GARCH

Empirical Study on the Factors Influencing Stock Market Volatility in China ArXiv ID: 2501.08668 “View on arXiv” Authors: Unknown Abstract This paper mainly utilizes the ARDL model and principal component analysis to investigate the relationship between the volatility of China’s Shanghai Composite Index returns and the variables of exchange rate and domestic and foreign bond yields in an internationally integrated stock market. This paper uses a daily data set for the period from July 1, 2010 to April 30, 2024, in which the dependent variable is the Shanghai Composite Index return, and the main independent variables are the spot exchange rate of the RMB against the US dollar, the 10-year treasury bond yields in China and the United States and their lagged variables, with the effect of the time factor added. Firstly, the development of the stock, foreign exchange and bond markets and the basic theories are reviewed, and then each variable is analyzed by descriptive statistics, the correlation between the independent variables and the dependent variable is expanded theoretically, and the corresponding empirical analyses are briefly introduced, and then the empirical analyses and modeling of the relationship between the independent variables and the dependent variable are carried out on the basis of the theoretical foundations mentioned above with the support of the daily data, and the model conclusions are analyzed economically through a large number of tests, then the model conclusions are analyzed economically. economic analysis of the model conclusions, and finally, the author proposes three suggestions to enhance the stability and return of the Chinese stock market, respectively. Key Words: Chinese Stock Market, Volatility, GARCH, ARDL Model ...

Risk forecasting using Long Short-Term Memory Mixture Density Networks ArXiv ID: 2501.01278 “View on arXiv” Authors: Unknown Abstract This work aims to implement Long Short-Term Memory mixture density networks (LSTM-MDNs) for Value-at-Risk forecasting and compare their performance with established models (historical simulation, CMM, and GARCH) using a defined backtesting procedure. The focus was on the neural network’s ability to capture volatility clustering and its real-world applicability. Three architectures were tested: a 2-component mixture density network, a regularized 2-component model (Arimond et al., 2020), and a 3-component mixture model, the latter being tested for the first time in Value-at-Risk forecasting. Backtesting was performed on three stock indices (FTSE 100, S&P 500, EURO STOXX 50) over two distinct two-year periods (2017-2018 as a calm period, 2021-2022 as turbulent). Model performance was assessed through unconditional coverage and independence assumption tests. The neural network’s ability to handle volatility clustering was validated via correlation analysis and graphical evaluation. Results show limited success for the neural network approach. LSTM-MDNs performed poorly for 2017/2018 but outperformed benchmark models in 2021/2022. The LSTM mechanism allowed the neural network to capture volatility clustering similarly to GARCH models. However, several issues were identified: the need for proper model initialization and reliance on large datasets for effective learning. The findings suggest that while LSTM-MDNs provide adequate risk forecasts, further research and adjustments are necessary for stable performance. ...

What events matter for exchange rate volatility ? ArXiv ID: 2411.16244 “View on arXiv” Authors: Unknown Abstract This paper expands on stochastic volatility models by proposing a data-driven method to select the macroeconomic events most likely to impact volatility. The paper identifies and quantifies the effects of macroeconomic events across multiple countries on exchange rate volatility using high-frequency currency returns, while accounting for persistent stochastic volatility effects and seasonal components capturing time-of-day patterns. Given the hundreds of macroeconomic announcements and their lags, we rely on sparsity-based methods to select relevant events for the model. We contribute to the exchange rate literature in four ways: First, we identify the macroeconomic events that drive currency volatility, estimate their effects and connect them to macroeconomic fundamentals. Second, we find a link between intraday seasonality, trading volume, and the opening hours of major markets across the globe. We provide a simple labor-based explanation for this observed pattern. Third, we show that including macroeconomic events and seasonal components is crucial for forecasting exchange rate volatility. Fourth, our proposed model yields the lowest volatility and highest Sharpe ratio in portfolio allocations when compared to standard SV and GARCH models. ...

