GARCH Research Articles

A new lattice approach for risk-minimization hedging under generalized autoregressive conditional heteroskedasticity models

This paper explores the calculation of risk-minimization hedging strategies, specifically local and global risk minimization strategies for contingent claims under affine and non-affine GARCH models with the known closed forms of its first four moments across times under the physical measure. A unified and efficient willow tree method is introduced for various GARCH models. Unlike methods that provide option values and hedging ratios solely at the inception time, the proposed willow tree method generates a comprehensive table of option values and hedging ratios at each discrete time step across possible asset prices. Additionally, the method showcases robust performance in hedging at lower frequencies than the underlying asset’s modeling frequency (e.g., weekly or monthly hedging using a daily GARCH model). Lastly, the willow tree method outperforms the Monte Carlo method, offering greater efficiency, accuracy, and flexibility in solving risk-minimization hedging problems.

Does Bitcoin Hedge Industry Credit Risk? A Comparison with Gold

Credit default swaps are considered indicators of default probability and used to measure credit risk in different sectors of the US industry. This study examines the effectiveness of hedging and safehaven options for US sectoral credit default swap indices, focusing on whether Bitcoin or gold can serve as effective assets for mitigating credit risk in US industries. The GARCH model with dummy variables and quantile regression are employed to estimate the hedging and safe-haven properties of Bitcoin and gold. The findings indicate that both Bitcoin and gold can be utilized as effective hedging and safe haven assets for US industry credit risk. Furthermore, the study highlights the superior hedging potential and safe-haven properties of Bitcoin compared to gold. Overall, the results suggest that investors and portfolio managers can effectively utilize Bitcoin and gold to protect against credit risk in different US sectors, regardless of market and economic conditions.

A comprehensive support-free slicing method library for variable posture additive manufacturing

Support-free slicing technology plays a critical role in additive manufacturing by reducing costs and simplifying post-processing. However, due to the complexity of geometric features, existing support-free slicing strategies often lack the necessary universality in industry. This paper proposes a method library comprising six basic support-free slicing methods to enhance the applicability and computational efficiency. The general methods in the library include facet-based methods and voxel-based methods, the former facilitates rapid slicing, while the latter enables the re-decomposition of complex structural parts. For parts that cannot be covered by general methods, customized methods are developed. These include constructing a support bridge for multi-direction slicing of overhanging regions in an arch model and extracting the optimal central axis for internal channels to achieve precise channel decomposition. Additionally, the methods in the library can be flexibly combined. By recognizing surface features and incorporating manual intervention, models can be decomposed into multiple sub-models, with the most computationally efficient method is matched to each sub-model. The layers and tool-paths of each sub-model are generated by the optimal method. Four typical models are deposited without any support in a five-axis printer to verify the feasibility of the proposed methods.

A frictional arch model for pile-cap-beam-supported embankment

The pile-cap-beam-supported (PCBS) system can strength the soil arching effect of embankment, increase the lateral stiffness, bending resistance and vertical bearing capacity of the rigid pile, however there is no frictional soil arch model of PCBS embankment. In this paper, first a frictional arch model for PCBS embankment modified from Russell’s frictional arching model was proposed. The proposed model in this paper considers the algorithm of lateral pressure coefficient k and a changing critical height of soil arch. In this new method, the influence of pile spacing, filling properties, height and pile spacing on critical height soil arch was comprehensively considered. Second, a series of numerical cases were performed to verify the effectiveness of the proposed model and study the arching effect of PCBS embankment. By comparing the vertical stress and settlement between the theoretical and simulation results, the rationality of the proposed method to estimate the stress and critical height of arch was validated. The effectiveness of the proposed method was further validated by comparing loading efficacy to a reported case. Last, the stress and deformation of PCBS and pile-cap-supported (PCS) embankment were analyzed and the superiority of PCBS system in improving the performance of embankment was observed finally.

Energy barriers govern catheter herniation during endovascular procedures: a 2.5D vascular flow model analysis.

