到有价值的证据或线索。针对内存信息的调查分析研究由此成为计算机法庭科学领域日益关注的焦点。通过以内存调查取证开源软件Volatility为背景,从进程及DLL、内存及VAD、驱动程序及内核对象、网络连接与注册表等多个角度描述内存信息的调查方法,并结合实例说明所述方法在实际工作中的具体应用。

Volatility forecasting in Chinese nonferrous metals futures market

This paper seeks to model and forecast the Chinese nonferrous metals futures market volatility and allows new insights into the time-varying volatility of realized volatility and leverage effects using high-frequency data.The LHAR-CJ model is extended and the empirical research on copper and aluminum futures in Shanghai Futures Exchange suggests the dynamic dependencies and time-varying volatility of realized volatility,which are captured by long memory HAR-GARCH model.Besides,the findings also show the significant weekly leverage effects in Chinese nonferrous metals futures market volatility.Finally,in-sample and out-of-sample forecasts are investigated,and the results show that the LHAR-CJ-G model,considering time-varyingvolatility of realized volatility and leverage effects,effectively improves the explanatory power as well as out-of sample predictive performance.

Understanding the influence of microwave on the relative volatility used in the pyrolysis of Indonesia oil sands

In this paper, pyrolysis of Indonesian oil sands （lOS） was investigated by two different heating methods to develop a better understanding of the microwave-assisted pyrolysis. Thermogravimetric analysis was conducted to study the thermal decomposition behaviors of lOS, showing that 550 ℃ might be the pyrolysis final temperature. A explanation of the heat-mass transfer process was presented to demonstrate the influence of mi- crowave-assisted pyrolysis on the liquid product distribution. The heat-mass transfer model was also useful to explain the increase of liquid product yield and heavy component content at the same heating rate by two differ- ent heating methods. Experiments were carried out using a fixed bed reactor with and without the microwave irradiation. The results showed that liquid product yield was increased during microwave induced pyrolysis, while the formation of gas and solid residue was reduced in comparison with the conventional pyrolysis. Moreover, the liquid product characterization by elemental analysis and GC-MS indicated the significant effect on the liquid chemical composition by microwave irradiation. High polarity substances （ε 〉 10 at 25 ℃）, such as oxy- organics were increased, while relatively low polarity substances （ε 〈 2 at 25℃）, such as aliphatic hydrocarbons were decreased, suggesting that microwave enhanced the relative volatility of high polarity substances. The yield improvement and compositional variations in the liquid product promoted by the microwave-assisted pyrolysis deserve the further exploitation in the future,

Effect of occurrence mode of heavy metal elements in a low rank coal on volatility during pyrolysis

The harmful trace elements will be released during coal utilization, which can cause environment pollution and further endangering human health, especially for heavy metal elements. Compared to combustion, the release of heavy metal elements during coal pyrolysis process, as a critical initial reaction stage of combustion, has not received sufficient attention. In the present paper, a low rank coal, from Xinjiang province in China, was pyrolyzed in a fixed bed reactor from room temperature, at atmospheric pressure, with the heating rate of 10 °C/min, and the final pyrolysis temperature was from 400 to 800℃ with the interval of 100℃. The volatility of heavy metal elements (including As, Hg, Cd and Pb) during pyrolysis process was investigated. The results showed the volatility of all heavy metal elements increased obviously with increasing temperature, and followed the sequence as Hg > Cd > As > Pb, which was mainly caused by their thermodynamic property and occurrence modes in coal. The occurrence modes of heavy metals were studied by sink-andfloat test and sequential chemical extraction procedure, and it can be found that the heavy metal elements were mainly in the organic and residual states (clay minerals) in the raw coal. And most of the organic heavy metals escaped during the pyrolysis process, the remaining elements were mainly in the residual state, and the elements in Fe-Mn state also tended to remain in the char.

Characterization of Organic Aerosol at a Rural Site in the North China Plain Region:Sources,Volatility and Organonitrates

The North China Plain(NCP)is a region that experiences serious aerosol pollution.A number of studies have focused on aerosol pollution in urban areas in the NCP region;however,research on characterizing aerosols in rural NCP areas is comparatively limited.In this study,we deployed a TD-HR-AMS(thermodenuder high-resolution aerosol mass spectrometer)system at a rural site in the NCP region in summer 2013 to characterize the chemical compositions and volatility of submicron aerosols(PM_(1)).The average PM_(1)mass concentration was 51.2±48.0μg m^(−3) and organic aerosol(OA)contributed most(35.4%)to PM_(1).Positive matrix factorization(PMF)analysis of OA measurements identified four OA factors,including hydrocarbon-like OA(HOA,accounting for 18.4%),biomass burning OA(BBOA,29.4%),lessoxidized oxygenated OA(LO-OOA,30.8%)and more-oxidized oxygenated OA(MO-OOA,21.4%).The volatility sequence of the OA factors was HOA>BBOA>LO-OOA>MO-OOA,consistent with their oxygen-to-carbon(O:C)ratios.Additionally,the mean concentration of organonitrates(ON)was 1.48−3.39μg m−3,contributing 8.1%-19%of OA based on cross validation of two estimation methods with the high-resolution time-of-flight aerosol mass spectrometer(HRToF-AMS)measurement.Correlation analysis shows that ON were more correlated with BBOA and black carbon emitted from biomass burning but poorly correlated with LO-OOA.Also,volatility analysis for ON further confirmed that particulate ON formation might be closely associated with primary emissions in rural NCP areas.

