GARCH Research Articles

Comparative analysis of machine learning and traditional models for financial option pricing

This study conducts a comparative analysis of traditional and machine learning models for financial option pricing, using historical stock prices and interest rates data. Traditional models such as the Black-Scholes, Heston, Merton Jump-Diffusion, and GARCH are evaluated against machine learning models including Multi-Layer Perceptrons (MLPs) and Long Short-Term Memory (LSTM) networks. The analysis employs performance metrics like Mean Squared Error (MSE), Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and R value. Results indicate that the GARCH model excels in predictive accuracy due to its ability to capture volatility clustering, while machine learning models, especially the Tuned Neural Network, demonstrate superior flexibility and adaptability in managing complex non-linear relationships in financial data. Traditional models, although theoretically robust, show limitations under varying market conditions. The study underscores the potential of hybrid approaches combining traditional and machine learning techniques to leverage their respective strengths for more accurate and reliable option pricing. Future research directions include exploring advanced machine learning architectures and improving model transparency through explainable AI.

Time‐series‐based ensemble model output statistics for temperature forecasts postprocessing

AbstractThe uncertainty in numerical weather prediction models is nowadays quantified by the use of ensemble forecasts. Although these forecasts are continuously improved, they still suffer from systematic bias and dispersion errors. Statistical postprocessing methods, such as the ensemble model output statistics (EMOS), have been shown to substantially correct the forecasts. This work proposes an extension of EMOS in a time‐series framework. Besides taking account of seasonality and trend in the location and scale parameter of the predictive distribution, the autoregressive process in the mean forecast errors or the standardized forecast errors is considered. The models can be further extended by allowing generalized autoregressive conditional heteroscedasticity. Furthermore, it is outlined how to use these models for arbitrary forecast horizons. To illustrate the performance of the suggested EMOS models in time‐series fashion, we present a case study for the postprocessing of 2 m surface temperature forecasts using five different lead times and a set of observation stations in Germany. The results indicate that the time‐series EMOS extensions are able to significantly outperform the benchmark models EMOS and autoregressive EMOS (AR‐EMOS) in most of the lead time–station cases.

Analyzing the Selective Stock Price Index Using Fractionally Integrated and Heteroskedastic Models

Stock market indices are important tools to measure and compare stock market performance. The Selective Stock Price (SSP) index reflects fluctuations in a set value of financial instruments of Santiago de Chile’s stock exchange. Stock indices also reflect volatility linked to high uncertainty or potential investment risk. However, economic shocks are altering volatility. Evidence of long memory in SSP time series also exists, which implies long-term persistence. In this paper, we studied the volatility of SSP time series from January 2010 to September 2023 using fractionally heteroskedastic models. We considered the Autoregressive Fractionally Integrated Moving Average (ARFIMA) process with Generalized Autoregressive Conditional Heteroskedasticity (GARCH) innovations—the ARFIMA-GARCH model—for SSP log returns, and the fractionally integrated GARCH, or FIGARCH model, was compared with a classical GARCH one. The results show that the ARFIMA-GARCH model performs best in terms of volatility fit and predictive quality. This model allows us to obtain a better understanding of the observed volatility and its behavior, which contributes to more effective investment risk management in the stock market. Moreover, the proposed model detects the influence volatility increments of the SSP index linked to external factors that impact the economic outlook, such as China’s economic slowdown in 2012 and the subprime crisis in 2008.

Volatility Transmission between Oil Price and Exchange Rate

This article presents a study on the transmission of oil price volatility to the exchange rates of 14 countries (net oil exporters and importers) during the period from 02/01/2000 to 31/11/2022. The aim is to compare the effect of oil price fluctuations on exchange rate volatility based on the country's nature. Using ARCH, GARCH, and GARCH-BEKK models, our results reveal that the real effective exchange rate is significantly linked to fluctuations in the real oil price for both categories of countries: oil importers and exporters. These findings have important implications for monetary, fiscal, inflationary, and trade policies for these countries.