Endovascular procedures rely on navigating guidewires, catheters and other devices through tortuous vasculature to treat disease. A critical challenge in these procedures is catheter herniation, in which the device deviates from its intended path, often irrecoverably. To elucidate the mechanics of herniation, we developed a physical flow model of the aortic arch that enables direct measurement of device curvature during experimentally simulated neuroendovascular procedures conducted from an upper arterial access. Combined with measurements of initial, unstressed device shapes and flexural rigidities, the method enables the experimental estimation of the device bending energies during these simulated procedures. Characteristic energy profiles revealed distinct stages in both herniation and successful navigation, governed by the interplay between device properties and vascular anatomy. A deterministic progression from successful navigation to herniation was identified, with catheter systems following paths determined by measurable energy barriers. Increasing guidewire stiffness or decreasing catheter stiffness reduced the energy barrier for successful navigation while increasing that for herniation. This framework enables the prediction of endovascular herniation risk and offers unique insight into improved device design and clinical decision-making.

Dynamic DeFi-G7 stock markets interactions and their potential role in diversifying and hedging strategies

AbstractThis study examines the link between stocks and decentralized finance (DeFi) in terms of returns and volatility. Major G7 exchange-traded funds (ETFs) and various highly traded DeFi assets are considered to ensure the robustness of the empirical experiment. Specifically, this study applies the vector autoregression generalized autoregressive conditional heteroskedasticity (VAR-GARCH) model to examine the information transmission of these two markets on a two-way basis and the dynamic conditional correlation (DCC)-GARCH model to assess the bivariate correlation structure between each DeFi and ETF pair. The volatility spillover analysis proves a contagion effect occurred between different geographic markets, and even between markets of different natures and typologies, during the most turbulent moments of the COVID-19 crisis and the war in the Ukraine. Our results also reveal a weak positive correlation between most DeFi and ETF pairs and positive hedge ratios that approach unity during turbulent times. In addition, DeFi assets, except for the Bazaar (BZR) Protocol, can offer diversification gains when included in financial investment portfolios. These results are particularly relevant for portfolio managers and policy-makers when designing investment strategies, especially during periods of financial crisis.

Crises and Stock Market Integration: Evidence from BRICS Countries

This paper examines the stock market integration in BRICS (a group of Brazil, Russia, India, China and South Africa) countries and explores the effect of two major events; COVID-19 and Russia-Ukraine war on the stock market linkages of these countries. The study is based on weekly observations of BSE SENSEX (India), Bovespa Index (Brazil), MOEX Index (Russia), Shanghai Composite Index (China), and JSE All Share Index (South Africa) collected from Yahoo Finance and Wallstreet Journal from January 2016 to December 2023. We utilize multivariate DCC GARCH (dynamic conditional correlation) model to discern the time varying conditional correlations (TVCCs) between these equity markets. Thereafter, these TVCCs are regressed on the dummy variables to capture the existence of contagion effects among the stock markets of BRICS countries during these major events. The findings of this study indicate the existence of co-movement in the stock markets prices of BRICS countries during the sample period. We find existence of significant contagion effects among the BRICS countries during the COVID period. Results show a significant downfall in the TVCCs between BRICS stock market returns following the beginning of Russia - Ukraine war.

Evaluating Volatility Using an ANFIS Model for Financial Time Series Prediction

This paper develops and implements an Autoregressive Integrated Moving Average model with an Adaptive Neuro-Fuzzy Inference System (ARIMA-ANFIS) for BTCUSD price prediction and risk assessment. The goal of these forecasts is to identify patterns from past data and achieve an understanding of the future behavior of the price and its volatility. The proposed ARIMA-ANFIS model is compared with a benchmark ARIMA-GARCH model. To evaluated the adequacy of the models in terms of risk assessment, we compare the confidence intervals of the price and accuracy measures for the testing sample. Additionally, we implement the diebold and Mariano test to compare the accuracy of the two volatility forecasts. The results revealed that each volatility model focuses on different aspects of the data dynamics. The ANFIS model, while effective in certain scenarios, may expose one to unexpected risks due to its underestimation of volatility during turbulent periods. On the other hand, the GARCH(1,1) model, by producing higher volatility estimates, may lead to excessive caution, potentially reducing returns.

