Value-at-Risk Forecasts Research Articles

Support vector regression-based heteroscedastic models for cryptocurrency risk forecasting

In this study, we aimed to combine support vector regression (SVR) with an autoregressive (AR) model and a generalized autoregressive conditional heteroscedastic (GARCH) or asymmetric GARCH model. We compared the performances of these combined models with the maximum likelihood estimation (MLE)-based models under a normal, Student’s t, or skewed Student’s t distributional assumption. We employed such models to protect the heteroscedastic risks of four major cryptocurrencies, namely, Bitcoin, Ethereum, Tether, and Binance Coin, before and during COVID-19. We accomplished this task by forecasting their volatility, Value-at-Risk (VaR), and Expected Shortfall (ES). The empirical results revealed that in terms of the root-mean-square error (RMSE) and mean-absolute error (MAE) metrics, the SVR-based models with a polynomial or radial basis kernel function, which is nonlinear, resulted in a more accurate volatility forecast compared to the MLE-based models under any distributional assumption. The superiority of the former models was more apparent when applied to Tether exhibiting the most stable volatility. This supports evidence of nonlinear characteristics in the cryptocurrency return and volatility series. A combination between SVR and an asymmetric GARCH model also confirms the presence of an asymmetrically nonlinear relationship between the returns and volatility. In addition, the correct-VaR and Kupiec’s backtesting results showed that the SVR-based models tended to produce the VaR forecasts for the four cryptocurrencies with better accuracy at the 1%, 5%, and 10% significance levels compared to the MLE-based ones. The use of the correct-ES metric also leads to the superior ES forecasting performance of the former models at any level. However, McNeil and Frey’s backtesting results demonstrated their worse ES forecasting performance at the 1% level. As the COVID-19 pandemic progressed, we also found an increase in the Bitcoin and Binance Coin market risks as well as a decrease in the Ethereum and Tether market risks.

Forecasting volatility of stock indices: Improved GARCH-type models through combined weighted volatility measure and weighted volatility indicators

This paper proposes an unbiased combined weighted (CW) volatility measure and weighted volatility indicators (WVI) that integrates the return- and range-based volatility measures to model the dynamics volatility of stock returns. The main feature of the CW measure is that it is formulated based on the weighted inter- and intra-price information to quantify the volatility directly, while the WVI effectively identifies signals on the shift of volatility. Empirical analysis using five stock indices demonstrates that the CW measure, utilising squared returns in combination with range-based Garman-Klass volatility measure, exhibits the lowest losses based on root mean squared error and quasi-likelihood when compared to 5-minute realised volatility as a proxy for true volatility. Furthermore, we investigate the feasibility of incorporating the CW measure and WVI as the exogenous variable(s) in the generalised autoregressive conditional heteroscedasticity (GARCH)-type models to enhance the forecasting performance. The findings indicate that the GARCH-CW-WVI and EGARCH-CW-WVI models exhibit superior in-sample model fit based on the Akaike information criterion than the existing GARCH and EGARCH models. Moreover, our proposed models also offer the best out-of-sample forecasts evaluated using various loss functions and further tested using Hansen’s model confidence set based on the mean squared error loss. Different risk levels of value-at-risk (VaR) and expected shortfall (ES) forecasts based on GARCH-CW-WVI and EGARCH-CW-WVI models are computed and examined with various backtests to confirm the accuracies of VaR and ES forecasts.

VaR and ES forecasting via recurrent neural network-based stateful models

Due to the widespread and quickly escalating effects of large negative returns, as well as due to the increase in the importance of regulatory framework for financial institutions, the accurate measurement of financial risks has become a relevant question in the academia and industry. This paper proposes three novel models based on stateful Recurrent Neural Networks (RNN) and Feed-Forward Neural Networks (FNN) to build forecasts for Value-at-Risk (VaR) and Expected Shortfall (ES). We apply the models to six asset return time series spanning over more than 20 years. Our results reveal that the RNN-based stateful models generally outperform the non-stateful RNN models and econometric benchmark models including rolling window models, Generalized AutoRegressive Conditional Heteroskedasticity (GARCH)-type models, and Generalized Autoregressive Score (GAS) models, in terms of VaR and ES forecasting.

