Value-at-Risk Models Research Articles

Statistical modelling of cryptocurrencies

There has been tremendous interest invested by researchers and academics in Bitcoin since it's introduction to the financial market. However, in recent years there has been an advancement of the cryptocurrency market where other cryptocurrencies such as Ethereum, Litecoin and Ripple have grown relatively quickly and could potentially challenge the dominant placement of Bitcoin. These cryprocurrencies have been utilized globally as a virtual currency for multiple transactions. The returns of cryptocurrencies are known to be volatile and have been observed to fluctuate quite a bit in recent times. This study assesses and differentiates the performance of generalized autoregressive score (GAS) models integrated with a few heavy-tailed distributions in Value-at-Risk (VaR) estimation of the four most popular cryptocurrencies' returns, i.e. Bitcoin returns, Ethereum returns, Litecoin returns and Ripple returns. This paper proposed VaR models for Bitcoin, Ethereum, Litecoin and Ripple returns, i.e. GAS models combined with the generalized hyperbolic distribution (GHD), the variance gamma (VG) distribution, the normal inverse Gaussian (NIG) distribution and the generalized lambda distribution (GLD). The Kupiec likelihood ratio test was adopted to evaluate the proposed models' adequacy and Backtesting VaR was used to select the superior set of models.

Comparative Analysis of Value-at-Risk in Market Risk Prediction in Banks Using GARCH Volatility

This study aims to compare the disclosure of Value at Risk (VaR) in market risk prediction among banks in Indonesia. By employing comparative and analytical methods, this research examines the effectiveness of VaR disclosure as a market risk prediction tool. Through the evaluation of VaR models disclosed by Indonesian banks and their comparison to a parametric model using asymmetric GARCH volatility for Variance Covariance Value at Risk, this study identifies the extent to which VaR disclosure can be relied upon to predict market risk. This research contributes to the understanding of risk management practices in the Indonesian banking sector and offers recommendations for improving market risk prediction accuracy through more effective VaR disclosures.

An Integrative Review of Portfolio Management

This paper delves into the evolution of portfolio theories, tracing their development from the seminal work of Markowitz's traditional portfolio theory to the contemporary landscape of modern portfolio management. Emphasizing the relevance for real-world investors, the study scrutinizes the advantages, applications, and limitations of these investment theories. The exploration commences with a comprehensive analysis of return, risk, and various factors integral to portfolio theory. Leveraging qualitative analysis and real-world examples, the paper elucidates the mathematical model underpinning the theory, furnishing investors with a structured investment strategy. The focal points of the paper are the VaR (Value at Risk) model and the beta coefficient. Through an in-depth examination of their mathematical foundations and theoretical underpinnings, the research elucidates the symbiotic relationship between their economic significance and mathematical intricacies. Furthermore, the paper expounds on their collective contribution to the overarching portfolio theory, shedding light on their role as guiding principles for risk-averse investors. By weaving together theoretical frameworks and practical implications, this paper seeks to provide a nuanced understanding of portfolio theories, equipping investors with valuable insights for informed decision-making in the dynamic landscape of financial markets.

Testing bitcoin’s safe-haven property and the correlation between Bitcoin, gold, oil, stock markets, and Google trends

Since its public introduction in 2009, Bitcoin has grown to be the most well-known cryptocurrency worldwide. There is still debate as to whether Bitcoin may be used as a hedge against other assets. The purpose of this study is to investigate the correlation between Bitcoin and conventional commodity markets such as gold, crude oil, stock markets, and investor interest (quantified via Google Trends). In addition, the paper also tests Bitcoin’s safe haven role compared to other commodity markets. The Vector Autoregression model using daily database collected during the period 2013–2021 is employed to investigate the relationship between Bitcoin and traditional commodity markets. The impulse response function is used to analyze Bitcoin price movements against economic shocks from gold, oil prices, and the Dow Jones Industrial Average. In addition, the value-at-risk (VaR) model is used to test Bitcoin’s safe-haven property compared to other conventional commodity markets. The research results show that Bitcoin has negative impacts on gold, crude oil prices, and the stock market. Besides, Bitcoin responds negatively to a sharp decline in investor interest. Furthermore, the results of the VaR model show that Bitcoin is the second most volatile and risky asset, only after the crude oil market, and much riskier than gold. This result proves that Bitcoin cannot yet be considered a safe-haven instrument. These findings have several implications for investors and policymakers to minimize the risks associated with this cryptocurrency. AcknowledgmentThe authors would like to send their sincere thanks to the Reviewers and Editorial Board of the Journal. Their valuable comments and helpful support helped improve the paper’s quality. No funding was granted for this study.

