Value-at-Risk Models Research Articles

On the factors of Bitcoin\u2019s value at risk

This study investigates the factors of Bitcoin’s tail risk, quantified by Value at Risk (VaR). Extending the conditional autoregressive VaR model proposed by Engle and Manganelli (2004), I examine 30 potential drivers of Bitcoin’s 5% and 1% VaR. For the 5% VaR, quantity variables, such as Bitcoin trading volume and monetary policy rate, were positively significant, but these effects were attenuated when new samples were added. The 5% VaR responds positively to the Internet search index and negatively to the fluctuation of returns on commodity variables and the Chinese stock market index. For the 1% VaR, variables related to the macroeconomy play a key role. The consumer sentiment index exerts a strong positive effect on the 1% VaR. I also find that the 1% VaR has positive relationships with the US economic policy uncertainty index and the fluctuation of returns on the corporate bond index.

Value at Risk estimation using GAS models with heavy tailed distributions for cryptocurrencies

Risk management and prediction of market losses of cryptocurrencies are of notable value to risk managers, portfolio managers, financial market researchers and academics. One of the most common measures of an asset’s risk is Value-at-Risk (VaR). This paper evaluates and compares the performance of generalized autoregressive score (GAS) combined with heavy-tailed distributions, in estimating the VaR of two well-known cryptocurrencies’ returns, namely Bitcoin returns and Ethereum returns. In this paper, we proposed a VaR model for Bitcoin and Ethereum returns, namely the GAS model combined with the generalized lambda distribution (GLD), referred to as the GAS-GLD model. The relative performance of the GAS-GLD models was compared to the models proposed by Troster et al. (2018), in other words, GAS models combined with asymmetric Laplace distribution (ALD), the asymmetric Student’s t-distribution (AST) and the skew Student’s t-distribution (SSTD). The Kupiec likelihood ratio test was used to assess the adequacy of the proposed models. The principal findings suggest that the GAS models with heavy-tailed innovation distributions are, in fact, appropriate for modelling cryptocurrency returns, with the GAS-GLD being the most adequate for the Bitcoin returns at various VaR levels, and both GAS-SSTD, GAS-ALD and GAS-GLD models being the most appropriate for the Ethereum returns at the VaR levels used in this study.

On the Elicitability and Risk Model Comparison of Emerging Markets Equities

The need for comparative backtesting in the Basel III framework presents the challenge for ranking of internal value-at-risk (VaR) and expected shortfall (ES) models. We use a joint loss function to score the elicitable joint VaR and ES models to select competing tail risk models for the top 9 emerging markets equities and the emerging markets composite index. We achieve this with the model confidence set (MCS) procedure. Our analysis span two sub-sample periods representing turbulent (Eurozone and Global Financial crises periods) and tranquil (post-Global Financial crisis period) market conditions. We find that many of the markets risk models are time-invariant and independent of market conditions. But for China and South Africa this is not true because their risk models are time-varying, market conditions-dependent, percentile-dependent and heterogeneous. Tail risk modelling may be difficult compared to other markets. The resemblance between China and South Africa can stem from the closeness between their equities composition. However, generally, there is evidence of more homogeneity than heterogeneity in risk models. This is indicated by a minimum of three models (out of six) per equity in most of the countries. This may ease the burden for risk managers to find the optimal set of models. Our study is important for internal risk modelling, regulatory oversight, reduce regulatory arbitrage and may bolster confidence in international investors with respect to emerging markets equities.

VALUE AT RISK WITH STOCHASTIC VOLATILITY PERTURBED BY HURST PARAMETER

The commonly adopted value at risk (VaR) model assumes the distribution of portfolio values that are normally distributed with stationary and independent increment, which restricts its usage for cases of arbitrary distributions. In this study, the current assumption is improved by constructing theoretical development of VaR model based on fractional Brownian motion, with Hurst parameter, H, as its underlying distribution. Empirical investigation is conducted to compare the standard model with the proposed model. The findings indicated that higher value of H provided higher value in VaR, thus suggesting greater probability to lose.

