Value-at-Risk Estimates Research Articles

Use of ARIMA-GARCH Model to Estimating Value-at-Risk in Gudang Garam (GGRM) Stock

Stocks are one of the best-known forms of investment and are still used today. In stock investment, it is necessary to know the movement and risk of loss that may be obtained from the stock investment, so that investors can consider the possible losses. One way to calculate risk is to use Value-at-Risk (VaR). Since the stock movement is in the form of a time series, a model can be formed to predict the movement of the stock, which can then be used for VaR calculations using time series analysis. The purpose of the study was to determine the Value-at-Risk value of Gudang Garam Tbk.’s (GGRM) shares using time series analysis. The data used for this research is the daily closing price of shares for three years. At the time series analysis stage, the models used in predicting stock movements are Autoregressive Integrated Moving Average (ARIMA) for the mean model and Generalized Autoregressive Conditional Heteroscedasticity (GARCH) for the volatility model. The average and variance values obtained from the model are then used in calculating the VaR of GGRM shares. Based on the results of the study, it was found that the GGRM stock has a VaR of 0.069598. In other words, if an investment of IDR 1,000,000.00 is made for GGRM shares for 37 days (5% of 747 days), the investment period with a 95% confidence level, the maximum loss that may be borne by the investor is IDR 69,598.00.

An ABC approach for CAViaR models with asymmetric kernels

ABSTRACTThe Value at Risk (VaR) is a risk measure that is widely used by financial institutions to allocate risk. Optimal conditional VaR estimates are typically generated using a likelihood function based on the check-loss function. However, issues such as VaR's bias estimation and asymmetric financial decision-making, based on the sign of the forecast error, can result in the use of combined losses or of intractable likelihood functions. In such cases, likelihood function intractability gives ground for Bayesian inference using likelihood-free methods such as the Approximate Bayesian Computation (ABC) one. This method generates posterior estimates when the likelihood function is analytically unavailable. Here, we introduce a novel ABC-MCMC algorithm based on asymmetric kernel density functions that allows for the asymmetric decision-making rule used in VaR estimation. We illustrate this method in CAViaR models where VaR is forecast using simulated and real financial data series.

A GARCH APPROACH TO VaR CALCULATION IN FINANCIAL MARKET

Value at Risk (VaR) has already becomes a standard measurement that must be carried out by financial institution for both internal interest and regulatory. VaR is defined as the value that portfolio will loss with a certain probability value and over a certain time horizon (usually one or ten days). In this paper we examine of VaR calculation when the volatility is not constant using generalized autoregressive conditional heteroscedastic (GARCH) model. We illustrate the method to real data from Indonesian financial market that is the stock of PT. Indosat Tbk.

Value at Risk Estimation Using the GARCH-EVT Approach with Optimal Tail Selection

A conditional Extreme Value Theory (GARCH-EVT) approach is a two-stage hybrid method that combines a Generalized Autoregressive Conditional Heteroskedasticity (GARCH) filter with the Extreme Value Theory (EVT). The approach requires pre-specification of a threshold separating distribution tails from its middle part. The appropriate choice of a threshold level is a demanding task. In this paper we use four different optimal tail selection algorithms, i.e., the path stability method, the automated Eye-Ball method, the minimization of asymptotic mean squared error method and the distance metric method with a mean absolute penalty function, to estimate out-of-sample Value at Risk (VaR) forecasts and compare them to the fixed threshold approach. Unlike other studies, we update the optimal fraction of the tail for each rolling window of the returns. The research objective is to verify to what extent optimization procedures can improve VaR estimates compared to the fixed threshold approach. Results are presented for a long and a short position applying 10 world stock indices in the period from 2000 to June 2019. Although each approach generates different threshold levels, the GARCH-EVT model produces similar Value at Risk estimates. Therefore, no improvement of VaR accuracy may be observed relative to the conservative approach taking the 95th quantile of returns as a threshold.