New runs‐based approach to testing value at risk forecasts

AbstractThe reformed Basel framework has left value at risk (VaR) as a basic tool of validating risk models. Within this framework, VaR independence tests have been regarded as critical to ensuring stability during periods of financial turmoil. However, until now, there is no consent among researchers regarding the choice of the appropriate test. The available procedures are either inaccurate in finite samples or need to rely on Monte Carlo simulations. To remedy these problems, we propose a new method for testing VaR models, based on the distribution of the number of runs. It outperforms the existing methods in two main aspects: First, it is exact in finite samples and thus allows for perfect control over the Type 1 error; second, its distribution is available in a closed form, so it does not require simulations before implementation. We show that it is the most adequate current procedure for testing low‐level VaR series, which corresponds to today's regulatory standards.

Forecasting the high‐frequency volatility based on the LSTM‐HIT model

AbstractVolatility forecasting from high‐frequency data plays a crucial role in many financial fields, such as risk management, option pricing, and portfolio management. Many existing statistical models could better describe and forecast the characteristics of volatility, whereas they do not simultaneously account for the long‐term memory of volatility, the nonlinear characteristics of high‐frequency data, and technical index information during the modeling phase. The purpose of this paper is to use the prediction advantage of deep learning long short‐term memory (LSTM) model to predict the volatility fusing three classes of information, that is, high frequency realized volatility (H), technical indicators (I), and the parameters of generalized autoregression conditional heteroskedasticity(GARCH), heterogeneous autoregressive (HAR), and c, resulting in a novel LSTM‐HIT model to forecast realized volatility. We employ the extreme value theory (EVT) of a semiparametric method to estimate the quantile of standardized return and construct the LSTM‐HIT‐EVT model to forecast the value at risk (VaR). Empirical results show that the LSTM‐HIT model provides the most accurate volatility forecast among the various considered models and that the LSTM‐HIT‐EVT model yields forecasts more accurate than other VaR models.

Integrating Value at Risk (VaR) Model into Behavior Economics for Consumer Behavior Marketing and Decision Analysis

This overview paper supplies a background for a potential suppose of a new research dimension, based on Value at Risk model analysis applying in a point of view based on behavior economics, and supposed theory of using the models of Value at Risk. This article proposes a novel research avenue by melding the Value at Risk (VaR) model with behavioral economics, aiming to enrich our comprehension and forecasting of consumer behavior in the marketing domain. The paper underscores the significance of the discussed topics, encompassing the VaR model, marketing strategies, consumer behavior patterns, behavioral economics, and a concise touch on econometric tools. Hypotheses are presented, showcasing a regression model that holds the potential to significantly contribute to upcoming research endeavors. The foundational context and recommended methodologies of this study are tailored to spotlight specific market segments when gauging market reactions. By employing this combined model, researchers can delve into the behavior of consumers within specific geographical or economic markets, offering insights into their likely reactions to shifts in the price of merit goods. This approach beckons further exploration in correlating domains, encompassing classical economics, marketing insights related to consumer behavior, and the broader realm of behavioral economics.

Risk Management in Derivatives Markets: Integrating Advanced Hedging Strategies with Empirical Analysis

This study provides a comprehensive analysis of hedging strategies in the Chinese 50ETF options market, emphasizing dynamic hedging, Value at Risk (VaR), and machine learning-based approaches. Each strategy is meticulously evaluated against various market conditions, revealing distinct strengths and weaknesses. Dynamic hedging proves cost-effective in stable markets but struggles in high volatility scenarios, limiting its risk reduction capacity. Conversely, the VaR model, while reducing risk effectively under extreme conditions, may lead to over-hedging in calmer markets due to high costs and dependence on historical data. Machine learning strategies excel in adapting to complex and nonlinear market dynamics, though their effectiveness is contingent on data accuracy and model robustness. The study highlights the criticality of aligning strategies with market specifics and investor risk profiles, advocating for adaptable risk management in the fluctuating realm of financial derivatives. It provides empirical insights into modern hedging methods, offering practical guidance for their application in dynamic financial markets.

