Conditional Coverage Tests Research Articles

ESTIMASI RISIKO PASAR PADA DATA RETURN KURS HARIAN DENGAN VALUE AT RISK MENGGUNAKAN MODEL–MODEL VOLATILITAS GARCH

Volatility is a critical tool in analyzing financial data. GARCH models are common tools widely use to forecast financial data volatility. This research discusses the measurement of market risk using the Value at Risk volatility model GARCH, IGARCH, and EGARCH for the USD major currency pairs which consist of seven currency pairs with the observation period July 2016 – September 2022. The results of the analysis show that the calculation of returns does not comply with the normal distribution, so the estimation of losses using the normal distribution VaR can be biased, instead this research used student’s t distribution error. The test results show that the IGARCH volatility model at a confidence level of 99% and 95% proves to be valid after the Kupiec test and Conditional Coverage Test are carried out on all tested currencies. Meanwhile, risk measurement using the EGARCH model is invalid on the EUR/USD, USD/CHF and AUD/USD exchange rates. Besides that, risk measurement using the SGARCH model is invalid on the EUR/USD and AUD/USD exchange rates.

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

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

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

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

Estimation of value at risk for stock prices in mobile phone industry

Risk management and market losses prediction played a vital role in the financial sector. Value-at-Risk (VaR) is one of the effective measures for financial risk management. This research studies three mobile phone companies which are Apple Inc, Google Inc and Microsoft Corporation. The stocks of these companies are listed under the National Association of Securities Dealers Automated Quotations stock exchange (NASDAQ). The Value-at-Risk is evaluated by using two non-parametric methods and four parametric methods. Two non-parametric methods used are the basic historical method and age-weighted historical method, while the four parametric methods are normal distribution, student’s t-distribution, generalized extreme value distribution, and variance gamma distribution. Shapiro-Wilk normality test indicates that the return series of the selected companies are not normally distributed. This study found that, at 95% confidence level, the risks of the selected stocks are different for each method, and the stock of Microsoft Corporation is the least risky stock as it gives the lowest VaR. Through the conditional coverage test, this study founds that the age-weighted historical method overestimated the VaR. In addition, this study also concludes that the basic historical method, generalized extreme value distribution and variance gamma distribution are superior to other methods in the backtesting procedure.

Modelling the Volatility of Central Bank of Kenya Currency Exchange Rates

In emerging countries, such as Kenya, the foreign exchange market is an important aspect in the economic development of a country. The currency exchange rate market, like the rest of the world's financial markets, has been marked by considerable instabilities over the last decade. The objective of this paper is to model the volatility of the KSH/USD exchange rate prices using and calculate the VaR using the GARCH-EVT model. In particular, this article uses the two-stage GARCH-EVT approach to estimate the value at risk of the Kenyan Shilling against the US dollar., particularly the one-day ahead Value-at-Risk forecast in risk control. The conditional and unconditional coverage test are used to back test the model. We compare the performance of the GARCH-EVT with the daily log returns of key currency in addition to modelling the value at risk in the Kenyan Foreign Exchange market (US dollar) foreign currencies from the period November 2004 – June 2021 for trading days with the exception of holidays and weekends. The mean equation that was best fitting for the data was ARMA (4,2). The optimal GARCH model for the returns of the KSH/USD exchange rate is the GARCH (1,3) with student-t innovations. The results of the backtesting show that GARCH-EVT can be utilized to estimate and forecast VaR at both 5% and 1% level of significance.

Research on RMB Exchange Rate Volatility Risk Based on MSGARCH-VaR Model

This paper captures the RMB exchange rate volatility using the Markov-switching GARCH (MSGARCH) models and traditional single-regime GARCH models. Through the Markov Chain Monte Carlo (MCMC) method, the model parameters are estimated to study the volatility dynamics of the RMB exchange rate. Furthermore, we compare the MSGARCH models to the single-regime GARCH specifications in terms of Value-at-Risk (VaR) prediction accuracy. According to the Deviance information criterion method, the research shows that MSGARCH models outperform the single-regime specifications in capturing the complexity of RMB exchange rate volatility. After the RMB exchange rate reform in 2015, the volatility is more asymmetric and persistent, and the probability of being in the turbulent volatility regime is significantly increased. The continuous escalation of Sino-US trade friction has increased the VaR of RMB exchange rate log-returns. From the evaluation results of the actual over expected exceedance ratio (AE), the conditional coverage (CC) test, and the dynamic quantile (DQ) test, we find strong evidence that two-regime MSGARCH models could forecast VaR more accurately, which provides practical value for China’s foreign exchange management authorities to manage the financial risk.

Real estate VaR estimation in Seoul and Busan, Korea

In this study, we estimtate the value-at-risk (VaR) of the 10-day average apartment prices of Gangnam-gu, Seoul and Haeundae-gu, Busan in Korea. For this purpose, we adopt the semiparametric quantile regression approach for the VaR calculation based on ARIMA-GARCH models, employing the well-known risk measures such as the conditional autoregressive value-at-risk (CAViaR) and conditional autoregressive expectile (CARE) methods. After conducting the unconditional coverage (UC) and conditional coverage (CC) tests on the estimated VaRs, we conclude that the two methods perform similarly for the Seoul case but the CARE method shows more stability than the CAViaR method in the Busan case.

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.

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.