Performance evaluation of the Bayesian and classical value at risk models with circuit breakers set up

Circuit breakers, like price limits and trading suspensions, are used to reduce price volatility in security markets. When returns hit price limits or missed, observed returns deviate from equilibrium returns. This creates a challenge for predicting stock returns and modelling value at risk (VaR). In Tehran Stock Exchange (TSE), the circuit breakers are applied to control for the excess price volatilities. This paper intend to address which models and what methodology should be applied by risk analysts to calculate the VaR when the returns are unobservable. To this end, we extend Wei's (2002) model, in the framework of Bayesian Censored and Missing-GARCH approach, to estimate VaR for a share index in TSE. Using daily data over June 2006 to June 2016, we show that the Censored and Missing- GARCH model with student-t distribution outperforms the other VaR estimation metods. Kullback-Leibler (KLIC), Kupic (1995) test and Lopez score (1998) outcomes show that estimated VaR by Censored and missing- GARCH model with student-t distribution is of the most accuracy among the other GARCH family estimated models.

Performance evaluation of the Bayesian and classical value at risk models with circuit breakers set up

Circuit breakers, like price limits and trading suspensions, are used to reduce price volatility in security markets. When returns hit price limits or missed, observed returns deviate from equilibrium returns. This creates a challenge for predicting stock returns and modelling value at risk (VaR). In Tehran Stock Exchange (TSE), the circuit breakers are applied to control for the excess price volatilities. This paper intend to address which models and what methodology should be applied by risk analysts to calculate the VaR when the returns are unobservable. To this end, we extend Wei's (2002) model, in the framework of Bayesian Censored and Missing-GARCH approach, to estimate VaR for a share index in TSE. Using daily data over June 2006 to June 2016, we show that the Censored and Missing- GARCH model with student-t distribution outperforms the other VaR estimation metods. Kullback-Leibler (KLIC), Kupic (1995) test and Lopez score (1998) outcomes show that estimated VaR by Censored and missing- GARCH model with student-t distribution is of the most accuracy among the other GARCH family estimated models.

Global financial crisis and multiscale systematic risk: Evidence from selected European stock markets

AbstractIn this paper, we have investigated the impact of the global financial crisis on the multihorizon nature of systematic risk and market risk using daily data of eight major European equity markets over the period of 2005–2018. The method is based on a wavelet multiscale approach within the framework of a capital asset pricing model. Empirical results demonstrate that beta coefficients have a multiscale tendency, and betas tend to increase at higher scales (lower frequencies). In addition, the size of betas and R2s tends to increase during the crisis period compared with the precrisis period. The multiscale nature of the betas is consistent with the fact that stock market investors have different time horizons due to different trading strategies. Our results based on scale dependent value at risk (VaR) suggest that market risk tends to be more concentrated at lower time scales (higher frequencies) of the data. Moreover, the scale‐by‐scale estimates of VaR have increased almost three folds for every market during the crisis period compared with the precrisis period. Finally, our approach allows for accurately forecasting time‐dependent betas and VaR.

ESTIMASI VALUE AT RISK MENGGUNAKAN VOLATILITAS DISPLACED DIFFUSION

Value at Risk (VaR) is a measure of risk that is able to calculate the worst possible loss that can occurs to stock prices with a certain level of confidence and within a certain period of time. The purpose of this study was to determine the VaR estimate from PT. Indonesian Telecommunications by using Displaced Diffusion volatility. The Displaced Diffusion Model is a stochastic volatility model that describes changes in a financial asset assuming volatility is not constant, but follows a stochastic process. Displaced Diffusion model are capable of modelling skewed implied volatility structures and frequently applied by interest rate quants. Based on the estimation of Displaced Diffusion volatility, it is found that volatility for PT. Indonesian Telecommunications is 0.010168 and VaR estimation using Displaced Diffusion volatility with a confidence level of 95 percent of 1.63%.