Are the intraday volatility estimations more representative than the conventional measures? Evidence from the EURTRL FX.

This paper aims to assess the accuracy and representativeness of Value at Risk (VaR) estimation models for the highly volatile Turkish lira (TRY) and Euro (EUR) FX rate. We compare the performance of various VaR models commonly used in the financial and banking industry and examine the effectiveness of intraday models, particularly the Garman and Klass (1980) and the Parkinson (1980) approaches, in improving VaR estimation relative to conventional models such as Variance Covariance and Exponential Weighted Moving Average. Additionally, we highlight certain shortcomings of the VaR legislation proposed by Vasileiou (2016, 2017). Our findings demonstrate that intraday volatility estimations not only enhance the accuracy of VaR estimations, but also provide a more representative assessment of real risk. The results of this study have significant implications for scholars, regulators, portfolio managers, and investors seeking to better understand and manage risk in the TRY-EUR FX market.

The Basel 2.5 capital regulatory framework and the COVID-19 crisis: evidence from the ethical investment market

PurposeThis research aims to evaluate the accuracy of several Value-at-Risk (VaR) approaches for determining the Minimum Capital Requirement (MCR) for Islamic stock markets during the pandemic health crisis.Design/methodology/approachThis research evaluates the performance of numerous VaR models for computing the MCR for market risk in compliance with the Basel II and Basel II.5 guidelines for ten Islamic indices. Five models were applied—namely the RiskMetrics, Generalized Autoregressive Conditional Heteroskedasticity, denoted (GARCH), fractional integrated GARCH, denoted (FIGARCH), and SPLINE-GARCH approaches—under three innovations (normal (N), Student (St) and skewed-Student (Sk-t) and the extreme value theory (EVT).FindingsThe main findings of this empirical study reveal that (1) extreme value theory performs better for most indices during the market crisis and (2) VaR models under a normal distribution provide quite poor performance than models with fat-tailed innovations in terms of risk estimation.Research limitations/implicationsSince the world is now undergoing the third wave of the COVID-19 pandemic, this study will not be able to assess performance of VaR models during the fourth wave of COVID-19.Practical implicationsThe results suggest that the Islamic Financial Services Board (IFSB) should enhance market discipline mechanisms, while central banks and national authorities should harmonize their regulatory frameworks in line with Basel/IFSB reform agenda.Originality/valuePrevious studies focused on evaluating market risk models using non-Islamic indexes. However, this research uses the Islamic indexes to analyze the VaR forecasting models. Besides, they tested the accuracy of VaR models based on traditional GARCH models, whereas the authors introduce the Spline GARCH developed by Engle and Rangel (2008). Finally, most studies have focus on the period of 2007–2008 financial crisis, while the authors investigate the issue of market risk quantification for several Islamic market equity during the sanitary crisis of COVID-19.

Review on Three New Value at Risk (VaR) Models

The emergence of financial derivatives complicates traditional financial products and increases financial market volatility. Individuals and financial institutions are both exposed to more complex and uncontrollable risks in this environment. Because of the risk's uncertainty, we must use reasonable methods to predict and estimate it in order to achieve the goal of risk control. This paper discusses three new VaR (Value at Risk) models that have emerged in recent years based on the ARCH family model using a method of literature review. The ARMA-EGARCH model, for example, combines the ARMA model to describe constant variance time series and the EGARCH model to describe heteroscedasticity phenomena, and theoretically can better describe the fluctuations of financial time series and obtain an independent time series with the same distribution. The sequence is processed using extreme value theory, which is the ARMA-EGARCH-GPPD model, in conjunction with the GPD model. We used the ARMA-EGARCH-semi-parametric method in conjunction with the historical simulation method and the parameter method to avoid cumbersome quantile calculation because the model algorithm is more complex. The generalized EWMA risk value prediction model has more advantages for financial data with large peaks.