Nonparametric expected shortfall forecasting incorporating weighted quantiles

A new semi-parametric expected shortfall (ES) estimation and forecasting framework is proposed. The proposed approach is based on a two-step estimation procedure. The first step involves the estimation of value at risk (VaR) at different quantile levels through a set of quantile time series regressions. Then, the ES is computed as a weighted average of the estimated quantiles. The quantile weighting structure is parsimoniously parameterized by means of a beta weight function whose coefficients are optimized by minimizing a joint VaR and ES loss function of the Fissler–Ziegel class. The properties of the proposed approach are first evaluated with an extensive simulation study using two data generating processes. Two forecasting studies with different out-of-sample sizes are then conducted, one of which focuses on the 2008 Global Financial Crisis period. The proposed models are applied to seven stock market indices, and their forecasting performances are compared to those of a range of parametric, non-parametric, and semi-parametric models, including GARCH, conditional autoregressive expectile (CARE), joint VaR and ES quantile regression models, and a simple average of quantiles. The results of the forecasting experiments provide clear evidence in support of the proposed models.

Inaccurate Value at Risk Estimations: Bad Modeling or Inappropriate Data?

Forecasting accurate Value-at-Risk (VaR) estimations is a crucial task in applied financial risk management. Even though there have been significant advances in the field of financial econometrics, many crises have been documented throughout the world in the last decades. An explanation for this discrepancy is that many contemporary models are too complex and cannot be easily understood and implemented in the financial industry (Fama in Financ Anal J 51:75–80, 1995; Ross in AIMR conference proceedings, vol. 1993, no. 6, pp. 11–15, Association for Investment Management and Research, 1993). In order to bridge this theory–practice gap, we present a computational method based on the leverage effect. This method allows us to focus on financial theory and remove complexity. Examining the US stock market (2000–2020), we provide empirical evidence that our newly suggested approach, which uses only the most appropriate observation period, significantly increases the accuracy of the Conventional Delta Normal VaR model and generates VaR estimations which are as accurate as those of advanced econometric models, such as GARCH(1,1).

Portfolio Value-at-Risk and expected-shortfall using an efficient simulation approach based on Gaussian Mixture Model

Monte Carlo Approaches for calculating Value-at-Risk (VaR) are powerful tools widely used by financial risk managers across the globe. However, they are time consuming and sometimes inaccurate. In this paper, a fast and accurate Monte Carlo algorithm for calculating VaR and ES based on Gaussian Mixture Models is introduced. Gaussian Mixture Models are able to cluster input data with respect to market’s conditions and therefore no correlation matrices are needed for risk computation. Sampling from each cluster with respect to their weights and then calculating the volatility-adjusted stock returns leads to possible scenarios for prices of assets. Our results on a sample of US stocks show that the Gmm-based VaR model is computationally efficient and accurate. From a managerial perspective, our model can efficiently mimic the turbulent behavior of the market. As a result, our VaR measures before, during and after crisis periods realistically reflect the highly non-normal behavior and non-linear correlation structure of the market.

Optimize your Investment Portfolio in Bearish Markets

Since the 2008-2009 global financial crisis, VaR (Value-at-Risk) techniques have become critical tools for monitoring and predicting the market risk and liquidity of financial assets. These financial risk modeling techniques, which have been recognized by the Bank for International Settlements (BIS) or the Basel Committee on capital adequacy and bank regulations, measure and prevent any potential losses that arise, not only from securities’ price changes and the interdependence between the different types of assets (stocks, currencies, interest rates or commodities), but also from their negative tail co-movements in bearish market conditions. In the event of a financial crisis or market downturn, adequate liquidity risk modeling is advisable. In fact, the main advantage of VaR models is their focus on downside risk (i.e., the impact of the results of negative tails) and their direct interpretation in monetary terms. Nevertheless, particularly in times of financial turbulence, traditional VaR models do not properly consider nonlinear dependence between portfolio assets and become inefficient in illiquid market scenarios. Despite the advances in measurement models, obtaining precise market liquidity risk estimations and applying them to optimize portfolios continues to be a challenge for financial institutions.

