Value-at-Risk Models Research Articles

Value-at-risk performance in emerging and developed countries

PurposeThe purpose of this paper is to evaluate the predictive capacity of market risk estimation models in times of financial crises.Design/methodology/approachFor this, value-at-risk (VaR) valuation models applied to the daily returns of portfolios composed of stock indexes of developed and emerging countries were tested. The Historical Simulation VaR model, multivariate ARCH models (BEKK, VECH and constant conditional correlation), artificial neural networks and copula functions were tested. The data sample refers to the periods of two international financial crises, the Asian Crisis of 1997, and the US Sub Prime Crisis of 2008.FindingsThe results pointed out that the multivariate ARCH models (VECH and BEKK) and Copula-Clayton had similar performance, with good adjustments in 100 percent of the tests. It was not possible to perceive significant differences between the adjustments for developed and emerging countries and of the crisis and normal periods, which was different to what was expected.Originality/valuePrevious studies focus on the estimation of VaR by a group of models. One of the contributions of this paper is to use several forms of estimation.

Predicting carbon market risk using information from macroeconomic fundamentals

Economic theories suggest that carbon price movements are closely related to economic fundamentals. This paper develops an economic state-dependent (SD) approach to evaluate carbon market Value-at-Risk (VaR) that incorporates information from macroeconomic fundamentals into carbon return VaR modeling and forecasting. This method implements an economic SD sampling scheme that utilizes historical carbon return observations from the relevant economic states to predict future carbon market VaR. Applying this SD method to the European Union (EU) carbon market, we confirm that the EU fundamental economy has two distinct states that correspond to “expansion” and “recession” periods and that the carbon returns have different distributions in the two states. We find that the SD method outperforms the traditional non-SD methods in out-of-sample VaR forecasts, and this is particularly evident when the carbon market experiences large-scale economy-driven structural breaks.

Back-Testing of Expected Shortfall: Main Challenges and Methodologies

In a context of an ever-changing regulatory environment over the last years, Banks have witnessed the draft and publication of several regulatory guidelines and requirements in order to frame and structure their internal Risk Management. Among these guidelines, one has been specifically designed for the risk measurement of market activities. In January 2016, the Basel Committee on Banking Supervision (BCBS) published the Fundamental Review of the Trading Book (FRTB). Amid the multiple evolutions discussed in this paper, the BCBS presents the technical context in which the potential loss estimation has changed from a Value-at-Risk (VaR) computation to an Expected Shortfall (ES) evaluation. The many advantages of an ES measure are not to be demonstrated, however this measure is also known for its major drawback: its difficulty to be back-tested. Therefore, after recalling the context around the VaR and ES models, this white paper will review ES back-testing findings and insights along many methodologies; these have either been drawn from the latest publications or have been developed by the Global Research & Analytics (GRA) team of Chappuis Halder & Co. As a conclusion, it has been observed that the existing methods rely on strong assumptions and that they may lead to inconsistent results. The developed methodologies proposed in this paper also show that even though the ES97.5% metric is close to a VaR99,9% metric, it is not as easily back-tested as a VaR metric; this is mostly due to the non-elicitability of the ES measure.

Value at Risk and Extreme Value Theory: Application To The Johannesburg Securities Exchange

Value at Risk (VaR) has been established as one of the most important and commonly used financial risk management tools. Nevertheless, the attractive features and wide-spread use of VaR could not help to avoid a number of financial crises and its severe impact on economies globally, the latest being the 2008 financial crisis. In isolation, VaR has, in the past, mostly focused on events that occur with a 1% or 5% probability. This is a popular reason offered for its failure of ‘predicting’ the financial crises, as the latter are viewed as ‘extreme’ events and can therefore not be classified as events with a 1% or 5% probability of happening. The use of Extreme Value Theory (EVT) in calculating VaR is a relatively new approach and attempts to expand on the traditional VaR-only approach to include potential extreme events. This approach has provided good results in developed markets and in this article we investigate if the same holds true in the more volatile South African equity space. We examine and compare the application of seven VaR and VaR-EVT models on the FTSE/JSE Total Return All Share Index. Our results suggest that the Filtered Historical Simulation VaR method is the best all-round model. It is, however, worthwhile to employ EVT in the form of the conditional Generalized Pareto Distribution (GPD) model when calculating very extreme quantiles such as the 0.1% quantile. Our results further highlight the importance of filtering the data in order to account for the conditional heteroskedasticity of the financial time series.