Measuring market risk with GARCH models under Basel III: selection and application to German firms

Measuring market risk with GARCH models under Basel III: selection and application to German firms

Are Indian markets insulated from the impact of cryptocurrencies? Unveiling the volatility linkages through multi‐index dynamic multivariate GARCH analysis

AbstractThis paper investigates the dynamic relationships between the volatility of Bitcoin and major Indian stock market indices. Employing a dynamic conditional correlation–generalized autoregressive conditional heteroskedasticity (DCC‐GARCH) model, we explore how volatility shocks and information flow influence the correlations between these asset classes. Our findings reveal a key characteristic: volatility spillovers tend to be short‐lived, indicated by a relatively low DCC‐GARCH parameter (dcca1). This suggests that while a surge in volatility in one market might lead to a temporary increase in correlation with the other, this heightened correlation is unlikely to persist for extended periods. However, the model also highlights a high DCC‐GARCH parameter (dccb1), signifying that the correlations themselves are responsive to new information. This implies that volatility linkages can adjust rapidly in response to market events or economic data releases. To enhance accessibility for a broad audience, we translate these findings into economic intuitions. We illustrate how the model can be interpreted through real‐world examples, such as the impact of sudden policy changes in India or global market flash crashes. By understanding the short‐lived nature of volatility spillovers and the responsiveness of correlations, investors in the Indian markets can make more informed decisions when considering the potential influence of Bitcoin's volatility while contributing to a deeper understanding of the dynamic interactions between cryptocurrency and traditional financial markets in the Indian context.

The impact of COVID-19 stringency measures on emerging stock market stability: Does economic resilience matter?

PurposeThe current research aims to investigate the impact of coronavirus 2019 (COVID-19) evolution, government stringency measures and economic resilience on stock market volatility in the Middle East and North African (MENA) emerging markets. Other macroeconomic factors were also taken into account.Design/methodology/approachBased on financial data from 10 selected MENA countries, we tested an integrated framework that has not yet been explored in prior research. The exponential generalized autoregressive conditional heteroskedasticity (E-GARCH) was adopted to analyze data from March 2020 to February 2022.FindingsOur research illustrates the direct and indirect effects of the virus outbreak on stock market stability and reports that economic resilience could alleviate the volatility shock. This finding is robust across the various proxies of economic resilience used in this study. We also argue that the negative impact of the pandemic on equity market variation gets more pronounced in countries with higher level of stringency scores.Practical implicationsPolicymakers ought to strengthen their economic structures and reinforce the economic governance at the national level to gain existing and potential investors’ trust and ensure lower stock market volatilities in times of crisis. Our study also recommends some key economic factors to consider while establishing efficient policies to tackle unexpected shocks and prevent financial meltdowns.Originality/valueOur findings add to the evolving literature on the reaction of economic and financial markets to the sanitary crisis, particularly in developing countries where research is still scarce. This study is the first of its kind to investigate the stock market reaction to stringency measures in the understudied MENA region.

Sustainable development and investor confidence: The safe‐haven appeal of green‐bond issuing firms

AbstractThis study investigates the performance of a green‐linked portfolio as a safe haven and hedge against traditional assets during periods of market turmoil, such as the COVID‐19 pandemic and the Russia‐Ukraine war. Utilizing a dynamic conditional correlation (DCC)‐generalized autoregressive conditional heteroscedasticity (GARCH) approach, the study analyzes the portfolio's correlations with global asse like SENSEX 30, BSE ESG 100, Gold, S&P Green Bond Index, and US 10‐year Treasury bonds, demonstrating its stability. Our findings demonstrate that the green‐linked portfolio outperforms both individual stocks and major indices as well as traditional safe havens like gold and US Treasury bonds. The portfolio exhibits superior risk‐adjusted returns and lower volatility, particularly during crisis periods. The portfolio's strong positive correlation with the S&P Green Bond Index highlights its alignment with the broader green market. Interestingly, with a 95% hedge effectiveness, it emerged as a viable safe haven investment, surpassing gold in stability during market uncertainties. Further, forecast matrix results and VAR analysis confirm the portfolio's potential as a diversifier and safe haven asset, characterized by significant positive returns. Additionally, the SAP‐LAP framework provides clarity to stakeholders on safe‐haven options within green markets. Moreover, while green bond markets are more mature in developed economies, our results suggest that green‐linked investments in emerging markets, such as India, offer a promising avenue for investors seeking both financial returns and environmental impact. Overall, the study provides empirical evidence supporting the inclusion of green‐linked assets in diversified portfolios to enhance risk management and capture long‐term growth opportunities.