Modeling Long Memory Volatilities of Nigeria Selected Macro Economic Variables with Arfima and Arfima Figarch

The research delved into analysing the stochastic characteristics of Nigeria's Real GDP, the exchange rate of the Naira to US Dollar, and the inflation rate employing Autoregressive fractionally integrated moving average (ARFIMA) and the Autoregressive Fractionally Integrated Moving Average Fractionally Integrated Generalized Autoregressive Conditional Heteroskedasticity (FIGARCH) modelling approach. The ability of the hybrid formation of ARFIMA-FIGARCH model with Nigeria macroeconomic variables in modeling the periodicity of long memory volatilities was examined. ARIMA GARCH method of modeling was also employed in analyzing the volatilities of Nigeria selected macroeconomic variables to enrich the study. The efficiency of ARFIMA, ARFIMA FIGARCH and ARIMA GARCH models were evaluated with the forecast evaluation measurements. Results revealed that ARFIMA FIGARCH and ARIMA GARCH models are more adequate in modeling the Inflation rate and the exchange rate while ARFIMA present more adequacies in modeling the RGDP. This result revealed evidence of high volatilities in Nigeria Inflation and the exchange rate of Naira to US dollar

Value-at-risk modeling of naira exchange rates

The naira exchange rate has experienced extreme volatility, and the use of derivatives to control interest rates and currency risks has grown quickly. These developments have made risk management research necessary. To this effect, this paper investigated the optimal volatility model that offers the best VaR forecasts and minimizes expected loss in the Naira exchange rate. The data was collected from FX time and consisted of the Euro to Naira exchange and the daily closing rate of the US dollar to Naira exchange rate from 24/10/2016 to 15/06/2018. These data were estimated using different symmetric and asymmetric GARCH models. The finding shows that there is less volatility in the USD to Naira exchange rate compared to the Euro to Naira exchange rate. The study shows that SPLINE- GJR under skewed student t distribution is the optimal model for the Euro to Naira exchange rate while GARCH is the optimal model for the US dollar to Naira exchange rate. This study suggests that model risk assessments be given careful consideration by regulators, banks, and other stakeholders and integrated into the process of operational and regulatory design.

Bayesian Lower and Upper Estimates for Ether Option Prices with Conditional Heteroscedasticity and Model Uncertainty

This paper aims to leverage Bayesian nonlinear expectations to construct Bayesian lower and upper estimates for prices of Ether options, that is, options written on Ethereum, with conditional heteroscedasticity and model uncertainty. Specifically, a discrete-time generalized conditional autoregressive heteroscedastic (GARCH) model is used to incorporate conditional heteroscedasticity in the logarithmic returns of Ethereum, and Bayesian nonlinear expectations are adopted to introduce model uncertainty, or ambiguity, about the conditional mean and volatility of the logarithmic returns of Ethereum. Extended Girsanov’s principle is employed to change probability measures for introducing a family of alternative GARCH models and their risk-neutral counterparts. The Bayesian credible intervals for “uncertain” drift and volatility parameters obtained from conjugate priors and residuals obtained from the estimated GARCH model are used to construct Bayesian superlinear and sublinear expectations giving the Bayesian lower and upper estimates for the price of an Ether option, respectively. Empirical and simulation studies are provided using real data on Ethereum in AUD. Comparisons with a model incorporating conditional heteroscedasticity only and a model capturing ambiguity only are presented.

Empirical performance of the optimal predictors under asymmetric loss GARCH vs. realized GARCH models

ABSTRACT We assess the forecast performance of the optimal predictor for returns under asymmetric loss using conditional volatility forecasts from conventional GARCH and realized GARCH models. We compare two classes of models for conditional volatility that is essential to the correction term for the optimal predictor, under asymmetric loss function. We find that when the conditional volatility forecasts from the realized GARCH models are used, the optimal predictor has better performance. The results strongly suggest using conditional volatility forecasts from the joint models of conditional volatility and realized volatility for short-to-moderate forecast horizons and low-to-moderate degrees of asymmetry in the optimal predictor expression to forecast daily returns.