A new generalization of skew-T distribution with volatility models

ABSTRACTIn this paper, we propose a new generalized alpha-skew-T (GAST) distribution for generalized autoregressive conditional heteroskedasticity (GARCH) models in modelling daily Value-at-Risk (VaR). Some mathematical properties of the proposed distribution are derived including density function, moments and stochastic representation. The maximum likelihood estimation method is discussed to estimate parameters via a simulation study. Then, the real data application on S&P-500 index is performed to investigate the performance of GARCH models specified under GAST innovation distribution with respect to normal, Student's-t and Skew-T models in terms of the VaR accuracy. Backtesting methodology is used to compare the out-of-sample performance of the VaR models. The results show that GARCH models with GAST innovation distribution outperforms among others and generates the most conservative VaR forecasts for all confidence levels and for both long and short positions.

Shrunk volatility value-at-risk: an application on US balanced portfolios

We test the naive model to forecast ex ante value-at-risk (VaR) using a shrinkage estimator between realized volatility estimated on past return time series and implied volatility quoted on the market. Implied volatility is often indicated as the operator’s expectation about future risk, while the historical volatility straightforwardly represents the realized risk prior to the estimation point, which by definition is backward looking. Therefore, the VaR prediction strategy uses information both on the expected future risk and on the past estimated risk. We examine Cesarone and Colucci’s 2016 model – Shrunk Volatility VaR (ShVolVaR) – and generalize it, assuming that returns are conditionally Student t distributed (the authors assume that returns are normally distributed, but normality is a particular case of Student t distribution with degrees of freedom that tend to infinity). The ShVolVaR results are compared with those of six benchmark industry VaR models. The performance of all VaR models is validated using both statistical accuracy and efficiency evaluation tests on thirty-nine equally spaced, balanced portfolios composed by US equity and bonds over an out-of-sample period that covers different crises. We evaluate model performances on four VaR confidence levels (95%, 99%, 99.5% and 99.9%). We also validate the models under loss function backtests; our results confirm the efficacy of implied volatility indexes as inputs for a VaR model, combined with realized volatilities. Further, we confirm Cesarone and Colucci’s 2016 conclusion in almost all balanced portfolios. In our empirical analysis, we find that a VaR model that correctly estimates VaR for all ε and all the balanced portfolios considered does not exist. However, for each confidence level, the ShVolVaR model, with appropriate values for the parameters α and v, can achieve the same results as the common VaR models that are widely used in the finance industry.

The validation of filtered historical value-at-risk models

Recent value-at-risk (VaR) models based on historical simulation often incorporate approaches where the volatility of the historical sample is rescaled or filtered to better reflect current market conditions. These filtered historical simulation (FHS) VaR models are now widely used in the industry and, as is usually the case with VaR models, they are validated through backtesting. However, while backtesting is a natural way of testing a percentile forecast, it is not specifically designed to capture other features of the model, such as its efficiency in adapting to new volatility conditions. In this paper, we discuss the limitations of backtesting as a tool to assess the performance of FHS models and, using a Monte Carlo simulation framework, we examine whether incorporating information about the size of the breaches (through the use of score functions, for example) can improve the efficiency of these tests. The results show that, even when incorporating the size of the VaR violations, tests based solely on the breaches generally fail as a tool to discriminate between different calibrations of the decay factor; they also tend to be biased. Among the alternative tests considered, the asymmetric piecewise linear score performs best overall, followed by the dynamic quantile test. We conclude by considering some empirical examples.

Portfolio optimization by using MeanSharp-βVaR and Multi Objective MeanSharp-βVaR models

The purpose of this study is to develop portfolio optimization and assets allocation using our proposed models. For this, three steps are considered. In the first step, the stock companies screen by their financial data. For second step, we need some inputs and outputs for solving Data Envelopment Analysis (DEA) models. Conventional DEA models assume non-negative data for inputs and outputs. However, many of these data take the negative value, therefore we propose the MeanSharp-?VaR (MSh?V) model and the Multi Objective MeanSharp-?VaR (MOMSh?V) model based on Range Directional Measure (RDM) that can take positive and negative values. Also, we consider one of downside risk measures named Value at Risk (VaR) and try to decrease it. After using our proposed models, the efficient stock companies will be selected for making the portfolio. In the third step, Multi Objective Decision Making (MODM) model was used to specify the capital allocation to the stock companies that was selected for the portfolio. Finally, a numerical example of the purposed method in Iranian stock companies is presented.

Kvantifikovanje ekstremnov tržišnog rizika na izabranim zemljama Zapadnog Balkana

The purpose of this paper is to investigate the performance of unconditional and conditional Value at Risk (VaR) and Expected Shortfall (ES) models based on EVT. The application of one unconditional VaR and ES model based on EVT and three variants of conditional models of VaR and ES based on EVT in the capital markets of the selected WBC was tested in the paper. To test the VaR model, a conditional and unconditional cover test was used, with the note that their results were subject to verification using the Monte Carlo test procedure. The obtained results suggests that these models can be successfully used to quantify extreme market risk in selected markets, in the context of Basel standards. ES models have been tested and ranked using loss function. By using the Bootstrap simulation, these results are subject to verification. The obtained results does not reveal which model is most suitable for the selected markets, since they are differently ranked in different markets.