Forecasting VaRs via hybrid EVT with normal and non-normal filters: A comparative analysis from the Chinese stock market

This paper studies the performance of hybrid methods combining normal and non-normal GARCH-type filters with extreme value theory (EVT) in predicting Value-at-Risk (VaR) for four major stock indices in the Chinese stock market. Based on the out-of-sample VaR forecasts results over the 24 models considered, we find that the hybrid EVT approaches illustrate substantial advantage over the corresponding GARCH-type models with parametric distributions, especially in the lower tail and extremal VaR evaluations (1% and 0.5% VaRs). Overall, the hybrid EVT methods with heavy-tailed filters (std-EVT, sstd-EVT) perform the best, followed by the hybrid EVT approaches with light-tailed filters (norm-EVT, snorm-EVT), and then the GARCH-type models with skewed student-t distribution. The conditional normal, skewed normal and student-t models are rejected and excluded from the Model Confidence Set (MCS) in predicting extremal VaRs for most cases, particularly for the lower tail. Additionally, we find that the results for alternative models in predicting VaRs vary sharply among alternative innovation specifications, but present trivial differences across the volatility models. Furthermore, our results based on the MCS tests and comparative backtests also indicate that the scoring function effectively discriminates predictive performance across methods for the lower tail, in contrast to showing less disparity for the upper tail. This emphasizes the importance of model selection in VaR forecasting performance for the lower tail. The above findings are robust to alternative threshold selections and the rolling-step chosen to update parameters. Similar analyses concerning the out-of-sample performance of the 24 models in predicting the Expected Shortfall (ES) show consistent results overall.

Forecasting value-at-risk and expected shortfall in emerging market: does forecast combination help?

PurposeThis paper investigates how various strategies for combining forecasts, both simple and optimised approaches, are compared with popular individual risk models in estimating value-at-risk (VaR) and expected shortfall (ES) in emerging market at alternative risk levels.Design/methodology/approachUsing the case study of the Vietnamese stock market, the author produced one-day-ahead VaR and ES forecast from seven individual risk models and ten alternative forecast combinations. Next, the author employed a battery of backtesting procedures and alternative loss functions to evaluate the global predictive accuracy of the different methods. Finally, the author investigated the relative performance over time of VaR and ES forecasts using fluctuation test.FindingsThe empirical results indicate that, although combined forecasts have reasonable predictive abilities, they are often outperformed by one individual risk model. Furthermore, the author showed that the complex combining methods with optimised weighting functions do not perform better than simple combining methods. The fluctuation test suggests that the poor performance of combined forecasts is mainly due to their inability to cope with periods of instability.Research limitations/implicationsThis study reveals the limitation of combining strategies in the one-day-ahead VaR and ES forecasts in emerging markets. A possible direction for further research is to investigate whether this finding holds for multi-day ahead forecasts. Moreover, the inferior performance of combined forecasts during periods of instability motivates further research on the combining strategies that take into account for potential structure breaks in the performance of individual risk models. A potential approach is to improve the individual risk models with macroeconomic variables using a mixed-data sampling approach.Originality/valueFirst, the authors contribute to the literature on the forecasting combinations for VaR and ES measures. Second, the author explored a wide range of alternative risk models to forecast both VaR and ES with recent data including periods of the COVID-19 pandemic. Although forecast combination strategies have been providing several good results in several fields, the literature of forecast combination in the VaR and ES context is surprisingly limited, especially for emerging market returns. To the best of the author’s knowledge, this is the first study investigating predictive power of combining methods for VaR and ES in an emerging market.

High-frequency enhanced VaR: A robust univariate realized volatility model for diverse portfolios and market conditions.