Investment Modelling Using Value at Risk Bayesian Mixture Modelling Approach and Backtesting to Assess Stock Risk

Background: Stock investment has been gaining momentum in the past years due to the development of technology. During the pandemic lockdown, people have invested more. One the one hand, stock investment has high potential profitability, but on the other, it is equally risky. Therefore, a value at risk (VaR) analysis is needed. One approach to calculate VaR is by using the Bayesian mixture model, which has been proven to be able to overcome heavy-tailed cases. Then, the VaR’s accuracy needs to be tested, and one of the ways is by using backtesting, such as the Kupiec test.Objective: This study aims to determine the VaR model of PT NFC Indonesia Tbk (NFCX) return data using Bayesian mixture modelling and backtesting. On a practical level, this study can provide information about the potential risks of investing that is grounded in empirical evidence.Methods: The data used was NFCX data retrieved from Yahoo Finance, which was then modelled with a mixture model based on the normal and Laplace distributions. After that, the VaR accuracy was calculated and then tested by using backtesting.Results: The test results showed that the VaR with the mixture Laplace autoregressive (MLAR) approach (2;[2],[4]) was accurate at 5% and 1% quantiles while mixture normal autoregressive MNAR (2;[2],[2,4]) was only accurate at 5% quantiles.Conclusion: The better performing NFCX VaR model for this study based on backtesting using Kupiec test is MLAR(2;[2],[4]).

Is Being “Robust” Beneficial? A Perspective from the Indian Market

Motivated by the progress made towards incorporating robust optimization in the framework of risk minimization, this work focuses on assessing the practical usefulness of the robust optimization approaches for the minimization of downside risk measures, such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). Accordingly, we perform empirical analysis of the performance of VaR and CVaR models with respect to their robust counterparts, namely, Worst-Case VaR and Worst-Case CVaR, using both simulated data and market data involving the Indian indices of S&P BSE 30 and S&P BSE 100. Additionally, we provide relevant insights regarding the viability of these robust models over their classical formulations from the perspective of an investment practitioner. We conclude by noting the superior performance of Worst-Case VaR and Worst-Case CVaR with respect to their classical versions in the cases involving higher number of stocks and simulated setup respectively.

Multiscale and partial correlation networks analysis of risk connectedness in global equity markets

This paper investigates the multiscale properties and the evolution patterns of risk connectedness in global equity markets using the sample from January 03, 2000 to December 24, 2018. GARCH–EVT–VaR model is used to measure systemic risk of global equity markets. We deal with the application of Univariate Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model and Extreme Value Theory (EVT) to measure the Value at Risk (VaR) of global equity markets. We then introduce the maximal overlap discrete wavelet transform (MODWT) method and partial correlation coefficients into the complex network theory to construct multiscale and partial correlation networks in global equity markets. We find the evidence of the strong risk connectedness among global equity markets in both the overall and multiscale networks, and their topological properties vary across time–frequency horizons. The US and Eurozone equity markets play a predominant role in the process of risk transmission. Most developing markets seem to remain inactive in the multiscale networks of risk connectedness. The rolling-window analysis based on time–frequency domain demonstrates that risk networks tend to be more concentrated not only at the mid-term scales but also during the financial crisis. Empirical results reveal multiscale risk connectedness characteristics, providing useful information for regulators to formulate macro prudential supervision policy and investors to update the portfolio strategies and risk prevention measures.

Value-at-risk backtesting: Beyond the empirical failure rate

The quality of Value at Risk (VaR) forecasts is typically determined by the empirical assessment of the frequency of VaR misspecifications. Additionally, the risk of clustered VaR misspecification over time, especially in volatile market times, is usually assessed within a joint testing framework.In this paper, we exclusively focus on the identification of clustered VaR misspecficiations and discuss competing backtesting procedures with respect to their ability to detect inadequate VaR models that are characterized by risk clustering.We present a simulation analysis which comprises different VaR scenarios and we find that the quality of competing backtesting procedures depends on the underlying sample size. Moreover, if sample size is small, it is the parsimonious F-test which describes a sensible choice for applied VaR assessment.

Value-at-Risk Analysis for Measuring Stochastic Volatility of Stock Returns: Using GARCH-Based Dynamic Conditional Correlation Model

To assess the time-varying dynamics in value-at-risk (VaR) estimation, this study has employed an integrated approach of dynamic conditional correlation (DCC) and generalized autoregressive conditional heteroscedasticity (GARCH) models on daily stock return of the emerging markets. A daily log-returns of three leading indices such as KSE100, KSE30, and KSE-ALL from Pakistan Stock Exchange and SSE180, SSE50 and SSE-Composite from Shanghai Stock Exchange during the period of 2009–2019 are used in DCC-GARCH modeling. Joint DCC parametric results of stock indices show that even in the highly volatile stock markets, the bivariate time-varying DCC model provides better performance than traditional VaR models. Thus, the parametric results in the DCC-GRACH model indicate the effectiveness of the model in the dynamic stock markets. This study is helpful to the stockbrokers and investors to understand the actual behavior of stocks in dynamic markets. Subsequently, the results can also provide better insights into forecasting VaR while considering the combined correlational effect of all stocks.