The Dissimilar Market Volatility in Neighboring Financial Markets: An Empirical Study Using A Multivariate Garch Model

ABSTRACT: Conventional knowledge of market volatility represents that two proximate financial markets operated in the same country would display a similar pattern in their time-varying volatility. In this paper, we propose that the heterogeneity in financial policy orientation of stock markets creates significant inter-market differences in terms of the volatility of stock returns, even if they are culturally and geographically linked to each other. For the empirical investigation of our proposition, the volatility data from two major stock exchanges in the Middle East, the Abu Dhabi Securities Exchange (ADX) and the Dubai Financial Market (DFM) are used. Both the ADX and DFM stock exchanges operate in the same country, the United Arab Emirates (UAE). The ADX is based in Abu Dhabi, the administrative capital, while the DFM is based in Dubai, the commercial and business hub of the UAE. They were both established in the year 2000, and their operational headquarters are located about 150 km from each other. This paper uses a multivariate GARCH model, in particular a diagonal VECH GARCH (1, 1) model to estimate volatility measures for stock returns between ADX-listed and DFM-listed stocks. The paper finds that the stock returns are significantly less volatile in the ADX compared to those in the DFM suggesting that the volatility transmission is incomplete between these two neighboring financial markets. This difference in volatility can potentially be attributed to the relatively conservative financial policies adopted by the oil-rich emirate of Abu Dhabi compared to the more market-oriented economic policies of Dubai, the country’s financial and commercial hub. Our findings have considerable implications for portfolio managers in ascertaining risk premiums when allocating investments across the two stock exchanges. For instance, this disparity in volatility should be taken into account by investors and policymakers when designing risk management strategies because it suggests that investors in the DFM may be exposed to higher levels of risk and uncertainty compared to their counterparts in the ADX. Investors operating in the DFM may require more robust risk management strategies, such as asset diversification and hedging, compared to their ASX counterparts.

Volatilitas Harga Daging Ayam Broiler di Tingkat Pedagang Pengecer pada Berbagai Kabupaten/Kota di Provinsi Jambi

This research aims to analyze broiler chicken meat price volatility at the retail trader level in various districts/cities in Jambi Province. Forecasting analysis of broiler chicken meat prices in Jambi Province using time series secondary data in the form of daily data on the price of purebred chicken meat from 1 January 2023 to 31 October 2023 sourced from the National Food Agency. The analytical method used to determine volatility and the appropriate forecasting model for broiler chicken meat prices in Jambi Province uses the ARIMA, ARCH/GARCH model. The volatility of broiler chicken meat prices at the retail trader level in 11 districts/cities in the Jambi Province region varies, with the volatility in Kerinci District being the highest. The appropriate forecasting model for determining the price of broiler chicken meat in Jambi Province is the ARCH Model, which performs well in predicting the price of broiler chicken meat in Jambi Province.

Estimation of tail risk using extreme expectiles in linear GARCH models with heavy-tailed error

Estimation of tail risk using extreme expectiles in linear GARCH models with heavy-tailed error

SARIMAX–GARCH Model to Forecast Composite Index with Inflation Rate and Exchange Rate Factors

Investors should consider the Indonesia Composite Index (ICI) as a key indicator before making investment decisions, as it reflects the performance of industries and the broader economic growth. In Indonesia, the ICI exhibits fluctuating movements, making accurate forecasting essential for understanding the country's economic conditions, which are closely tied to capital flows, growth, and tax revenues. This study aims to forecast the ICI using the SARIMAX-GARCH model, incorporating macroeconomic factors such as the inflation rate and exchange rate. The findings reveal that both variables significantly impact the ICI, with the model achieving a Mean Absolute Percentage Error (MAPE) of 0.952% for training data and 5.233% for test data. The model's performance is supported by an R² value of 0.9782 and a Mean Squared Error (MSE) of 0.0003. This research not only improves the accuracy of ICI forecasts but also supports Indonesia's 8th Sustainable Development Goal (SDG) for decent work and economic growth. Doi: 10.28991/HIJ-2024-05-03-014 Full Text: PDF

Volatility Spillover of Crude Palm Oil (CPO) Commodity between Spot and Futures Market in Indonesia

The development of trade globalization has led to the expansion of market interactions between countries, specifically for Crude Palm Oil (CPO) commodities. This study aims to determine the volatility of CPO prices between the Medan spot market and the futures market consisting of the Jakarta futures market, Malaysia futures market, and the Rotterdam forward market. The daily data on CPO prices in each market from January 2016 to December 2020. The data analysis method uses the GARCH model (1.1). The results showed a volatility transmission from the entire futures market to the Medan spot market. Thus, the CPO commodity futures market influences price volatility and the price formation process in the Medan spot market. Therefore, CPO commodity market players must be alert to the information occurring in the futures market to determine investment strategies.