In the field of financial risk management, the accuracy of portfolio Value-at-Risk (VaR) forecasts is of critical importance to both practitioners and academics. This study pioneers a comprehensive evaluation of a univariate model that leverages high-frequency intraday data to improve portfolio VaR forecasts, providing a novel contrast to both univariate and multivariate models based on daily data. Existing research has used such high-frequency-based univariate models for index portfolios, it has not adequately studied their robustness for portfolios with diverse risk profiles, particularly under changing market conditions, such as during crises. Our research fills this gap by proposing a refined univariate long-memory realized volatility model that incorporates realized variance and covariance metrics, eliminating the necessity for a parametric covariance matrix. This model captures the long-run dependencies inherent in the volatility process and provides a flexible alternative that can be paired with appropriate return innovation distributions for VaR estimation. Empirical analyses show that our methodology significantly outperforms traditional univariate and multivariate Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) models in terms of forecasting accuracy while maintaining computational simplicity and ease of implementation. In particular, the inclusion of high-frequency data in univariate volatility models not only improves forecasting accuracy but also streamlines the complexity of portfolio risk assessment. This research extends the discourse between academic research and financial practice, highlighting the transformative impact of high-frequency data on risk management strategies within the financial sector.

Improving Value-at-Risk forecast using GA-ARMA-GARCH and AI-KDE models

The classical autoregressive moving average (ARMA) and generalized autoregressive conditional heteroskedastic (GARCH) models have been widely adopted to forecast Value-at-Risk (VaR), the most popular risk measure in quantitative risk management. Their parameters are commonly estimated using the maximum likelihood estimation (MLE) method, which may show biasedness. This reason motivated us to require optimization through a genetic algorithm (GA) or implement artificial intelligence (AI) to improve the VaR forecast. In this paper, we aimed to compare the performances of the GA-based ARMA-GARCH model and the AI models (linear regression, support vector regression, multilayer perceptron, and long short-term memory) in forecasting the VaR. More specifically, we examined which model performs best. Using Bitcoin, crude oil, and stock index returns, we showed that the GA-ARMA-GARCH and AI models outperformed the benchmark MLE-ARMA-GARCH model. We also revealed that the AI models (particularly multilayer perceptron) integrated with kernel density estimation (KDE) performed relatively better than the GA-ARMA-GARCH model because the former resulted in a higher p-value of the VaR backtesting with a smaller error value. In addition, the cross combination between our models was found to have a higher potential to produce an improvement in the VaR forecast.

An Empirical Investigation of Value at Risk (VaR) Forecasting Based on Range-Based Conditional Volatility Models

Value at Risk (VaR) is a widely used measure of market risk. Precision in the estimation of volatility leads to accurate VaR forecasts. As volatility is time-varying and has a clustering effect, GARCH class of volatility models is helpful in modeling volatility more precisely. Studies have also shown that range-based volatility estimates are more efficient than traditional models that use only closing prices. Therefore, this study uses the GARCH family of volatility models to model and forecast VaR. The study compares conventional models that use closing prices alone, like GARCH and TARCH, with range-based models like RGARCH and RTARCH models, where the range defined as daily high price minus low price is introduced as an exogenous variable, to explore if the latter provides better predictive accuracy. All the models are back-tested using the Kupiec (1995) unconditional coverage and Christoffersen (1998) conditional coverage tests. The data period in the study ranges from 2003-2021, and we consider five BRICS indices and three major developed economies, namely, the USA, the UK, and Germany. An empirical investigation shows that range-based models do a better job in VaR forecasting as it has more information content than daily closing prices, thereby giving more accurate VaR estimates. The study hopes this finding will greatly help stakeholders like financial institutions, regulators, and practitioners in more effective market risk management.

A method for predicting VaR by aggregating generalized distributions driven by the dynamic conditional score

Constructing a more effective value at risk (VaR) prediction model has long been a goal in financial risk management. In this paper, we propose a novel parametric approach and provide a standard paradigm to demonstrate the modeling. We establish a dynamic conditional score (DCS) model based on high-frequency data and a generalized distribution (GD), namely, the GD-DCS model, to improve the forecasts of daily VaR. The model assumes that intraday returns at different moments are independent of each other and obey the same kind of GD, whose dynamic parameters are driven by DCS. By predicting the motion law of the time-varying parameters, the conditional distribution of intraday returns is determined; then, the bootstrap method is used to simulate daily returns. An empirical analysis using data from the Chinese stock market shows that Weibull-Pareto -DCS model incorporating high-frequency data is superior to traditional benchmark models, such as RGARCH, in the prediction of VaR at high risk levels, which proves that this approach contributes to the improvement of risk measurement tools.