Value at Risk, Legislative Framework, Crises, and Procyclicality: what goes wrong?

This study highlights some deficiencies of the stock markets’ risk legislation framework, and particularly the CESR (2010) guidelines. We show that the current legislative framework fails to offer incentives to financial management companies to invest in advanced models for more representative Value at Risk (VaR) estimations, and for this reason, in many cases conventional VaR models are applied. We use data from the DAX, CAC 40, FTSE, FTSEMIB and IBEX indices, and then we apply them to the widely accepted Delta Normal VaR model. The empirical findings show that the conventional VaR models not only fail to provide information for the upcoming financial crises, but also contribute to such phenomena as procyclicality and overreaction in the stock market. We suggest additional tests and we empirically show how these tests could reduce the procyclicality issue and promote a more sustainable investment environment. Even though this study is mainly focused on CESR (2010) guidelines, it could be useful for any similar legislative framework, such as the Basel Accords.

Volatility specifications versus probability distributions in VaR forecasting

AbstractWe provide evidence suggesting that the assumption on the probability distribution for return innovations is more influential for value‐at‐risk (VaR) performance than the conditional volatility specification. We also show that some recently proposed asymmetric probability distributions and the APARCH and FGARCH volatility specifications beat more standard alternatives for VaR forecasting, and they should be preferred when estimating tail risk. The flexibility of the free power parameter in conditional volatility in the APARCH and FGARCH models explains their better performance. Indeed, our estimates suggest that for a number of financial assets the dynamics of volatility should be specified in terms of the conditional standard deviation. We draw our results on VaR forecasting performance from (i) a variety of backtesting approaches, (ii) the model confidence set approach, as well as (iii) establishing a ranking among alternative VaR models using a precedence criterion that we introduce in this paper.

A conditional heteroscedastic VaR approach with alternative distributions

Objective: The purpose of this paper is to explored different distributions in conditional Value at Risk (VaR) modeling as an option in the Mexican market. Methodology: We estimate a GARCH model under the Gaussian, Normal Inverse Gaussian, Skew Generalized t and the Stable distribution assumption, then we implement the model in predicting one-day ahead VaR and finally we examine the performance among the four VaR models during a period of high volatility. Results: The backtesting result confirms that the stable-VaR approach outperforms the other models in the VaR’s prediction at 99% confidence level. Limitations: Although the VaR is a widely used risk measure is not a coherent risk measure, for this reason, a natural extension of our work should be to estimate the expected shortfall and this may produce different insights. Conclusions: Our findings reveal that models that consider some empirical characteristic of financial returns such as leptokurtic, volatility clustering and asymmetry improve the VaR predicting capacity. This finding is important in the search of more robust approaches for VaR estimates. Recepción: 09/08/2018 Aceptación: 31/10/2019

Risk Optimization for Revenue-Driven Wireless Video Broadcasting Systems: A Copula-Based Framework

The revenue of wireless service providers (WSPs) relies on their ability to efficiently satisfy the variable demands from end users (EUs). However, emerging video services create new risks owing to the diverse content requirements of heterogeneous EUs operating in uncertain markets. It is challenging as the risks created by demands and prices are highly uncertain. In this work, a risk problem of high revenues is studied in which multiple video content items with different prices are broadcast to wireless EUs. The video content prices differ in their value functions in terms of popularity, ratings, and types. The objective is to maximize the revenue of WSPs under a certain Value-at-Risk (VaR) by adjusting the content prices and allocation of bandwidth resources. Furthermore, a VaR-based optimization framework for wireless video broadcasting systems is presented. First, the content characteristics are analyzed, and a copula model is then used to build the content value structure. The copula of a multivariate distribution corresponds to the description of the price-dependent structure. Second, a risk analysis for the effects of price fluctuations on revenues caused by uncertainty is conducted. A VaR model is associated with changes in the prices and allocated rates. Copulas are used to derive a bound on the VaR for functions of dependent risks. Subsequently, detailed representations are provided to identify the distributional bounds for revenue functions of dependent risks. Lastly, a VaR-based framework that optimizes pricing and bandwidth provision is presented. For the solution, the risk regions of WSPs are modeled as polymatroidal structures to minimize the risk caused by different service demands and variable market prices. Experiments on different price markets demonstrated that the proposed method is effective, thereby verifying the feasibility of the proposed method.

