Value-at-Risk Models Research Articles

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.

Reducing the risk in tail risk forecasting models

This paper demonstrates that existing quantile regression models used for forecasting Value-at-Risk (VaR) and expected shortfall (ES) are sensitive to initial conditions. A 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, a new additive-type model is developed for the ES component that is 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.

Mixed value-at-risk and its numerical investigation

We study an extension of value-at-risk (VaR) measure, named as Mixed VaR, a weighted sum of multiple VaRs quantified at different confidence levels. Classical VaR or single VaR computed at a fixed confidence level corresponds to a single percentile of distribution and therefore, is unable to reveal much information of risk involved in it. As a remedy to this, we propose to investigate the role of Mixed VaR and its deviation version in risk management of extreme events in the portfolio selection problem. We analyze the computational performance of portfolios from optimization models minimizing single VaR and Mixed VaR (and their deviation variants) for different combinations of confidence levels over historical as well as on simulated data in various financial performance parameters including mean value, risk measures (VaR and CVaR values quantified at multiple confidence levels), and risk-reward measures (Sharpe ratio, Sortino ratio, Sharpe with VaR, and Sharpe with CVaR). We also study the numerical comparison between Mixed VaR with its most crucial counterpart, the Mixed conditional value-at-risk (Mixed CVaR). We find that the performance of portfolios from Mixed VaR model is lying between the performance of its single VaR counterparts and rarely yield any worst value in any of the considered performance parameters. A similar observation is concluded for the deviation version of the models. Further, we find that Mixed VaR outperforms Mixed CVaR with respect to risk-reward measures considered in the study on both of the data sets, historical as well as on simulated.

Semi-parametric dynamic asymmetric Laplace models for tail risk forecasting, incorporating realized measures

This paper extends the joint Value-at-Risk (VaR) and expected shortfall (ES) quantile regression model of Taylor (2019), by incorporating a realized measure to drive the tail risk dynamics, as a potentially more efficient driver than daily returns. Furthermore, we propose and test a new model for the dynamics of the ES component. Both a maximum likelihood and an adaptive Bayesian Markov chain Monte Carlo method are employed for estimation, the properties of which are compared in a simulation study. The results favour the Bayesian approach, which is employed subsequently in a forecasting study of seven financial market indices. The proposed models are compared to a range of parametric, non-parametric and semi-parametric competitors, including GARCH, realized GARCH, the extreme value theory method and the joint VaR and ES models of Taylor (2019), in terms of the accuracy of one-day-ahead VaR and ES forecasts, over a long forecast sample period that includes the global financial crisis in 2007–2008. The results are favorable for the proposed models incorporating a realized measure, especially when employing the sub-sampled realized variance and the sub-sampled realized range.

Comparison of VaR Models to the Brazilian Stock Market Under the Hypothesis of Serial Independence in Higher Orders: Are Garch Models Really Indispensable?

Our objective in this article was to verify which models for the Value at Risk (VaR), among those that do not consider conditional volatility (Extreme Values Theory and the traditional Historical Simulation), and those that do consider it (GARCH and IGARCH), are adequate for the main index of the Brazilian stock market, the IBOVESPA. For this purpose, backtesting of adherence and the independence of first and higher orders were implemented for the four models mentioned, over forecast horizons of 1 and 10 days. The contribution is based on a the more rigorous criteria than those used in the literature for validating VaR models, as we performed backtesting for violation independence of higher orders on forecast horizons of 10 days. The results show that only GARCH family models were adequate. Thus, it is recommended to entities of the National Financial System that keep relevant positions in the Brazilian stock market, the utilization of internal risk models based on conditional volatility, in order to minimize the occurrence of violation clusters.