Assessing the accuracy of exponentially weighted moving average models for Value-at-Risk and Expected Shortfall of crypto portfolios

A plethora of academic papers on generalized autoregressive conditional heteroscedasticity (GARCH) models for bitcoin and other cryptocurrencies have been published in academic journals. Yet few, if indeed any, of these are employed by practitioners. Previous academic studies produce results that are fragmented, confusing and conflicting, so there is no commercial incentive to drive an expensive implementation of complex multivariate GARCH models, which anyway would commonly require more data for calibration than are available in the history of most cryptocurrencies, at least at the daily frequency. Consequently, this paper assesses the forecasting accuracy of simple parametric RiskMetrics type volatility and covariance models, with a focus on ad hoc parameter choice instead of a data-intensive calibration procedure. We provide extensive backtests of hourly and daily Value-at-Risk (VaR) and Expected Shortfall (ES) forecasts that are regarded as best practice in the industry and commonly used for regulatory approval. Our results demonstrate that much simpler models in the exponentially weighted moving average (EWMA) class are just as accurate as GARCH models for VaR and ES forecasting, provided they capture an asymmetric volatility response and a heavy-tailed returns distribution. Moreover, on ranking each model's variance and covariance forecasts using average scores generated from proper univariate and multivariate scoring rules, there is no evidence of superior performance of variance and covariance forecasts generated by GARCH models, using either daily or hourly data.

Predicting Returns, Volatilities and Correlations of Stock Indices Using Multivariate Conditional Autoregressive Range and Return Models

This paper extends the conditional autoregressive range (CARR) model to the multivariate CARR (MCARR) model and further to the two-stage MCARR-return model to model and forecast volatilities, correlations and returns of multiple financial assets. The first stage model fits the scaled realised Parkinson volatility measures using individual series and their pairwise sums of indices to the MCARR model to obtain the fitted volatilities. Then covariances are calculated to construct the fitted variance–covariance matrix of returns which are imputed into the stage-two return model to capture the heteroskedasticity of assets’ returns. We investigate different choices of mean functions to describe the volatility dynamics. Empirical applications are based on the Standard and Poor 500, Dow Jones Industrial Average and Dow Jones United States Financial Service Indices. Results show that the stage-one MCARR models using asymmetric mean functions give better in-sample model fits than those based on symmetric mean functions. They also provide better out-of-sample volatility forecasts than those using CARR models based on two robust loss functions. We also find that the stage-two return models with constant means and multivariate Student-t errors give better in-sample fits than the Baba–Engle–Kraft–Kroner generalised autoregressive conditional heteroskedasticity models. The estimates and forecasts of value-at-risk (VaR) and conditional VaR based on the best MCARR-return models for each asset are provided and tested using backtests to confirm the accuracy of the VaR forecasts.

Is Tether a safe haven of safe haven amid COVID-19? An assessment against Bitcoin and oil using improved measures of risk

Bitcoin is a new speculative investment with extremely volatile movement, thus possibly failing to act as a safe haven for crude oil when the price of this energy commodity plummeted following the global outbreak of COVID-19. Meanwhile, Tether is designed to behave similarly to the US dollar with stable fluctuation. In this study, we assessed their safe-haven properties in terms of risk reduction opportunities by proposing an improved version of Value-at-Risk (VaR) and Expected Shortfall (ES). Using vine copula-based AR-GJR-GARCH models, we demonstrated that Bitcoin exhibited inconsistent risk reduction capability for oil, particularly before COVID-19. When adding Tether into a portfolio containing oil and Bitcoin, the risk reduction was achieved for any portfolio allocation and was more pronounced amid the COVID-19 period. This suggests that Tether consistently served strong support for Bitcoin to protect oil investors against extreme risk and received a significant impact from the COVID-19 outbreak. However, the consistent safe-haven functionality of Tether was not as good as that of the US dollar in most cases, and this implied the vanishing of its stability. These results were robust when considering another asymmetric volatility model and another dependence model. Furthermore, the proposed improved VaR and ES forecasts outperformed their corresponding unimproved version in quantifying portfolio risk and therefore provided a more accurate assessment of safe-haven roles.