Quantitative method for evaluating detailed volatility of wind power at multiple temporal-spatial scales

With the increasing proportion of wind power integration, the volatility of wind power brings huge challenges to the safe and stable operation of the electric power system. At present, the indexes commonly used to evaluate the volatility of wind power only consider its overall characteristics, such as the standard deviation of wind power, the average of power variables, etc., while ignoring the detailed volatility of wind power, that is, the features of the frequency distribution of power variables. However, how to accurately describe the detailed volatility of wind power is the key foundation to reduce its adverse influences. To address this, a quantitative method for evaluating the detailed volatility of wind power at multiple temporal-spatial scales is proposed. First, the volatility indexes which can evaluate the detailed fluctuation characteristics of wind power are presented, including the upper confidence limit, lower confidence limit and confidence interval of power variables under the certain confidence level. Then, the actual wind power data from a location in northern China is used to illustrate the application of the proposed indexes at multiple temporal(year–season–month–day) and spatial scales(wind turbine–wind turbines–wind farm–wind farms) using the calculation time windows of 10 min, 30 min, 1 h, and 4 h. Finally, the relationships between wind power forecasting accuracy and its corresponding detailed volatility are analyzed to further verify the effectiveness of the proposed indexes. The results show that the proposed volatility indexes can effectively characterize the detailed fluctuations of wind power at multiple temporal-spatial scales. It is anticipated that the results of this study will serve as an important reference for the reserve capacity planning and optimization dispatch in the electric power system which with a high proportion of renewable energy.

Can the Baidu Index predict realized volatility in the Chinese stock market?

This paper incorporates the Baidu Index into various heterogeneous autoregressive type time series models and shows that the Baidu Index is a superior predictor of realized volatility in the SSE 50 Index.Furthermore,the predictability of the Baidu Index is found to rise as the forecasting horizon increases.We also find that continuous components enhance predictive power across all horizons,but that increases are only sustained in the short and medium terms,as the long-term impact on volatility is less persistent.Our findings should be expected to influence investors interested in constructing trading strategies based on realized volatility.

On the volatility of daily stock returns of Total Nigeria Plc: evidence from GARCH models, value-at-risk and backtesting

This study investigates the volatility in daily stock returns for Total Nigeria Plc using nine variants of GARCH models:sGARCH,girGARCH,eGARCH,iGARCH,aGARCH,TGARCH,NGARCH,NAGARCH,and AVGARCH along with value at risk estimation and backtesting.We use daily data for Total Nigeria Plc returns for the period January 2,2001 to May 8,2017,and conclude that eGARCH and sGARCH perform better for normal innovations while NGARCH performs better for student t innovations.This investigation of the volatility,VaR,and backtesting of the daily stock price of Total Nigeria Plc is important as most previous studies covering the Nigerian stock market have not paid much attention to the application of backtesting as a primary approach.We found from the results of the estimations that the persistence of the GARCH models are stable except for few cases for which iGARCH and eGARCH were unstable.Additionally,for student t innovation,the sGARCH and girGARCH models failed to converge;the mean reverting number of days for returns differed from model to model.From the analysis of VaR and its backtesting,this study recommends shareholders and investors continue their business with Total Nigeria Plc because possible losses may be overcome in the future by improvements in stock prices.Furthermore,risk was reflected by significant up and down movement in the stock price at a 99%confidence level,suggesting that high risk brings a high return.

Dynamics of volatility spillover between stock market and foreign exchange market: evidence from Asian Countries

Background:The purpose of this study is to examine volatility spillover effects between stock market and foreign exchange market in selected Asian countries;Pakistan,India,Sri Lanka,China,Hong Kong and Japan.This study considered daily data from 4th January,1999 to 1st January,2014.Methods:This study opted EGARCH(Exponential Generalized Auto Regressive Conditional Heteroskedasticity)model for the purpose of analyzing asymmetric volatility spillover effects between stock and foreign exchange market.Results:The EGARCH analyses reveal bidirectional asymmetric volatility spillover between stock market and foreign exchange market of Pakistan,China,Hong Kong and Sri Lanka.The results reveal unidirectional transmission of volatility from stock market to foreign exchange market of India.The analysis reveals no evidence of volatility transmission between the two markets in reference to Japan.Conclusions:The result of this study provide valuable insights to economic policy makers for financial stability perspective and to investors regarding decision making in international portfolio and currency risk strategies.

Effects of investor sentiment on stock volatility:new evidences from multi-source data in China’s green stock markets

The effect of investor sentiment on stock volatility is a highly attractive research question in both the academic field and the real financial industry.With the proposal of China’s"dual carbon"target,green stocks have gradually become an essential branch of Chinese stock markets.Focusing on 106 stocks from the new energy,environmental protection,and carbon–neutral sectors,we construct two investor sentiment proxies using Internet text and stock trading data,respectively.The Internet sentiment is based on posts from Eastmoney Guba,and the trading sentiment comes from a variety of trading indicators.In addition,we divide the realized volatility into continuous and jump parts,and then investigate the effects of investor sentiment on different types of volatilities.Our empirical findings show that both sentiment indices impose significant positive impacts on realized,continuous,and jump volatilities,where trading sentiment is the main factor.We further explore the mediating effect of information asymmetry,measured by the volume-synchronized probability of informed trading(VPIN),on the path of investor sentiment affecting stock volatility.It is evidenced that investor sentiments are positively correlated with the VPIN,and they can affect volatilities through the VPIN.We then divide the total sample around the coronavirus disease 2019(COVID-19)pandemic.The empirical results reveal that the market volatility after the COVID-19 pandemic is more susceptible to investor sentiments,especially to Internet sentiment.Our study is of great significance for maintaining the stability of green stock markets and reducing market volatility.