Mapping Risk–Return Linkages and Volatility Spillover in BRICS Stock Markets through the Lens of Linear and Non-Linear GARCH Models

This paper explores the influence of the risk–return relationship and volatility spillover on stock market returns of emerging economies, with a particular focus on the BRICS countries. This research is undertaken in a context where discussions on de-dollarization and the expansion of BRICS membership are gaining momentum, making it a novel and distinct exercise compared to prior studies. Utilizing econometric techniques to investigate daily market returns from 1 April 2008 to 31 March 2023, a period that witnessed major events like the global financial crisis, the COVID-19 pandemic, and the Russia–Ukraine conflict, linear and non-linear models like ARCH, GARCH, GARCH-M, EGARCH, and TGARCH, are employed to assess stock return volatility behaviour, assuming a Gaussian distribution of error terms. The diagnostic test confirms that the distribution is non-normal, stationary, and heteroscedastic. The key findings indicate a lack of the risk–return relationship across all BRICS stock markets, except for South Africa; a more pronounced effect of unpleasant news over pleasant news; a slow mean-reverting process in volatility; the EGARCH model is the best fit model as evidenced by a higher log likelihood and lower Akaike information criterion and Schwardz information criterion parameters; and finally, the presence of significant bidirectional and unidirectional spillover effects in the majority of instances. These findings are valuable for investors, regulators, and policymakers in enhancing returns and mitigating risk through portfolio diversification and informed decision making.

Observable or latent Markov chains for score-driven regime-switching volatility?

ABSTRACT We study the statistical and forecasting performances of two regime-switching Beta-t-EGARCH (exponential generalized autoregressive conditional heteroscedasticity) models, i.e. observable-switching (OS) Beta-t-EGARCH and Markov-switching (MS) Beta-t-EGARCH. Both are non-path-dependent score-driven regime-switching volatility models, and their regime-switching specifications can be related to corresponding non-path-dependent Markov-switching GARCH (MS-GARCH) specifications. We present the estimation procedures for OS-Beta-t-EGARCH and MS-Beta-t-EGARCH. We use data on the weekly log-returns of the Standard & Poor’s 500 (S&P 500) index and a random sample of 50 stocks from the S&P 500 from March 1986 to July 2024 ( T = 2 , 000 ). The out-of-sample forecasting window is from May 2005 to July 2024 ( T f = 1 , 000 ). We compare the in-sample statistical and out-of-sample density forecasting performances of Beta-t-EGARCH, OS-Beta-t-EGARCH, and MS-Beta-t-EGARCH. We find that the statistical and density forecasting performances of OS-Beta-t-EGARCH are superior to MS-Beta-t-EGARCH, motivating its practical use by investors and risk managers.

DYNAMIC LINKS BETWEEN COMMODITY MARKETS & PAKISTANI SECTORAL INDICES: IMPLICATIONS FOR PORTFOLIO DIVERSIFICATION

This research aimed to examine the inter-connections among international commodities markets and sectoral indices of Pakistan over the most recent period ranging from July 19, 2016, to December 29, 2023. This time period is selected based on recent important events of global significance including COVID-19 pandemics and recent geopolitical crisis emerged due to Russia-Ukraine war in Feb, 2022. This study is utilizing Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model for the deeper inquiry of interplay among the variables. The findings of the study indicate significant spillovers among variables with varying degrees of significance. The results show that various sectors of Pakistan economy showed asymmetric behavior indicating that some sectors were the risk transmitters while other were risk recipients. Moreover, volatility linkages are time-varying with heightened transmissions during turbulent periods. The results provide the significant information in reaching the desired conclusion and making decisions. The findings of study thus had important implications for investors (individual & institutional), fund managers and policy makers while devising strategies for diversification and risk mitigation in the Pakistani context especially in stressful periods.

PENERAPAN MODEL ASYMMETRIC POWER AUTOREGRESSIVE CONDITIONAL HETEROSCEDASTICITY (APARCH) TERHADAP HARGA MINYAK MENTAH DUNIA

Heteroscedasticity poses a challenge in ARIMA modeling by causing residual variance to be non-constant, leading to less efficient estimates. This issue often arises in time series data due to volatility, which measures data fluctuation over time. To address heteroscedasticity, models like ARCH and GARCH incorporate variance changes into forecasting. However, they lack the ability to capture asymmetry, the difference in impact between good and bad news on volatility. The APARCH model, on the other hand, addresses this by modeling volatility with asymmetry elements. Daily world crude oil prices, known for high volatility, serve as a case study for this research. By employing the APARCH model, the study aims to forecast these prices accurately. Results indicate that the APARCH(1,1) model outperforms the best GARCH model, ARCH(2), as it yields a smaller Mean Absolute Percentage Error (MAPE) of 6.033487. This highlights the superior accuracy of APARCH in forecasting data with heteroscedasticity issues, particularly in the context of daily crude oil prices.