Dynamic graph neural networks for enhanced volatility prediction in financial markets ArXiv ID: 2410.16858 “View on arXiv” Authors: Unknown Abstract Volatility forecasting is essential for risk management and decision-making in financial markets. Traditional models like Generalized Autoregressive Conditional Heteroskedasticity (GARCH) effectively capture volatility clustering but often fail to model complex, non-linear interdependencies between multiple indices. This paper proposes a novel approach using Graph Neural Networks (GNNs) to represent global financial markets as dynamic graphs. The Temporal Graph Attention Network (Temporal GAT) combines Graph Convolutional Networks (GCNs) and Graph Attention Networks (GATs) to capture the temporal and structural dynamics of volatility spillovers. By utilizing correlation-based and volatility spillover indices, the Temporal GAT constructs directed graphs that enhance the accuracy of volatility predictions. Empirical results from a 15-year study of eight major global indices show that the Temporal GAT outperforms traditional GARCH models and other machine learning methods, particularly in short- to mid-term forecasts. The sensitivity and scenario-based analysis over a range of parameters and hyperparameters further demonstrate the significance of the proposed technique. Hence, this work highlights the potential of GNNs in modeling complex market behaviors, providing valuable insights for financial analysts and investors. ...

The Hybrid Forecast of S&P 500 Volatility ensembled from VIX, GARCH and LSTM models ArXiv ID: 2407.16780 “View on arXiv” Authors: Unknown Abstract Predicting the S&P 500 index volatility is crucial for investors and financial analysts as it helps assess market risk and make informed investment decisions. Volatility represents the level of uncertainty or risk related to the size of changes in a security’s value, making it an essential indicator for financial planning. This study explores four methods to improve the accuracy of volatility forecasts for the S&P 500: the established GARCH model, known for capturing historical volatility patterns; an LSTM network that utilizes past volatility and log returns; a hybrid LSTM-GARCH model that combines the strengths of both approaches; and an advanced version of the hybrid model that also factors in the VIX index to gauge market sentiment. This analysis is based on a daily dataset that includes S&P 500 and VIX index data, covering the period from January 3, 2000, to December 21, 2023. Through rigorous testing and comparison, we found that machine learning approaches, particularly the hybrid LSTM models, significantly outperform the traditional GARCH model. Including the VIX index in the hybrid model further enhances its forecasting ability by incorporating real-time market sentiment. The results of this study offer valuable insights for achieving more accurate volatility predictions, enabling better risk management and strategic investment decisions in the volatile environment of the S&P 500. ...

Estimation of tail risk measures in finance: Approaches to extreme value mixture modeling ArXiv ID: 2407.05933 “View on arXiv” Authors: Unknown Abstract This thesis evaluates most of the extreme mixture models and methods that have appended in the literature and implements them in the context of finance and insurance. The paper also reviews and studies extreme value theory, time series, volatility clustering, and risk measurement methods in detail. Comparing the performance of extreme mixture models and methods on different simulated distributions shows that the method based on kernel density estimation does not have an absolute superior or close to the best performance, especially for the estimation of the extreme upper or lower tail of the distribution. Preprocessing time series data using a generalized autoregressive conditional heteroskedasticity model (GARCH) and applying extreme value mixture models on extracted residuals from GARCH can improve the goodness of fit and the estimation of the tail distribution. ...

Beyond the Bid-Ask: Strategic Insights into Spread Prediction and the Global Mid-Price Phenomenon ArXiv ID: 2404.11722 “View on arXiv” Authors: Unknown Abstract This research extends the conventional concepts of the bid–ask spread (BAS) and mid-price to include the total market order book bid–ask spread (TMOBBAS) and the global mid-price (GMP). Using high-frequency trading data, we investigate these new constructs, finding that they have heavy tails and significant deviations from normality in the distributions of their log returns, which are confirmed by three different methods. We shift from a static to a dynamic analysis, employing the ARMA(1,1)-GARCH(1,1) model to capture the temporal dependencies in the return time-series, with the normal inverse Gaussian distribution used to capture the heavy tails of the returns. We apply an option pricing model to address the risks associated with the low liquidity indicated by the TMOBBAS and GMP. Additionally, we employ the Rachev ratio to evaluate the risk–return performance at various depths of the limit order book and examine tail risk interdependencies across spread levels. This study provides insights into the dynamics of financial markets, offering tools for trading strategies and systemic risk management. ...