Cryptocurrency Trading and Downside Risk

Since the debut of cryptocurrencies, particularly Bitcoin, in 2009, cryptocurrency trading has grown in popularity among investors. Relative to other conventional asset classes, cryptocurrencies exhibit high volatility and, consequently, downside risk. While the prospects of high returns are alluring for investors and speculators, the downside risks are important to consider and model. As a result, the profitability of crypto market operations depends on the predictability of price volatility. Predictive models that can successfully explain volatility help to reduce downside risk. In this paper, we investigate the value-at-risk (VaR) forecasts using a variety of volatility models, including conditional autoregressive VaR (CAViaR) and dynamic quantile range (DQR) models, as well as GARCH-type and generalized autoregressive score (GAS) models. We apply these models to five of some of the largest market capitalization cryptocurrencies (Bitcoin, Ethereum, Ripple, Litecoin, and Steller, respectively). The forecasts are evaluated using various backtesting and model confidence set (MCS) techniques. To create the best VaR forecast model, a weighted aggregative technique is used. The findings demonstrate that the quantile-based models using a weighted average method have the best ability to anticipate the negative risks of cryptocurrencies.

Do econometric advances lead to more accurate VaR estimations when the legislation requirements are applied? The case of Turkish Lira FX Market.

This paper empirically tests the benefits of econometric advances in the field of Value at Risk (VaR) within the existing legal framework that regulates the Banking (Basel III) and Asset Management industry (CESR (2010)). We test several VaR models, from the simplest and the most easily applied, i.e. the Historical VaR (HVaR), Variance Covariance VaR (VCVaR), and the Exponential Weighted Moving Average VaR (EWMAVaR), to advanced models such as GARCH(1,1). We test these models by examining the extremely volatile FX market of the Turkish Lira (TRY) and we evaluate the models according to the criteria set by the legal framework on VaR. The empirical findings suggest that the HVaR model is a very reliable model if the goal of a risk manager is to satisfy the legislation requirements. However, we should mention that models that make use advances in econometrics lead to more accurate and more representative VaR estimations than the HVaR. The law should give incentives to adopt more representative models in the financial industry in order to take advantage of advances in financial modeling.
 
 JEL Classification: C53; G15
 Keywords: Value-at-risk; GARCH estimation; Historical VaR; Variance Covariance; Exponential Weighted Moving Average VaR; Back-testing; Legislation; FX Market
 

Asset Portfolio Risk Management Study-Empirical Analysis Based on VaR Model

This research paper is based on an empirical analysis of portfolio risk management using the value-at-risk (VaR) model. First, the theoretical foundations of portfolio management are introduced, including portfolio theory, asset pricing models, risk management theory and methods, and VaR models. Then the research methodology is described, including data sources and processing, VaR model construction, and risk metric calculation and interpretation. The empirical results section shows the risk analysis and source identification of asset portfolios, the estimation of VaR model parameters and confidence intervals, and the results of VaR calculations and risk measures at different confidence levels. Finally, the results are discussed and analyzed, including the interpretation and comparison of the risk measure results and the advantages and disadvantages of the VaR model. The paper also provides practical risk management recommendations and decision support for investors based on the results of the study. Limitations of the study and future research directions are also discussed. Overall, insights into portfolio risk management using VaR models are provided and a useful reference for researchers and investors interested in this area.

THE APPLICATION OF GUMBEL COPULA TO ESTIMATE VALUE AT RISK WITH BACKTESTING IN TELECOMMUNICATION STOCK

The Value at Risk (VaR) method refers to a statistical risk measurement tool used to determine the maximum loss of an investment, while the distribution that must be met is the normal distribution. This is not in line with the actual situation, because the distribution of the return value is found to be not normally distributed but depends on market conditions that occurred at that time, thus invalidating the VaR estimate and resulting in greater portfolio risk. Therefore, in this study, the estimation of risk value will be carried out using the Gumbel Copula method which can model the dependency structure between stocks and is flexible enough to model financial return data from https://finance.yahoo.com/. The parameter estimates produced by the Gumbel Copula method are then used to calculate the VaR at 90%, and 99% confidence levels. The resulting VaR values ​​are 0,076 and 0.231. To test the feasibility of the VaR model, backtesting was carried out and concluded that the VaR value obtained was valid and suitable for use in the risk assessment of PT. XL Axiata Tbk and PT. Telkomunikasi Indonesia Tbk.