Carbon exchange-traded funds market and economic policy uncertainty

This study empirically analyses the relationship between economic policy uncertainty (EPU) and three carbon exchange-traded funds (ETFs) using wavelet coherence analysis as well as dynamic conditional correlation (DCC) from a multivariate GARCH model. The analysis techniques employed allow us to analyze the nature of the relationship which may depend on time and frequency. Our findings indicate that there exists a significant negative correlation between EPU and the ETFs for almost all times and frequencies. However, for some times and frequencies, the identified negative relationship is not significant. Interestingly, we also find that for some times and frequencies, EPU leads the ETFs and for some other times and frequencies ETFs lead the EPU.

Performance comparison of alternative volatility models applied to economic indexes: the role of asymmetric effects

ABSTRACT This article examines the empirical relationship between economic indexes – namely the industrial production and the consumer confidence – and their volatility by using the United States data over the periods 1919–2023 and 1960–2023, respectively. To address this topic, several GARCH-family models including volatility feedback and the asymmetric effects are estimated. We find that (i) the industrial production index exhibits asymmetric effects, with significant fitting performance over the standard GARCH model; (ii) the inclusion of t -distributed innovations in the error term improves the fitting performance of the competing models against their counterparts with a normal distribution assumption; (iii) both models tested for the consumer confidence index exhibit similar performance to fit with the data; (iv) by excluding the months during and after the COVID-19 pandemics and the Russia–Ukraine conflict, it leads to the same results and conclusions for both economic indexes. Conditional heteroscedasticity, economic growth, GARCH models, asymmetric effects, volatility feedback

African and international financial markets interdependencies: Does Covid-19 media coverage make any difference?

This study examines the co-movement and time-varying integration between equity, exchange rate, and international market volatility indices across different time–frequency domains using the wavelet and dynamic conditional correlation-generalised autoregressive conditional heteroskedasticity (DCC-GARCH) model and BEKK GARCH for selected African countries. First, the findings indicate that the co-movement between equity and exchange rates during the pandemic was exacerbated by global COVID-19 media coverage. The findings indicate that there has been a substantial risk transfer between exchange rates and stock returns during the COVID-19 pandemic, resulting in a decline in domestic stock returns and subsequent capital outflows, which in turn increased the exchange rate. Given the growing difficulties in diversification, specific information on the volatility of financial market connectedness is required to plan hedging strategies. To explore the influence of global market volatility on Africa’s equity and currency markets, it is crucial to analyse the relationship between regional and global market fluctuations, especially given the negative impact of the COVID-19 pandemic. Our empirical research demonstrates that the VIX and OVXCL indices play a significant role in transmitting spillovers to currency and equity markets in Africa. This suggests that the sentiment indicators provided by the VIX and OVXCL can be useful in predicting the behaviour of Africa’s currency and equity markets

Cybersecurity strategies for protecting big data in business intelligence systems: Implication for operational efficiency and profitability

The alarming increase in consumers goods and services with concurrent devaluations of naira have necessitated the need to examine the effects of NUSX(Nigerian naira/1 US dollar), NFX (Nigerian naira/1 France franc) and NCX (Nigerian naira/1 Chinese yuan) rates on inflation(measured by CPI) and its volatility in Nigeria using data sets spanning from 2008 to 2022. The auxiliary autoregressive AAR(3) order of integration test specify that all the variables are stationary at first difference. Adopting multiple regression model with least square method of estimation and generalized autoregressive conditional heteroskedasticity (GARCH(1, 1)) as measure of volatility, the results indicate that NCX (Nigerian naira/1 Chinese yuan), NFX (Nigerian naira/1 France franc) and NUSX(Nigerian naira/1 US dollar) have no influence on both inflation and its volatility in Nigeria. This implies that variation in exchange rates system is not sufficient to explain the sudden increase in the prices of goods and services in Nigeria. Therefore, the government should look beyond exchange rates in finding solution to rising inflation phenomenon in Nigeria’s economic space.

Bitemark analysis comparing the use of digital scans and 3D resin casts.

