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.

An empirical examination of investor sentiment and stock market volatility: evidence from India

Understanding the irrational sentiments of the market participants is necessary for making good investment decisions.Despite the recent academic effort to examine the role of investors’sentiments in market dynamics,there is a lack of consensus in delineating the structural aspect of market sentiments.This research is an attempt to address this gap.The study explores the role of irrational investors’sentiments in determining stock market volatility.By employing monthly data on market-related implicit indices,we constructed an irrational sentiment index using principal component analysis.This sentiment index was modelled in the GARCH and Granger causality framework to analyse its contribution to volatility.The results showed that irrational sentiment significantly causes excess market volatility.Moreover,the study indicates that the asymmetrical aspects of an inefficient market contribute to excess volatility and returns.The findings are crucial for retail investors as well as portfolio managers seeking to make an optimum portfolio to maximise profits.

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.

Quasi-variable Discount Rates and Market Volatility: An Empirical Study

This paper proposes an assumption of quasi-variable discount rates to explain the excess volatility puzzle of stock market. Under the assumption, the ARMAX model is derived based on the CCAPM model and CRRA utility function to describe the linear relationship between the discount rate and the consumption growth rate. We conducted empirical research on this model using historical data of the US stock market. The results confirm a significantly negative relationship between consumption growth rate and discount rate. Subsequently, the results of Monte Carlo simulation show that given the risk preference coefficient and dividend sequence, the rational expectations price fluctuation obtained under the assumption of quasivariable discount rate is the largest.

A MULTISCALE MODELING APPROACH INCORPORATING ARIMA AND ANNS FOR FINANCIAL MARKET VOLATILITY FORECASTING

The financial market volatility forecasting is regarded as a challenging task because of irreg ularity, high fluctuation, and noise. In this study, a multiscale ensemble forecasting model is proposed. The original financial series are decomposed firstly different scale components （i.e., approximation and details） using the maximum overlap discrete wavelet transform （MODWT）. The approximation is pre- dicted by a hybrid forecasting model that combines autoregressive integrated moving average （ARIMA） with feedforward neural network （FNN）. ARIMA model is used to generate a linear forecast, and then FNN is developed as a tool for nonlinear pattern recognition to correct the estimation error in ARIMA forecast. Moreover, details are predicted by Elman neural networks. Three weekly exchange rates data are collected to establish and validate the forecasting model. Empirical results demonstrate consistent better performance of the proposed approach.

A CAUSALITY ANALYSIS OF SOCIETAL RISK PERCEPTION AND STOCK MARKET VOLATILITY IN CHINA

Modem China is undergoing a variety of social conflicts as the arrival of new era with thetransformation of the principal contradiction. Then monitoring the society stable is a huge workload.Online societal risk perception is acquired by mapping on-line public concerns respectively intosocietal risk events including national security, economy ＆ finance, public morals, daily life, socialstability, government management, and resources ＆ environment, and then provides one kind ofmeasurement toward the society state. Obviously, stable and harmonious social situations are the basicguarantee for the healthy development of the stock market. Thus we concern whether the variations ofthe societal risk are related to stock market volatility. We study their relationships by two steps, firstthe relationships between search trends and societal risk perception; next the relationships betweensocietal risk perception and stock volatility. The weekend and holiday effects in China stock market aretaken into consideration. Three different econometric methods are explored to observe the impacts ofvariations of societal risk on Shanghai Composite Index and Shenzhen Composite Index. 3 majorfindings are addressed. Firstly, there exist causal relations between Baidu Index and societal riskperception. Secondly, the perception of finance ＆ economy, social stability, and governmentmanagement has distinguishing effects on the volatility of both Shanghai Composite Index and Shenzhen Composite Index. Thirdly, the weekend and holiday effects of societal risk perception on the stock market are verified. The research demonstrates that capturing societal risk based on on-line public concerns is feasible and meaningful.

The role of oil futures intraday information on predicting US stock market volatility

This study investigates the role of oil futures price information on forecasting the US stock market volatility using the HAR framework.In-sample results indicate that oil futures intraday information is helpful to increase the predictability.Moreover,compared to the benchmark model,the proposed models improve their predictive ability with the help of oil futures realized volatility.In particular,the multivariate HAR model outperforms the univariate model.Accordingly,considering the contemporaneous connection is useful to predict the US stock market volatility.Furthermore,these findings are consistent across a variety of robust checks.

BM(book-to-market ratio) factor: mediumterm momentum and long-term reversal

To explain medium-term momentum and long-term reversal,we use the difference between the optional model and the CAPM model to construct a winner-loser portfolio.According to the CAPM model’s zero explanatory ability with respect to stock market anomalies,we obtain an anomaly interpretative model.This study shows that this anomaly interpretative model can explain stock market perceptions and medium-term momentum.Most importantly,BM is a critical factor in the model’s explanatory ability.We present a robustness test,which includes selecting new sample data,adding new auxiliary variables,changing sample years,and adding industry fixed effects.In general,the BM effect does have considerable explanatory power in medium-term momentum and long-term reversal.

Agents’ Behavior in Market Bubbles： Herding and Information Effects

This paper explores some behavioral factors that may explain the formation of speculative bubbles in financial markets. The study adopts an experimental approach focused on the agents’ behavior when facing a “true” bubble and is incentivized to herd and/or receive information about the market sentiment. For this purpose, a straightforward laboratory experiment that reproduces the dotcom market bubble and asks subjects to forecast asset prices in a true dynamic information scenario. The experiment was conducted in the laboratory of the Faculty of Economics at the University of Salamanca and involved 137 undergraduate students in the degree of economics. The results show that incentives to the herding behavior increase the forecasted volatility and thus contribute to the bubble inflation. Nevertheless, this effect may be offset by giving information to the agents about the expected market trend. Therefore, under herding effects, it is the absence of clear signals about market sentiments what inflates the bubble.

Volatility Prediction via Hybrid LSTM Models with GARCH Type Parameters

Since the establishment of financial models for risk prediction,the measurement of volatility at risky market has improved,and its significance has also grown.For high-frequency financial data,the degree of investment risk,which has always been the focus of attention,is measured by the variance of residual sequence obtained following model regression.By integrating the long short-term memory(LSTM)model with multiple generalized autoregressive conditional heteroscedasticity(GARCH)models,a new hybrid LSTM model is used to predict stock price volatility.In this paper,three GARCH models are used,and the model that can best fit the data is determined.