Value-at-risk models: a systematic review of the literature

This paper presents a systematic review of the literature (SRL) on value-at-risk (VaR). More specifically, we review the models that have been applied to estimate VaR, with the following two aims: to find the most used models in the literature and to verify whether their popularity has changed since the 2007–9 financial crisis. The SRL is based on Scopus for the period from 1996 to 2017. Our results show that (generalized) autoregressive conditional heteroscedasticity models and extreme value theory, together with Monte Carlo simulation, historical simulation and variance–covariance, were the most used models. Since the crisis, the autoregressive conditional heteroscedasticity (ARCH) and generalized autoregressive conditional heteroscedasticity (GARCH) models have clearly been the most popular, while no significant difference has been found in the percentage of articles on the other models. This study can be considered the first SRL on VaR models because (to the best of our knowledge) no previous work of a similar nature has been carried out on this topic. This study provides a rich background for researchers and professionals interested in the topic, contributing detailed information about the papers published, classifying them by, for example, the model used, author(s), citation count, journals and year published.

A comparison of market risk measures from a twofold perspective: accurate and loss function

Under the new regulation based on Basel solvency framework, known as Basel III and Basel IV, financial institutions must calculate the market risk capital requirements based on the Expected Shortfall (ES) measure, replacing the Value at Risk (VaR) measure. In the financial literature, there are many papers dedicated to compare VaR approaches but there are few studies focusing in comparing ES approaches. To cover this gap, we have carried out a comprenhensive comparative of VaR and ES models applied to IBEX-35 stock index. The comparison has been carried out from a twofold perspective: accurate risk measure and loss functions. The results indicate that the method based on the conditional Extreme Value Theory (EVT) is the best in estimating market risk, outperforming Parametric method and Filter Historical Simulation.

Value-at-risk and the global financial crisis

Using daily data for seven large international banks, we examine the forecasting ability of bank value-at-risk (VaR) estimates around the 2007–9 global financial crisis (GFC) period. We find that the banks’ internal VaR estimates are very inaccurate. They systematically overstated VaR during the pre- and postcrisis periods, with mixed performance during the GFC. Some banks inflated their VaRs, while others experienced excessive VaR exceptions and clustering. VaR estimates based on simple models of generalized autoregressive conditional heteroscedasticity (GARCH) type easily outperform internal VaR estimates. The VaR estimated via a GARCH-t distribution captures the extreme losses reasonably well. We attribute the poor VaR estimates at banks to the banks’ inappropriate choice of internal VaR models.

A Bayesian approach for more reliable tail risk forecasts

This paper demonstrates that existing quantile regression models used for jointly forecasting Value-at-Risk (VaR) and expected shortfall (ES) are sensitive to initial conditions. Given the importance of these measures in financial systems, this sensitivity is a critical issue. A new Bayesian quantile regression approach is proposed for estimating joint VaR and ES models. By treating the initial values as unknown parameters, sensitivity issues can be dealt with. Furthermore, new additive-type models are developed for the ES component that are more robust to initial conditions. A novel approach using the open-faced sandwich (OFS) method is proposed which improves uncertainty quantification in risk forecasts. Simulation and empirical results highlight the improvements in risk forecasts ensuing from the proposed methods.

BACK-TESTING APPROACHES FOR VALIDATING VAR MODELS

Value at risk (VaR) is one of the important market risk measures. It measures the possible potential loss on given investment in terms of value, with certain probability for certain time horizon. In this paper, our aim is to discuss different back-testing approaches to validate VaR models, and also test it the real market data. We back tested VaR of Nifty 50 index obtained by Variance Co-variance method, Historical simulation method, Monte-Carlo simulation, and cubic polynomial regression method. We have used Total exceptions by binary back-testing over entire population. we have also used Basel Traffic Light Zone Test, Kupiec POF-test, Kupiec TUFF-test, and Haas’ Mixed-Kupiec test and analyzed the above methods.