Although dental patterns are unique, the use of bitemark analysis in personal identification remains controversial. To accurately reproduce and compare three-dimensional models of bitemarks and dental arches, intraoral three-dimensional scans, commonly utilized in clinical dental practice for precise and stable digital impressions, are recommended. This study aims to compare two different techniques for bitemark analysis: a digital method based on the superimposition of digital scans of dental patterns and lesions, and a visual method based on the physical superimposition of impressions and resin casts produced by 3D printing. A sample of 12 volunteers (6 males and 6 females) with a mean age of 26 years was collected as biters. Each subject was asked to bite on custom supports made from semi-rigid water bottles covered with imprintable dental wax. The dental arches and bitemarks were then recorded using an intraoral scanner and dental impressions. Scan superimposition analysis was conducted using CloudCompare software, while resin casts were printed using a 3D printer and physically superimposed on the bitemark impressions by a blind operator, who was not involved in sample collection, bite test execution, prior cast acquisition, or CloudCompare analysis. Both superimposition techniques relied on the selection of 10 corresponding landmarks (on canines and central and lateral incisors of the upper and lower arches) between the dental arches and impressions. The digital superimposition showed an average concordance of 92.5% for the upper arch landmarks and 85% for the lower arch landmarks, with an overall average concordance of 88.8% for both arches combined. In contrast, the visual analysis of resin casts showed an average concordance of 77.5% for the upper arch and 76.7% for the lower arch, with an overall average of 77.1% for both arches combined. In the analysis performed using CloudCompare, the maxillary arch demonstrated the best superimposition, with 4 landmarks (R0, R1, R2, R5) consistently overlapping. The digital analysis outperformed the visual analysis in all four quadrants, particularly in the upper right arch compared to the lower left arch, thereby supporting the integration of digital techniques in forensic applications. Further studies are necessary to validate the digital technique on a larger sample, including subjects with different dental characteristics, bite dynamics, and varying types of supports and substrates.

Applications of GARCH Models in Forecasting Financial Market Volatility: Insights from Leading Global Stock Indexes

This study investigates the volatility dynamics of major global stock indexes, including the FTSE 100, Hang Seng Index, NIKKEI 225, and S&P 500, using a range of Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models. The analysis spans a comprehensive 20-year period from January 1, 2004, to December 31, 2023, encompassing diverse market conditions such as bull and bear markets, the 2008 financial crisis, and the COVID-19 pandemic. The methodology includes preprocessing steps such as calculating daily log returns, performing descriptive statistics, and conducting stationarity and ARCH effect tests to ensure data suitability for volatility modelling. The study evaluates several GARCH models, including GARCH, EGARCH, NGARCH, APARCH, GJR-GARCH, and TGARCH, to forecast volatility and address both symmetric and asymmetric effects. The TGARCH model exhibits strong performance in capturing leverage effects and asymmetries, particularly for the FTSE 100 and Hang Seng Index. The APARCH model performs well for the S&P 500, demonstrating sensitivity to past shocks. Overall, the findings underscore the importance of advanced GARCH models in accurately predicting volatility in global financial markets, highlighting the TGARCH model's effectiveness in addressing asymmetries and providing insights into selecting appropriate models for enhanced financial analysis and risk management.

Volatility in the Equity Stock Market in India from 2019 to 2024: An Empirical Analysis

This research investigates the volatility and fluctuations in the Indian equity stock market from 2019 to 2024, a period characterized by unprecedented global and domestic challenges. The Indian stock market, like many emerging markets, experienced heightened volatility due to a confluence of events, including the COVID-19 pandemic, geopolitical tensions, economic reforms, and shifts in global financial conditions. The study employs advanced econometric models, including GARCH (Generalized Autoregressive Conditional Heteroskedasticity) and event study analyses, to capture the time-varying nature of market volatility and to identify the key factors driving these fluctuations. Our findings reveal that the COVID-19 pandemic triggered the most significant spikes in volatility, particularly during the early months of 2020, as uncertainty regarding the pandemic's impact on the economy led to sharp market corrections and investor panic. Additionally, the study highlights the influence of macroeconomic variables such as GDP growth, inflation, and monetary policy changes on market behavior. The paper also explores the role of investor sentiment and market liquidity in exacerbating volatility during crisis periods. The results provide valuable insights into the dynamics of the Indian equity market, offering implications for investors seeking to manage risk and for policymakers aiming to enhance market stability. The study underscores the need for robust risk management strategies and proactive regulatory measures to mitigate the adverse effects of such volatility, especially in an increasingly interconnected global financial environment. Keywords: Equity Stock Market, Volatility, India, COVID-19, Economic Reforms, 2019-2024