Comparison of Value at Risk (VaR) Multivariate Forecast Models.

We investigate the performance of VaR (Value at Risk) forecasts, considering different multivariate models: HS (Historical Simulation), DCC-GARCH (Dynamic Conditional Correlation-Generalized Autoregressive Conditional Heteroskedasticity) with normal and Student's t distribution, GO-GARCH (Generalized Orthogonal-Generalized Autoregressive Conditional Heteroskedasticity), and copulas Vine (C-Vine, D-Vine, and R-Vine). For copula models, we consider that marginal distribution follow normal, Student's t and skewed Student's t distribution. We assessed the performance of the models using stocks belonging to the Ibovespa index during the period from January 2012 to April 2022. We build portfolios with 6 and 12 stocks considering two strategies to form the portfolio weights. We use a rolling estimation window of 500 and 1000 observations and 1%, 2.5%, and 5% as significance levels for the risk estimation. To evaluate the quality of the risk forecasts, we compute the realized loss and cost. Our results show that the performance of the models is sensitive to the use of different significance levels, rolling windows, and strategies to determine portfolio weights. Furthermore, we find that the model that presents the best trade-off between the costs from risk overestimation and underestimation does not coincide with the model suggested by the realized loss.

A high-frequency approach to VaR measures and forecasts based on the HAR-QREG model with jumps

The occurrence of extreme events has brought tremendous impact to stock markets, and the accuracy of measuring and forecasting value at risk (VaR) has important theoretical and practical value for the risk management of stock markets. This paper proposes a heterogeneous auto-regression quantile regression (HAR-QREG) model based on 5-min high frequency data and incorporating positive and negative jumps to explore the heterogeneity of different volatility components on returns under different market states and to make sliding forecasting of VaR. The results show that: (1) in the conditional quantile tail of returns, short-term daily and medium-term weekly volatility have a greater impact on returns than long-term monthly volatility in the Chinese stock market. (2) Volatility of different maturities has a significantly greater impact on returns in bear markets than in oscillating and bull markets. (3) There is heterogeneity in the impact of jump volatility on returns across different market states, with a greater impact in bear and bull markets, but the degree of impact decreases as the duration lengthens. Furthermore, the model has better results for out-of-sample VaR forecasting.

Oil tail-risk forecasts: from financial crisis to COVID-19

The coronavirus outbreak has caused unprecedented volatility in oil prices. This paper extends previous studies on oil Value-at-Risk (VaR) by providing extra insights into Expected Shortfall (ES) forecasting over the last decade, including several oil crises. We introduce a conditional volatility model combined with the Cornish–Fisher expansion for ES forecasting. In comparison to the widely used volatility models and innovation distributions, this approach is superior for predicting the ES of long positions but overestimates VaR for short positions. Overall, the volatility model addressing leverage effects with skewed t innovation produces the most accurate joint VaR and ES forecasting. Moreover, the magnitude of ES relative to VaR varies across models and time, implying that ES should be used in conjunction with VaR to inform timely risk management decisions. The results would be of interest to the regulatory authorities, energy companies, and financial institutions for oil tail-risk forecasting.

Value-at-Risk forecasting: A hybrid ensemble learning GARCH-LSTM based approach

This study proposes a new hybrid model that combines LSTM and BiLSTM neural networks with GARCH type model forecasts using an ensemble approach to forecast volatility for one-day ahead 95% and 99% Value-at-Risk (VaR) estimates using the Parametric (PAR) and Filtered Historical Simulation (FHS) method. The forecasting abilities of the standard GARCH (GARCH), exponential GARCH (eGARCH), and threshold GARCH (tGARCH) models are combined with the LSTM networks to capture different characteristics of the underlying volatility. We evaluate the model using log returns on Crude Oil during two periods of extreme volatility: the 2007-09 Financial Crisis and the Covid Recession of 2020–21. The performance of hybrid models is compared against several traditional VaR methods like the Historical Simulation, Bootstrap, Age weighted method, and the volatility-based VaR models using the GARCH, LSTM, and BiLSTM model forecasts. The unconditional and conditional coverage tests and a combination of regulator and firm loss functions are used to evaluate the quality of VaR forecasts. We find a significant improvement in the quality and accuracy of the VaR forecasts of the hybrid models over all the other models across all loss functions and coverage tests. The FHS-BiLSTM-HYBRID, a proposed FHS-based hybrid model, combining the BiLSTM model with three GARCH-type models, is the best performing, with the lowest values for both loss functions. The traditional and GARCH-type models do not efficiently model volatility during the crisis periods resulting in poor VaR forecasts. The FHS consistently performs as the best method for generating VaR compared to all other approaches.