Old-fashioned parametric models are still the best: a comparison of value-at-risk approaches in several volatility states

Numerous advances in the modeling techniques of value-at-risk (VaR) have provided financial institutions with a wide range of market risk approaches. However, which model to use depends on the state of volatility. We present backtesting results for 1% and 2.5% VaR of six indexes from emerging and developed countries using several of the best-known VaR models, including generalized autoregressive conditional heteroscedasticity (GARCH), extreme value theory (EVT), conditional autoregressive VaR (CAViaR) and filtered historical simulation (FHS) with multiple sets of parameters. The backtesting procedure is based on the excess ratio, Kupiec and Christoffersen tests for multiple thresholds and cost functions. The main contribution of this paper is that we compared the models in four different scenarios, with different states of volatility in the training and testing samples. The results indicate that the best of the models, ie, the least affected by changes in the volatility, is GARCH(1,1) with a standardized Student t distribution. Nonparametric techniques (eg, CAViaR with GARCH setup or FHS with a skewed normal distribution) have very prominent results in testing periods with low volatility, but they are worse in turbulent periods. We also discuss an automatic method to set an extreme distribution threshold for EVT models as well as several ensembling methods for VaR, of which the minimum VaR estimate from the best models – in particular, a minimum of GARCH(1,1) with a standardized Student t distribution and either the EVT or the CAViaR model – has been proven to give very good results.

What do the value-at-risk measure and the respective legislative framework really offer to financial stability? Critical views and pro-cyclicality

In this paper, we examine how value at risk (VaR) contributes to the financial market's stability. We apply the Guidelines on Risk Measurement and the Calculation of Global Exposure and Counterparty Risk for UCITS of the Committee of European Securities Regulators (CESR 2010) to the main indices of the 12 stock markets of the countries that have used the euro as their official currency since its initial circulation. We show that gaps in the legislative framework give incentives to investment funds to adopt conventional models for the VaR estimation in order to avoid the increased costs that the advanced models involve. For this reason, we apply the commonly used historical simulation VaR (HVaR) model, which is: (i) taught at most finance classes; (ii) widely applied in the financial industry; and (iii) accepted by CESR (2010). The empirical evidence shows the HVaR does not really contribute to financial stability, and the legislative framework does not offer the appropriate guidance. The HVaR model is not representative of the real financial risk, and does not give any signal for trends in the near future. The HVaR is absolutely backward-looking and this increases the stock market's overreaction. The fact that the suggested confidence level in CESR (2010) is set at 99 percent leads to hidden pro-cyclicality. Scholars and researchers should focus on issues such as the abovementioned, otherwise the VaR estimations will become, sooner or later, just a formality, and such conventional statistical measures rarely contribute to financial stability.

Selection of Value-at-Risk models for MENA Islamic indices

PurposeThe purpose of this study is to investigate the performance of Value-at-Risk (VaR) models for nine Middle East and North Africa Islamic indices using RiskMetrics and VaR parametric models.Design/methodology/approachThe authors test the performance of several VaR models using Kupiec and Engle and Manganelli tests at 95 and 99 per cent levels for long and short trading positions, respectively, for the period from August 10, 2006 to December 14, 2014.FindingsThe authors’ findings show that the VaR under Student and skewed Student distribution are preferred at a 99 per cent level VaR. However, at 95 per cent level, the VaR forecasts obtained under normal distribution are more accurate than those generated using models with fat-tailed distributions. These results suggest that VaR is a good tool for measuring market risk. The authors support the use of RiskMetrics during calm periods and the asymmetric models (Generalized Autoregressive Conditional Heteroskedastic and the Asymmetric Power ARCH model) during stressed periods.Practical implicationsThese results will be useful to investors and risk managers operating in Islamic markets, because their success depends on the ability to forecast stock price movements. Therefore, because a few Islamic financial institutions use internal models for their capital calculations, the regulatory committee should enhance market risk disclosure.Originality/valueThis study contributes to the knowledge in this area by improving our understanding of market risk management for Islamic assets during the stress periods. Then, it highlights important implications regarding financial risk management. Finally, this study fills a gap in the literature, as most empirical studies dealing with evaluating VaR prediction models have focused on quantifying the model risk in the conventional market.