Evaluating South Africa’s market risk using asymmetric power auto-regressive conditional heteroscedastic model under heavy-tailed distributions

Orientation: Value-at-risk (VAR) and other risk management tools, such as expected shortfall (conditional VAR), are heavily reliant on a suitable set of underlying distributional conjecture. Thus, distinguishing the underlying distribution that best captures all properties of stock returns is of great interest to both scholars and risk managers. Research purpose: Comparing the execution of the generalised auto-regressive conditional heteroscedasticity (GARCH)-type model combined with heavy-tailed distributions, namely the Student’s t -distribution, Pearson type-IV distribution (PIVD), generalised Pareto distribution (GPD) and stable distribution (SD), in estimating VAR of Johannesburg Stock Exchange (JSE) All Share Price Index (ALSI) returns. Motivation for the study: The proposed models have the potential to apprehend volatility clustering and the leverage effect through the GARCH scheme and at the same time model the heavy-tailed behaviour of the financial returns. Research approach/design and method: The GARCH-type model combined with heavy-tailed distributions, namely the Student’s t -distribution, PIVD, GPD and SD, is developed to estimate VAR of JSE ALSI returns. The model performances are assessed through Kupiec likelihood ratio test. Main findings: The results show that the asymmetric power auto-regressive conditional heteroscedastic models combined with GPD and PIVD are the robust VAR models for South African’s market risk. Practical/managerial implications: The outcomes of this study are expected to be of salient value to financial analysts, portfolio managers, risk managers and financial market researchers, thus giving a better understanding of the South African financial market. Contributions/value-add: Asymmetric power auto-regressive conditional heteroscedastic model combined with heavy-tailed distributions provides a good option for modelling stock returns.

Designing optimal jet fuel hedging strategies for airlines – Why hedging will not always reduce risk exposure

Using a historical simulation based Value at Risk (VaR) model, we provide the first empirical study quantifying the benefits and the costs associated with the fuel hedging activities of airlines. More specifically, we quantify the jet fuel risk exposure and estimate the cash collateral required to support jet fuel hedging using exchange traded futures. The results from our VaR model suggest that although hedging significantly reduces risk exposure, the associated collateral costs are large enough to offset, to a large extent, the potential financial benefits of the hedge to airlines. Increasing the hedging ratio beyond 60–70% results in a marginal reduction in the market risk exposure but significantly increases the cash collateral requirements. Our results demonstrate that the amount of cash collateral is a key factor in hedging decisions of airlines and, while this somewhat contradicts extant literature, is consistent with recent management practice.

A VaR-based Downside Risk Analysis of Indian Equity Mutual Funds in the Pre- and Post-global Financial Crisis Periods

This article analyses downside risk of Indian equity mutual funds from 1999 to 2014 using a value at risk (VaR)-based approach. We use weekly return data of a sample of 349 equity mutual funds during the said period to estimate their weekly VaRs on a rolling basis using some parametric and non-parametric models. Moving average (MA), exponentially weighted MA and GARCH (1, 1) are the parametric models and historical simulation (HS) is the non-parametric model. We also carry out backtesting of the models using three popular approaches—two under the unconditional coverage approach, namely Jorion’s ‘Failure Rate’ approach and Kupiec’s proportion of ‘failures’ (POF) test, and one under the conditional coverage approach, namely the Christoffersen’s Independence test—to test the robustness of the VaR models. Our results show that Indian equity mutual funds exhibit considerable downside risk during the chosen period, in terms of the magnitude of the projected VaRs. Moreover, significant proportions of the funds ‘fail’ the predicted VaRs, particularly during times of crisis for some of the models, raising questions about their robustness in an investment setting in India. On the whole, both from failure proportion as well as backtesting perspective, the GARCH (1,1) seems to be the most robust of the models. JEL codes: G32, G15, G23

Dynamic semiparametric models for expected shortfall (and Value-at-Risk)

Expected Shortfall (ES) is the average return on a risky asset conditional on the return being below some quantile of its distribution, namely its Value-at-Risk (VaR). The Basel III Accord, which will be implemented in the years leading up to 2019, places new attention on ES, but unlike VaR, there is little existing work on modeling ES. We use recent results from statistical decision theory to overcome the problem of “elicitability” for ES by jointly modeling ES and VaR, and propose new dynamic models for these risk measures. We provide estimation and inference methods for the proposed models, and confirm via simulation studies that the methods have good finite-sample properties. We apply these models to daily returns on four international equity indices, and find the proposed new ES–VaR models outperform forecasts based on GARCH or rolling window models.