Switching latent factor value-at-risk models for conditionally heteroskedastic portfolios: A comparative approach

In this paper, a computationally efficient Monte Carlo-based latent factor modeling approach for portfolio Value-at-Risk (VaR) estimation is introduced. We examine whether the inclusion of conditional heteroskedasticity in financial returns, and taking into account for possible hidden (Markovian) “regime changes” in the latent correlation structure of the portfolio can enhance the accuracy of VaR forecasts. Practical details of training such models with the expectation-maximization algorithm are also discussed. In conjunction with an approximated version of the Kalman filter, we show how to calculate maximum likelihood estimates of the model parameters, and to yield inferences about the unobservable path of the common factors, their volatilities and the hidden state sequence of the Markov process. The methodology is illustrated by an example using data from the Tunisian foreign exchange market, over the period of the Tunisian revolution from January 02, 2010 to December 30, 2012. We found that this new specification exhibits a good fit to the data, improves the accuracy of VaR predictions of the Tunisian foreign public debt portfolio and reduces the number and average size of back-testing breaches when a financial crisis occurs.

Does the tail risk index matter in forecasting downside risk?

AbstractThis study employs an augmented realized GARCH (RGARCH) model to examine whether two well‐known tail risk measures, namely the SKEW and VVIX indices, can improve the daily value‐at‐risk (VaR) forecasting accuracy for S&P500 index returns. We find that the RGARCH‐VVIX model exhibits better predictive accuracy than the RGARCH and RGARCH‐SKEW models. The VVIX index provides economically valuable information in forecasting VaR. Given its ability to improve both accuracy and efficiency for VaR forecasts, the RGARCH‐VVIX model is helpful for a risk manager to determine capital requirement and for investors to assess the downside risk of their investments.

Do realized higher moments have information content? - VaR forecasting based on the realized GARCH-RSRK model

In this paper, we develop a new model, the Realized GARCH-RSRK, to determine the time-varying distribution of financial returns with realized higher moments. Based on Gram-Charlier expansion (GCE) density, we first explicitly link the expansion parameters with moments that are calculated based on intraday returns using our new model. Then, the Cornish-Fisher expansion is applied to forecast Value-at-Risk (VaR) with estimated moments to demonstrate the economic significance of this new model. Compared with the daily-return-based dynamic higher moments models, the inclusion of realized higher moments significantly improves this model's ability to forecast extreme tails. The empirical results indicate that this new model outperforms the benchmark models when forecasting extreme VaR. In addition, we provide a formula to correct the moments associated with the commonly used squared transformation of GCE. Our empirical evidence highlights the importance of using corrected moments in VaR forecasting.

Encompassing Tests for Value at Risk and Expected Shortfall Multistep Forecasts Based on Inference on the Boundary

AbstractWe propose forecast encompassing tests for the expected shortfall (ES) jointly with the value at risk (VaR) based on flexible link (or combination) functions. Our setup allows testing encompassing for convex forecast combinations and for link functions that preclude crossings of the combined VaR and ES forecasts. As the tests based on these link functions involve parameters that are on the boundary of the parameter space under the null hypothesis, we derive and base our tests on nonstandard asymptotic theory on the boundary. Our simulation study shows that the encompassing tests based on our new link functions outperform tests based on unrestricted linear link functions for one-step and multistep forecasts. We further illustrate the potential of the proposed tests in a real data analysis for forecasting VaR and ES of the S&P 500 index.