Value-at-Risk Based on Time-Varying Risk Tolerance Level

The conventional judgement-based method for fixing the risk tolerance level in the Value-at-Risk (VaR) model might be a suboptimal method, because the procedure induces the possibility of bias in risk measurement. Conversely, a superior risk management practice might be one, where input parameters are determined by a quantitative process which is “non-subjective to the risk modeller’s preferences”. Based on this insight, we have improved on the VaR model. Our model allows time variation of the risk tolerance level and so is suitable for scenario-wise risk analysis.

Forecasting Value-at-Risk (VaR) in the Major Asian Economies

This is an empirical study of forecasting Value-at-Risk (VaR) in the major Asian economies. The VaR is first forecasted for Singapore, Malaysia, Hong Kong of China, Indonesia, South Korea, Philippines, Thailand, China, Taiwan of China and India using different competing models. The VaR estimates are then backtested using unconditional coverage test, conditional coverage test and loss function to arrive at the best VaR model for each of the economies. The results are mixed with the highest success rate of FIGARCH model. Also, the appropriateness of the models changes across quantiles and between tails.

The Burr X Pareto Distribution: Properties, Applications and VaR Estimation

In this paper, a new three-parameter Pareto distribution is introduced and studied. We discuss various mathematical and statistical properties of the new model. Some estimation methods of the model parameters are performed. Moreover, the peaks-over-threshold method is used to estimate Value-at-Risk (VaR) by means of the proposed distribution. We compare the distribution with a few other models to show its versatility in modelling data with heavy tails. VaR estimation with the Burr X Pareto distribution is presented using time series data, and the new model could be considered as an alternative VaR model against the generalized Pareto model for financial institutions.

A Skewed Student-T Value-at-Risk Approach for Long Memory Volatility Processes in Japanese Financial Markets

This paper investigates the relevance of skewed Student-t distributions in capturing long memory volatility properties in the daily return series of Japanese financial data (Nikkei 225 Index and JPY-USD exchange rate). For this purpose, we assess the performance of two long memory Value-at-Risk (VaR) models (FIGARCH and FIAPARCH VaR model) with three different distribution innovations: the normal, Student-t, and skewed Student-t distributions. From our results, we find that the skewed Student-t distribution model produces more accurate VaR estimations than normal and Student-t distribution models. Thus, accounting for skewness and excess kurtosis in the asset return distribution can provide suitable criteria for VaR model selection in the context of long memory volatility and enhance the performance of risk management in Japanese financial markets.

How to Choose the Return Model for Market Risk? Getting Towards a Right Magnitude of Stressed VAR

Value at Risk (VaR) and stressed value at Risk (SVaR) or expected shortfall are important risk measures widely used in the financial services industry for risk management and market risk capital computation. Fundamental to any (S)VaR model is the choice of the return type model for each risk factor. Because the resulting SVaR numbers are highly sensitive to the chosen return type model it is important to make a prudent choice on the return type modelling. We propose to reconstruct the return type model from historic data without making an a priori model assumption on the return model. We explain the fundamentals of return type modelling and how it impacts magnitude of SVaR. We further show how to obtain a global return type model from a set of similar return type models by using geometric calculus. Numerical simulations and illustrations are provided. In this paper the focus is on interest rates, but the proposed methodology is general and can be applied to any other asset class such as inflation, credit spread, equity or fx.

A novel process economics risk model applied to biodiesel production system

Abstract In this paper, the concept of value at risk (VAR) is introduced to study process economics related to biodiesel production and use. Although the VAR concept is actively used in financial engineering for stock investment and trading, it has never been used in process economics. A methodology to develop a VAR model for a biodiesel process facility has been proposed and analysed. The impact of different cost related risk factors is modelled using a stochastic process and interdependence in a Bayesian Network format. The analysis reveals that cost underestimation is the most significant risk factor in biodiesel economics. The VAR model is analysed for 1, 5, and 10 VAR for 5 years of plant operations. Analysing VAR at any point of time (i.e. year 2) shows that with a 1% chance, 5% chance and 10% chance, the maximum loss would be $6.26, $9.52 and $11.34 million respectively (up to year 2). When VAR is considered in the process economics the return period is significantly affected and is increased by 21 months. This study recommends that VAR should be considered as an integral part of process economics, especially for new product or process design.