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 estimate 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 the 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, we consider interest rate data, but the proposed methodology is general and can be applied to any other asset class such as inflation, credit spread, equity or fx.

Forecasting robust value-at-risk estimates: evidence from UK banks

In this paper, we present a novel approach for forecasting Value-at-Risk (VaR) by combining a Bayesian GARCH(1,1) model with Student's-t distribution for the underlying volatility models, vine copula functions to model dependence, and the peaks-over-threshold (POT) method of extreme value theory (EVT) to model the tail behaviour of asset returns. We further propose a new approach for threshold selection in extreme value analysis, which we call a hybrid method. The empirical results and back-testing analysis show that the model captures VaR quite well through periods of calmness and crisis; therefore, it is suitable for use as a measure of risk. Our results also suggest that with a correct implementation of the VaR model, Basel III is not needed.

Two-sided exponential–geometric distribution: inference and volatility modeling

In this paper, two-sided exponential–geometric (TSEG) distribution is proposed and its statistical properties are studied comprehensively. The proposed distribution is applied to the GJR-GARCH model to introduce a new conditional model in forecasting Value-at-Risk (VaR). Nikkei-225 and BIST-100 indexes are analyzed to demonstrate the VaR forecasting performance of GJR-GARCH-TSEG model against the GJR-GARCH models defined under normal, Student-t, skew-T and generalized error innovation distributions. The backtesting methodology is used to evaluate the out-of-sample performance of VaR models. Empirical findings show that GJR-GARCH-TSEG model produces more accurate VaR forecasts than other competitive models.

A novel multi period mean-VaR portfolio optimization model considering practical constraints and transaction cost

The portfolio optimization literature has spent a little effort to consider the fat tail characteristic of asset returns as well as their extreme events. To remove such shortcomings, in this paper, a novel portfolio optimization model is developed in which Value at Risk (VaR) is utilized as a risk measure to account extreme risk so that VaR is estimated use of Extreme Value Theory (EVT). To enrich the practicality of our proposed model, set of real trading constraints are considered such as cardinality, budget, floor and ceiling constraints. Since these modifications lead to a non-convex NP-hard problem which is computationally difficult, a new design of Non-dominated Sorting Genetic Algorithm (NSGA-II) is proposed to solve it. To evaluate the performance of EVT approach in our proposed mean-VaR model, three well-known alternative VaR estimation methods are also considered such as historical simulation, GARCH and t-student GARCH. Experimental results using historical daily financial market data from S & P 100 indices demonstrates that our proposed NSGA-II has great capability of treating the mean-VaR portfolio optimization problem. In addition, the validation study confirmed that our enhanced NSGA-II not only offers superior result compared with that of delivered by benchmark problem in a much lower solving time, but its performance is better than the original NSGA-II. Also, the results indicate that our proposed model outperforms other mean-VaR models especially in low risk area of Pareto front. Finally, the proposed algorithm is compared with set of Non-dominated-based algorithms including SPEA-II, NSPSO and NSACO which results illustrated that our enhanced NSGA-II suggests superior solutions rather than other algorithms. • A novel Multiperiod portfolio optimization model with real constraints is proposed. • Four different VaR models are deployed to account portfolio risk measure. • An enhanced NSGA-II algorithm is developed by utilizing a new repairing mechanism. • The Proposed model offers more appropriate results relative to other Mean-VaR models. • The proposed NSGA-II outperforms other metaheuristics SPEA-II, NSACO and NSPSO.