Analyzing Currency Fluctuations: A Comparative Study of GARCH, EWMA, and IV Models for GBP/USD and EUR/GBP Pairs ArXiv ID: 2402.07435 “View on arXiv” Authors: Unknown Abstract In this study, we examine the fluctuation in the value of the Great Britain Pound (GBP). We focus particularly on its relationship with the United States Dollar (USD) and the Euro (EUR) currency pairs. Utilizing data from June 15, 2018, to June 15, 2023, we apply various mathematical models to assess their effectiveness in predicting the 20-day variation in the pairs’ daily returns. Our analysis involves the implementation of Exponentially Weighted Moving Average (EWMA), Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models, and Implied Volatility (IV) models. To evaluate their performance, we compare the accuracy of their predictions using Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) metrics. We delve into the intricacies of GARCH models, examining their statistical characteristics when applied to the provided dataset. Our findings suggest the existence of asymmetric returns in the EUR/GBP pair, while such evidence is inconclusive for the GBP/USD pair. Additionally, we observe that GARCH-type models better fit the data when assuming residuals follow a standard t-distribution rather than a standard normal distribution. Furthermore, we investigate the efficacy of different forecasting techniques within GARCH-type models. Comparing rolling window forecasts to expanding window forecasts, we find no definitive superiority in either approach across the tested scenarios. Our experiments reveal that for the GBP/USD pair, the most accurate volatility forecasts stem from the utilization of GARCH models employing a rolling window methodology. Conversely, for the EUR/GBP pair, optimal forecasts are derived from GARCH models and Ordinary Least Squares (OLS) models incorporating the annualized implied volatility of the exchange rate as an independent variable. ...

From GARCH to Neural Network for Volatility Forecast ArXiv ID: 2402.06642 “View on arXiv” Authors: Unknown Abstract Volatility, as a measure of uncertainty, plays a crucial role in numerous financial activities such as risk management. The Econometrics and Machine Learning communities have developed two distinct approaches for financial volatility forecasting: the stochastic approach and the neural network (NN) approach. Despite their individual strengths, these methodologies have conventionally evolved in separate research trajectories with little interaction between them. This study endeavors to bridge this gap by establishing an equivalence relationship between models of the GARCH family and their corresponding NN counterparts. With the equivalence relationship established, we introduce an innovative approach, named GARCH-NN, for constructing NN-based volatility models. It obtains the NN counterparts of GARCH models and integrates them as components into an established NN architecture, thereby seamlessly infusing volatility stylized facts (SFs) inherent in the GARCH models into the neural network. We develop the GARCH-LSTM model to showcase the power of the GARCH-NN approach. Experiment results validate that amalgamating the NN counterparts of the GARCH family models into established NN models leads to enhanced outcomes compared to employing the stochastic and NN models in isolation. ...

Modelling and Predicting the Conditional Variance of Bitcoin Daily Returns: Comparsion of Markov Switching GARCH and SV Models ArXiv ID: 2401.03393 “View on arXiv” Authors: Unknown Abstract This paper introduces a unique and valuable research design aimed at analyzing Bitcoin price volatility. To achieve this, a range of models from the Markov Switching-GARCH and Stochastic Autoregressive Volatility (SARV) model classes are considered and their out-of-sample forecasting performance is thoroughly examined. The paper provides insights into the rationale behind the recommendation for a two-stage estimation approach, emphasizing the separate estimation of coefficients in the mean and variance equations. The results presented in this paper indicate that Stochastic Volatility models, particularly SARV models, outperform MS-GARCH models in forecasting Bitcoin price volatility. Moreover, the study suggests that in certain situations, persistent simple GARCH models may even outperform Markov-Switching GARCH models in predicting the variance of Bitcoin log returns. These findings offer valuable guidance for risk management experts, highlighting the potential advantages of SARV models in managing and forecasting Bitcoin price volatility. ...