An Online Sequential Learning Non-parametric Value-at-Risk Model for High-Dimensional Time Series

Online Value-at-Risk (VaR) analysis in high-dimensional space remains a challenge in the era of big data. In this paper, we propose an online sequential learning non-parametric VaR model called OS-GELM which is an autonomous cognitive system. This model uses a Generalized Autoregressive Conditional Heteroskedasticity (GARCH) process and an online sequential extreme learning machine (OS-ELM) to cognitively calculate VaR, which can be used for online risk analysis. The proposed model not only learns the data one-by-one or chunk-by-chunk but also calculates VaR in real time by extending OS-ELM from machine learning to the non-parametric GARCH process. The GARCH process is also extended to one-by-one and chunk-by-chunk mode. In OS-GELM, the parameters of hidden nodes are randomly selected. The output weights are analytically determined based on the sequentially arriving data. In addition, the generalization performance of the OS-GELM model attains a small training error and generates the smallest norm of weights. Experimentally obtained VaRs are compared with those given by GARCH-type models and conventional OS-ELM. The computational results demonstrate that the OS-GELM model obtains more accurate results and is better at forecasting the online VaR. OS-GELM model is an autonomous cognitive system to dynamically calculate Value-at-Risk, which can be used for online financial risk assessment about human being’s behavior. The OS-GELM model can calculate VaR in real time, which can be used as a tool for online risk management. OS-GELM can handle any bounded, non-constant, piecewise-continuous membership function to realize real-time VaR monitoring.

A Study of Risk Spillover in the Crude Oil and the Natural Gas Markets

This article examines the upside and downside risk spillover effects among crude oil (WTI and Brent) and Henry Hub natural gas markets. We consider value-at-risk (VaR) as a measure of risk and model both upside and downside 95 per cent, 99 per cent and 99.5 per cent VaR using various VaR approaches. The VaR models are evaluated using Christoffersen’s (1998) conditional coverage test and Lopez’s loss function approach to select the best-performing VaR model. Finally, we apply Hong, Liu and Wang’s (2009) approach to examine the upside and the downside risk spillover among crude oil and Henry Hub natural gas markets. We find significant two-way as well as one-way upside and downside risk spillover between WTI and Brent crude oil. Our results provide weak evidence of upside risk spillover from natural gas market to crude oil markets for 99.5 per cent VaR.

Commodities returns’ volatility in financialization era

PurposeThis paper aims to indirectly evaluate the accuracy of various volatility models using a value-at-risk (VaR) approach and to investigate the relationship between the accuracy of volatility modelling and investments performance in the financialized commodity markets.Design/methodology/approachThis paper uses the VaR back-testing approach at six different commodities, seven different volatility models and five different time horizons.FindingsThis paper finds that the moving average (MA) VaR model tends to be the best for oil, copper, wheat and corn (long horizon) whereas the exponential generalized autoregressive conditional heteroscedastic (E-GARCH) VaR model tends to be the best for gold, silver and corn (short horizon). Our findings indicate that MA volatility model should be used for oil, copper, wheat and corn (for longer time horizons) commodities whereas E-GARCH volatility model should be used for gold, silver and corn (for short time horizons) commodities. We also find that there is a positive relationship between an accurate VaR performance and commodity return. This indicates that a good job in modelling volatility will be rewarded by higher returns in financialized commodity markets.Originality/valueThis paper indirectly evaluates the accuracy of volatility model via VaR measure and investigates the relationship between the accuracy of volatility and investments performance in financialized commodity markets. This paper contributes to the literature by offering VaR approach in evaluating volatility model performance and reporting the importance of performing accurate volatility modelling in financialized commodity markets.

Volatility Speciications Versus Probability Distributions in VAR Forecasting

We 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 not be specified in terms of the conditional variance. We draw our results on the basis of: i) performance in a variety of backtesting approaches, ii) the Model Confidence Set approach, as well as, iii) applying a dominance criterion among alternative VaR models that we introduce in this paper.

A Bayesian encompassing test using combined value-at-risk estimates

The Value at Risk (VaR) is a risk measure that is widely used by financial institutions in allocating risk. VaR forecast estimation involves the conditional evaluation of quantiles based on the currently available information. Recent advances in VaR evaluation incorporate conditional variance into the quantile estimation, yielding the Conditional Autoregressive VaR (CAViaR) models. However, the large number of alternative CAViaR models raises the issue of identifying the optimal quantile predictor. To resolve this uncertainty, we propose a Bayesian encompassing test that evaluates various CAViaR models predictions against a combined CAViaR model based on the encompassing principle. This test provides a basis for forecasting combined conditional VaR estimates when there are evidences against the encompassing principle. We illustrate this test using simulated and financial daily return data series. The results demonstrate that there are evidences for using combined conditional VaR estimates when forecasting quantile risk.