Calibration of VaR models with overlapping data

Abstract Under the European Union’s Solvency II regulations, insurance firms are required to use a one-year VaR (Value at Risk) approach. This involves a one-year projection of the balance sheet and requires sufficient capital to be solvent in 99.5% of outcomes. The Solvency II Internal Model risk calibrations require annual changes in market indices/term structure for the estimation of risk distribution for each of the Internal Model risk drivers. This presents a significant challenge for calibrators in terms of: Robustness of the calibration that is relevant to the current market regimes and at the same time able to represent the historically observed worst crisis; Stability of the calibration model year on year with arrival of new information. The above points need careful consideration to avoid credibility issues with the Solvency Capital Requirement (SCR) calculation, in that the results are subject to high levels of uncertainty. For market risks, common industry practice to compensate for the limited number of historic annual data points is to use overlapping annual changes. Overlapping changes are dependent on each other, and this dependence can cause issues in estimation, statistical testing, and communication of uncertainty levels around risk calibrations. This paper discusses the issues with the use of overlapping data when producing risk calibrations for an Internal Model. A comparison of the overlapping data approach with the alternative non-overlapping data approach is presented. A comparison is made of the bias and mean squared error of the first four cumulants under four different statistical models. For some statistical models it is found that overlapping data can be used with bias corrections to obtain similarly unbiased results as non-overlapping data, but with significantly lower mean squared errors. For more complex statistical models (e.g. GARCH) it is found that published bias corrections for non-overlapping and overlapping datasets do not result in unbiased cumulant estimates and/or lead to increased variance of the process. In order to test the goodness of fit of probability distributions to the datasets, it is common to use statistical tests. Most of these tests do not function when using overlapping data, as overlapping data breach the independence assumption underlying most statistical tests. We present and test an adjustment to one of the statistical tests (the Kolmogorov Smirnov goodness-of-fit test) to allow for overlapping data. Finally, we explore the methods of converting “high”-frequency (e.g. monthly data) to “low”-frequency data (e.g. annual data). This is an alternative methodology to using overlapping data, and the approach of fitting a statistical model to monthly data and then using the monthly model aggregated over 12 time steps to model annual returns is explored. There are a number of methods available for this approach. We explore two of the widely used approaches for aggregating the time series.

Counteracting Money Laundering as a Tool to Minimize the Shadow Economy

The subject of the research is the establishment of procedures for counteracting money laundering in order to minimize the level of the shadow economy. The relevance of the topic is determined by the following reasons. First, the money laundering risks any business may be subject to, affects the sustainable development of national economies. Second, the criminal income legalization activity is closely connected with the phenomena of capital outflow, corruption, use of offshore zones to conceal sources of income as well as tax evasion and illegal cashing of funds that are factors of the shadow economy. Third, at the end of 2018 in Russia, the Financial Action Task Force (FATF) is going to perform scheduled activities under the fourth round of audits related to assessment of anti-money laundering effectiveness. The purpose of the research was to analyze tools of countering the money laundering that can be used to minimize the level of the shadow economy based on the banking sector of Russia. A model for assessment of potential losses of credit institutions based on the VaR (Value at Risk) model is proposed.

Comparing Hedging Effectiveness of Portfolios in the Greater Chinese Stock Exchanges: Evidence from a Modified Value-at-Risk Model

ABSTRACTThe higher moments of hedged portfolio returns often influence the calculation of value-at-risk (VaR). To establish future short and long hedged portfolios, this study proposes a new modified VaR model, an expected utility maximization (EUM) subject to the modified VaR of higher moments (EUM-MVaR) of stock index futures in markets in greater China. EUM-MVaR has the greatest hedging effectiveness in determining hedged portfolios, while the minimum variance (MV) model had the least hedging effectiveness; the consideration of higher moments of a hedged portfolio return is more effective than non-consideration in determining the hedging effectiveness.