VALUE AT RISK PADA PORTOFOLIO SAHAM DENGAN COPULA ALI-MIKHAIL-HAQ

Investment is one alternative to increase assets in the future. Investors can invest in a portfolio to reduce the level of risk. Value at Risk (VaR) is a measuring tool that can calculate the worst loss over a given time period at a given confidence level. GARCH (Generalized Autoregressive Conditional Heteroskedasticity) is used to model data with high volatility. The teory of copula is a powerful tool for modeling joint distribution for any marginal distributions. Ali-Mikhail-Haq copula from Archimedean copula family can be applied to data with dependencies τ between -0.1817 to 0.3333. This research uses Ali-Mikhail-Haq copula with a Monte Carlo simulation to calculate a bivariate portfolio VaR from a combination stocks of PT Pembangunan Perumahan Tbk. (PTPP), PT Bank Tabungan Negara Tbk. (BBTN), and PT Jasa Marga Tbk. (JSMR) in the period of March 3, 2014 - March 1, 2019. The results of VaR calculation on bivariate portfolio for next 1 day period obtained the lowest VaR is owned by bivariate portfolio between PTPP and JSMR with a weight of 30% and 70% at confidence level of 99%, 95%, and 90% respectively are 4.014%, 2.545%, and 1.876%.Keywords: Value at Risk, GARCH, Ali-Mikhail-Haq Copula, Monte Carlo

Application of mathematical modeling value-at-risk (VaR) to optimize decision making in distribution networks

Managers and capital masters of companies and factories try to adopt methods that maximize their profit and minimize their costs. A way for increasing profit is risk management. The risk management and the type of risk are defined in the literature of financial management. For measurement of the risk, many methods are defined which are all created in the recent century and it means the risk and risk management are rather new concepts. Among the newest tools for measuring the risk is value-at-risk (VaR), which was modified by Morgan (Riskmetrics technical document, Morgan Guaranty Trust Company, New York, 1996). VaR represents the maximum expected loss over a certain period of time and at a given confidence level. Many parametric, semi-parametric and nonparametric methods for VaR estimation have been developed. In this article using the mean–variance method one of the parametric techniques of VaR, has been tried to minimize the cost arisen due to locating the supply chain and minimize the maximum level of capital losses, to optimize decision making in the distribution network. The calculated model is tested with numerical examples by MATLAB and Lingo software, and this example supported the resulting model.

Data driven value-at-risk forecasting using a SVR-GARCH-KDE hybrid

Appropriate risk management is crucial to ensure the competitiveness of financial institutions and the stability of the economy. One widely used financial risk measure is Value-at-Risk (VaR). VaR estimates based on linear and parametric models can lead to biased results or even underestimation of risk due to time varying volatility, skewness and leptokurtosis of financial return series. The paper proposes a nonlinear and nonparametric framework to forecast VaR that is motivated by overcoming the disadvantages of parametric models with a purely data driven approach. Mean and volatility are modeled via support vector regression (SVR) where the volatility model is motivated by the standard generalized autoregressive conditional heteroscedasticity (GARCH) formulation. Based on this, VaR is derived by applying kernel density estimation (KDE). This approach allows for flexible tail shapes of the profit and loss distribution, adapts for a wide class of tail events and is able to capture complex structures regarding mean and volatility. The SVR-GARCH-KDE hybrid is compared to standard, exponential and threshold GARCH models coupled with different error distributions. To examine the performance in different markets, one-day-ahead and ten-days-ahead forecasts are produced for different financial indices. Model evaluation using a likelihood ratio based test framework for interval forecasts and a test for superior predictive ability indicates that the SVR-GARCH-KDE hybrid performs competitive to benchmark models and reduces potential losses especially for ten-days-ahead forecasts significantly. Especially models that are coupled with a normal distribution are systematically outperformed.