Unveiling change-point detection with ARMA-GARCH models

This paper delves into the asymptotic theory of a Cumulative Sum (CUSUM)-type test designed for detecting change points in the variance of AutoRegressive Moving-Average models, incorporating Generalized Autoregressive Conditional Heteroscedasticity innovations. We demonstrate that, under the null hypothesis (no change), the CUSUM test statistic converges to the supremum of a standard Brownian bridge. Using a Monte Carlo simulation, we highlight the strong performance of our proposed test when compared to the methods by Song and Kang. Furthermore, we provide a real-world data analysis to showcase the practical application of our test.

Portfolio Diversification Opportunities between Europe and India do Exist

In this article, a humble effort has been made to check the volatility transmission from European stock markets (FTSE100, DAX30, CAC40 and SMI20) to the Indian stock market (NIFTY50) to determine whether there is any opportunity for portfolio managers to diversify their portfolio. Various statistical tools and econometric models, such as vector autoregression (VAR) and dynamic conditional correlation (DCC)-multivariate generalised autoregressive conditional heteroscedasticity (MGARCH), are used to detect the volatility transmission from the European market to the Indian market. The FTSE100 and the NIFTY50 have been found to have bidirectional causality. VAR results suggest that only the DAX30 and SMI20 (Germany and Switzerland) markets have an impact on the Indian market. Finally, using DCC-MGARCH, the researcher found that information spillover takes place from all European countries to India over a longer period of time, but portfolio diversification between the London market (FTSE) and the Indian market (NIFTY) and German market (DAX) with Indian market (NIFTY) is possible over a shorter period of time. JEL Codes: C01, G1, G17

Predictive performance of denoising algorithms in S&P 500 and Bitcoin returns

This paper aims to investigate the effectiveness of both the Hankel matrix and the Wavelet denoise methods to address the issue of denoising volatility in datasets, specifically squared returns, and to enhance the accuracy of post-sample forecasting. When converting data from levels to volatility, noise levels are amplified, and the forecasting models suffer from structural bias, leading to reduced accuracy gains. The main challenge in denoising operations is preserving systemic impulses while extracting sporadic and unpredictable components. While conventional denoising algorithms struggle to distinguish systemic patterns from noise, the Hankel matrix approach surpasses them in performance, resulting in improved predictive accuracy. Additionally, this paper explores the Wavelet denoise method, which is found to be less effective than the Hankel matrix approach for GARCH models. The empirical work showcases the denoising process and the accuracy improvements achieved in various datasets for GARCH models. By implementing the Hankel matrix approach, simulations reveal a notable accuracy gain of over 10%.

Research on the volatility forecasting model of KOSPI index returns using AR(M)-GARCH(P,Q) model

In this study, we estimated the volatility of the KOSPI index returns and analyzed volatility trends. The data used in the study consisted of monthly observations from January 2005 to December 2022, and the KOSPI index raw data was transformed into log returns. The volatility estimation model used the AR(m)-GARCH(p,q) model, which combines the autoregressive error model and the GARCH model that explains the persistence of volatility at low orders. The goodness of fit of the model was confirmed using the Portmanteau Q-test and LM-test. Applying the autoregressive error model revealed significant autocorrelation in the log returns of the KOSPI index at lags 3 and 6. Residual analysis indicated that the residuals followed white noise, but the squared residuals exhibited heteroscedasticity. Therefore, after fitting the autoregressive error model, we applied the GARCH model and conducted residual analysis, finding both the residuals and squared residuals significant at a 5% significance level. The volatility forecasting results indicated a continuous increase in volatility. The findings of this study are expected to provide important implications for policymakers responsible for risk management in the Korean stock market.