On Estimating Bitcoin Value at Risk: A Comparative Analysis

We compare several models that forecast ex-ante Bitcoin one-day Value-at-Risk (VaR), starting from the simplest ones like Parametric Normal and Historical Simulation and arriving at Historical Filtered Bootstrap and Extreme Value Theory Historical Filtered Bootstrap. We also consider Gaussian and Student-t innovation in the GARCH model specification. The performance of all VaR models is validated using both statistical accuracy and efficiency evaluation tests. We evaluate model performances on four VaR confidence level (95%, 99%, 99.5% and 99.9%). We also validate the models under loss function backtests and our results confirm the efficacy of Historical Filtered Bootstrap as a methodology to estimate VaR. Furthermore, we find that the GARCH model with Gaussian innovation provides the best fit in term of estimating ex Ante VaR. In our empirical analysis, we find that, on the observed data (from November 8, 2012, to May 11, 2018), Historical Filtered Bootstrap AR-GARCH with Gaussian innovation correctly estimates VaR for all e. The Parametric Normal and the standard Historical Simulation show their limitations and we suggest to avoid to use them. For backtest based on loss function, we find that for investors’ viewpoint it seems better to choice Gaussian innovation in the GARCH specification, while under regulators’ viewpoint suggest using Student-t innovation at least in the far tail.

A Practical Guide to Market Risk Model Validations (Part II - VaR Estimation)

The VaR (Value at Risk) concept has emerged back in 1994 when JP Morgan started routinely using it in its daily reporting. Simply said, it represents a lower bound of large rare losses. The VaR metric became an industry standard for measuring market risk because it is intuitive and easy to interpret. This led to the adaptation of VaR for market risk capital calculations in the 1996 market risk amendment (also know as Basel II). Following the failure of this capitalization approach during the 2008 financial crisis, Basel Committee strengthened capital requirements by introducing stressed VaR (in Basel 2.5) and tail VaR (in Fundamental Review of the Trading Book) metrics. The VaR process involves a number of steps that include input processing, curve building, pricing, hedging, risk factor identification, simulation, and VaR estimation. In this paper, we will focus on the VaR estimation only. All VaR estimation models can be categorized by their simulation technique, simulation object and revaluation methodology. We will define a broad validation framework that includes assessment of the conceptual soundness and performance of various VaR models. Common modeling issues and practical solutions will be discussed as well.

Politiques Publiques, Insertion Des Jeunes Et Secteurs d’Emplois d’Actualite

This paper focuses on open public policies that are related to youth employment and hence to human capital or skills training. From the objective of this study, it is important to recognize that debates around public development policies, focused on external openness and youth employment, have always existed in both developed and underdeveloped countries. Inspired by all these debates, we were able to develop our hypothesis and, subsequently, an adequate methodology to verify them. This shows a causality between the variables: external openness, employment and qualifying training or public policy. Thus, we will start from the neoclassical economic theory that relates production, capital, and employment to develop our econometric model. We, therefore, found that it is appropriate to use VAR (value at risk) modeling to analyze the interrelationship between the variables: open access, human capital and employment. The data come from the World Bank, specifically from the "World Development Indicators" , which has earned us a longitudinal sectional study over the period from 1979 to 2014. It uses Word and Excel software to ensure the processing of our data as well as Eviews for the analysis of our data. In this way, we arrive at the result and the recommendations according to which it is necessary to upgrade the GESP (strategy documents for growth and employment in Cameroon). In their elaboration in August 2009, they were focused on the global economic crisis in providing, among other things, appropriate responses to the problems raised by the so-called crisis. This has also placed growth and employment in Cameroon at the center of their actions. To this end, the integration of young people should start from public policies according to the sectors of news and concerns of the jobs of subcontracting and the jobs of transition. It insists on the formations qualifying and, in the long run, the auto employment of the young people.

Refining value-at-risk estimates using a Bayesian Markov-switching GJR-GARCH copula-EVT model.

In this paper, we propose a model for forecasting Value-at-Risk (VaR) using a Bayesian Markov-switching GJR-GARCH(1,1) model with skewed Student’s-t innovation, copula functions and extreme value theory. A Bayesian Markov-switching GJR-GARCH(1,1) model that identifies non-constant volatility over time and allows the GARCH parameters to vary over time following a Markov process, is combined with copula functions and EVT to formulate the Bayesian Markov-switching GJR-GARCH(1,1) copula-EVT VaR model, which is then used to forecast the level of risk on financial asset returns. We further propose a new method for threshold selection in EVT analysis, which we term the hybrid method. Empirical and back-testing results show that the proposed VaR models capture VaR reasonably well in periods of calm and in periods of crisis.