Volatility modeling and the asymmetric effect for China’s carbon trading pilot market

China’s carbon trading pilot programs are proceeding gradually, and play a positive role in promoting the development of a domestic carbon market. Because of the late start, deficiencies still exist in the understanding, modeling, and exploration of China’s carbon trading pilot market. Our goal is to model the carbon price dynamics and explore the regularities of seven city-based carbon trading pilots. Based on the daily carbon price time series, we analyzed the behavior of the carbon log-returns from 2013 to 2018, modeled them with the ARMA–EGARCH–SGED process, assessed the impact of news on volatility, and carried out the backtesting Value-at-Risk (VaR) analysis. Statistical analysis shows that the log-returns are skewed kurtosis, fat tail, non-normal distribution, and have significantly volatility clustering. The estimated models perform well and capture the asymmetric impact of news on volatility. Positive news increases bigger volatility than a negative one, except for Hubei and Chongqing. The Shenzhen pilot shows the best performance in resisting markets’ risk, while lower-capability in that are found in Hubei and Tianjin. Moreover, the estimated models for seven pilots have adequate capital to cope with large unexpected losses and VaR estimates give a good prediction of market risk at 99%, 97.5%, and 95% confidence level.

ACCURACY VERSUS COMPLEXITY TRADE-OFF IN VaR MODELING: COULD TECHNICAL ANALYSIS BE A SOLUTION?

Accurate Value at Risk (VaR) estimations are crucial for the robustness and stability of a financial system. Even though significant advances have been made in the field of risk modeling, many crises have emerged during the same period, and an explanation for this is that the advanced models are not widely applied in the financial industry due to their mathematical complexity. In contrast to the mathematically complex models that torture the data in the output stage, we suggest a new approach that filters the data inputs, based on Technical Analysis (TA) signals. When the trading signals suggest that the conditions are positive (negative) for investments we use data from the previously documented positive (negative) periods in order to calculate the VaR. In this way, we use input data that are more representative of the financial conditions under examination and thus VaR estimations are more accurate and more representative (nonprocyclical) than the conventional models’ estimation that use the last nonfiltered [Formula: see text]-day observations. Testing our assumptions in the US stock market for the period 2000–2017, the empirical data confirmed our hypothesis. Moreover, we suggest specific legislative adjustments that contribute to more accurate and representative VaR estimations: (i) an extra backtesting procedure at a lower than the 99% confidence level as a procyclicality test and (ii) to ease the minimum requirement of 250 observations that is currently the input threshold because it leads to less accurate VaR estimations.

Forecast combinations for value at risk and expected shortfall

Combining provides a pragmatic way of synthesising the information provided by individual forecasting methods. In the context of forecasting the mean, numerous studies have shown that combining often leads to improvements in accuracy. Despite the importance of the value at risk (VaR), though, few papers have considered quantile forecast combinations. One risk measure that is receiving an increasing amount of attention is the expected shortfall (ES), which is the expectation of the exceedances beyond the VaR. There have been no previous studies on combining ES predictions, presumably due to there being no suitable loss function for ES. However, it has been shown recently that a set of scoring functions exist for the joint estimation or backtesting of VaR and ES forecasts. We use such scoring functions to estimate combining weights for VaR and ES prediction. The results from five stock indices show that combining outperforms the individual methods for the 1% and 5% probability levels.

On the uncertainty of VaR of individual risk

Value at risk (VaR) is a prevalent risk measure used in financial risk management. The calculation of VaR relies on the distribution of the potential loss position which is generally unknown in practice. In this article, we introduce a model of uncertainty for the distribution of a loss variable and investigate the effect on VaR using a worst scenario approach. The proposed model is flexible and can be applied to various types of distributions. The robust VaR and an associated worst scenario measure are identified. It is shown that the choice of the loss model is still important when there is an uncertainty model.

Estimating Value-at-Risk and Expected Shortfall using the intraday low and range data

Value-at-Risk (VaR) is a popular measure of market risk. To convey information regarding potential exceedances beyond the VaR, Expected Shortfall (ES) has become the risk measure for trading book bank regulation. However, the estimation of VaR and ES is challenging, as it requires the estimation of the tail behaviour of daily returns. In this paper, we take advantage of recent research that develops joint scoring functions for VaR and ES. Using these functions, we present a novel approach to estimating the two risk measures based on intraday data. We focus on the intraday range, which is the difference between the highest and lowest intraday log prices. In contrast to intraday observations, the intraday low and high are widely available for many financial assets. To alleviate the challenge of modelling extreme risk measures, we propose the use of the intraday low series. We draw on a theoretical result for Brownian motion to show that a quantile of the daily returns can be estimated as the product of a constant term and a less extreme quantile of the intraday low returns, which we define as the difference between the lowest log price of the day and the log closing price of the previous day. In view of this, we use estimates of the VaR and ES of the intraday low returns to estimate the VaR and ES of the daily returns. We provide empirical support for the new proposals using data for five stock indices and five individual stocks.

Regime-Switching Processes and Mean-Reverting Volatility Models in Value-at-Risk Estimation: Evidence from the Taiwan Stock Index

ABSTRACT This article develops a model that can accurately forecast the volatility of Taiwan stock returns and efficiently estimate value-at-risk (VaR). Because the volatility in the Taiwan stock market has been shown to die down and shift quickly, we find that the model able to outperform others is one that allows the parameters of the volatility models to switch between regimes and conditional volatility to revert quickly to near-normal levels following extremely volatile periods. Compared with nested models, this model has the best performance in terms of the statistical fit of in-sample data and out-of-sample volatility forecasts and VaR estimates.

CONDITIONAL EXTREME VALUES THEORY AND TAIL-RELATED RISK MEASURES: EVIDENCE FROM LATIN AMERICAN STOCK MARKETS

The purpose of this work is to extend McNeil and Frey´s (2000) methodology by combining two component GARCH models and extreme value theory to evaluate the performance of the Value at Risk (VaR) and Expected Shortfall (ES) measures in the Latin American stock markets. In-sample analysis, the results of the backtesting indicate that there is no a model that predominates to the others in the estimation of VaR at any confidence level. However, the p-values of the Kupiec test confirm the out-of-sample predictive ability of the CGARCH-EVT models to estimate the VaR for long and short financial positions from Argentina and Mexico, although their performance is insufficient to provide accurate estimates of the ES. The modeling of fat tails, asymmetry and long memory have important implications for risk management, and hedging strategies in volatile stock markets.Keywords: Conditional extreme value theory, Value at Risk, Expected Shortfall.JEL Classifications: G15, G17.DOI: https://doi.org/10.32479/ijefi.7596

Generalized extreme value distribution for value at risk analysis on gold price

Gold investment has some benefits, it’s not only safe in value but also easily stored, durable, and the rate of return is relatively stable even several years tends to rise. Gold prices give us positive and negative side depending on the different event. To managing the negative side of holding gold, the investor has to measure the risk of gold at a given period. The most popular measurement of gold investment risk is Value at Risk (VaR). Determination of inappropriate methods will make VaR calculations inaccurate. The gold’s price from year to year is suspected to have fat tail distributed (heavy tail), the Extreme Value Theory (EVT) is considered as precise methods to find VaR. In this study, the Generalized Extreme Value (GEV) approach used in EVT estimated. GEV distribution identifies extreme values based on the maximum value of each block. Test results show that monthly block usage yield VaR value is more accurate than 0,899%. It means that for one coming period with a 95% confidence level the maximum loss that investors may experience is 0.899% of the total investment.

Simulation-based Value-at-Risk for nonlinear portfolios

Value-at-risk (VaR) has been playing the role of a standard risk measure since its introduction. In practice, the delta-normal approach is usually adopted to approximate the VaR of portfolios with option positions. Its effectiveness, however, substantially diminishes when the portfolios concerned involve a high dimension of derivative positions with nonlinear payoffs; lack of closed form pricing solution for these potentially highly correlated, American-style derivatives further complicate the problem. This paper proposes a generic simulation-based algorithm for VaR estimation that can be easily applied to any existing procedures. Our proposal leverages cross-sectional information and applies variable selection techniques to simplify the existing simulation framework. Asymptotic properties of the new approach demonstrate faster convergence due to the additional model selection component introduced. We have also performed sets of numerical results that verify the effectiveness of our approach in comparison with some existing strategies.