The Optimal Confidence Intervals for Agricultural Products’ Price Forecasts Based on Hierarchical Historical Errors

With the levels of confidence and system complexity, interval forecasts and entropy analysis can deliver more information than point forecasts. In this paper, we take receivers’ demands as our starting point, use the trade-off model between accuracy and informativeness as the criterion to construct the optimal confidence interval, derive the theoretical formula of the optimal confidence interval and propose a practical and efficient algorithm based on entropy theory and complexity theory. In order to improve the estimation precision of the error distribution, the point prediction errors are STRATIFIED according to prices and the complexity of the system; the corresponding prediction error samples are obtained by the prices stratification; and the error distributions are estimated by the kernel function method and the stability of the system. In a stable and orderly environment for price forecasting, we obtain point prediction error samples by the weighted local region and RBF (Radial basis function) neural network methods, forecast the intervals of the soybean meal and non-GMO (Genetically Modified Organism) soybean continuous futures closing prices and implement unconditional coverage, independence and conditional coverage tests for the simulation results. The empirical results are compared from various interval evaluation indicators, different levels of noise, several target confidence levels and different point prediction methods. The analysis shows that the optimal interval construction method is better than the equal probability method and the shortest interval method and has good anti-noise ability with the reduction of system entropy; the hierarchical estimation error method can obtain higher accuracy and better interval estimation than the non-hierarchical method in a stable system.

Daily value-at-risk modeling and forecast evaluation: The realized volatility approach

One of the main applications of conditional volatility modeling and forecasting of financial assets is the value-at-risk (VaR) estimation that is used by financial institutions for reporting the daily capital in risk. It remains a question on whether realized volatility (RV) models that incorporate the use of intraday data produce better VaR forecasts compared to methodologies that are based solely on daily returns. This study provides extensive comparison of out-of-sample volatility and VaR forecast performance on three equity market indices: S&P500, FTSE100, and DAX30 using 13 risk models that consist of 5 GARCH specifications, 4 ARFIMAX specifications and 4 HARX specifications. The out-of-sample volatility forecasts are evaluated by various loss functions and simple scoring procedures in order to identity the model that produces the overall best volatility forecasts. For VaR forecasts, the models are evaluated using a two-stage backtesting procedure where the models undergo unconditional and conditional coverage tests to eliminate underperforming models and the qualified models are then evaluated using the quadratic probability score (QPS) function that is computed based on various VaR loss functions. The results showed that RV models outperform GARCH models for volatility forecasts, but a simple EGARCH model outperforms the rest models for most of the VaR forecasts. The results also indicated that capturing the asymmetric behavior of volatility dynamics is essential for accurate volatility and VaR forecasts. The findings of this study provide useful information for market risk regulation, financial risk management and further investigations such as extension to derivative markets and options pricing.

조건부 Value-at-Risk와 Expected Shortfall 추정을 위한 준모수적 방법들의 비교 연구

Basel committee suggests using Value-at-Risk (VaR) and expected shortfall (ES) as a measurement for market risk. Various estimation methods of VaR and ES have been studied in the literature. This paper compares semi-parametric methods, such as conditional autoregressive value at risk (CAViaR) and conditional autoregressive expectile (CARE) methods, and a Gaussian quasi-maximum likelihood estimator (QMLE)-based method through back-testing methods. We use unconditional coverage (UC) and conditional coverage (CC) tests for VaR, and a bootstrap test for ES to check the adequacy. A real data analysis is conducted for S&P 500 index and Hyundai Motor Co. stock price index data sets.

Measuring Extreme Market Risk: The Sri Lankan Context

Abstract Many empirical studies have been carried out in developed and emerging markets using methods to account for extreme market risk. A front-runner in the methods used is Extreme Value Theory (EVT). In this study, these methods are applied to the All Share Price Index (ASPI) of the Colombo Stock Exchange (CSE) to obtain risk forecasts for VaR (Value at Risk) and ES (Expected Shortfall) at 99% confidence level. Recognizing the merits of both conditional and unconditional models for risk measures the most suitable unconditional model and conditional model are found for the ASPI. Contrary to other studies the Historical Simulation method was found to be more appropriate for obtaining static estimates than the static EVT model. The Two-Step Approach of McNeil and Frey which combines EVT and Generalized Auto-Regressive Conditional Heteroskedasticity (GARCH) methodologies was found to be the most appropriate conditional model. Backtesting of models is done using a binomial test, Christoferssen’s conditional coverage test and McNeil and Frey’s ES test.

Predicting Conditional Autoregressive Value-at-Risk for Stock Markets during Tranquil and Turbulent Periods

This paper analyzes the predictive performance of the Conditional Autoregressive Value at Risk (CAViaR) developed by Engle & Manganelli (2004) for major equity markets during tranquil and turbulent periods. The CAViaR model shifts the focus of attention from the distribution of returns directly to the behaviour of the quantile. We compare the predictive performance of four alternative CAViaR specifications, namely Adaptive, Symmetric Absolute Value, Asymmetric Slope and Indirect GARCH(1,1) models due to Engle & Manganelli (2004) along with the improved asymmetric CAViaR (I-CAViaR) model due to Huang et al. (2009). We employ daily returns for six stock markets indices, namely S & P500, FTSE100, NIKKEI225, DAX30, CAC40 and Athens Exchange General index for the period January 2, 1995 to August 23, 2013. We compare the predictive performance of the alternative specifications for three subperiods: before, during and after the recent 2007-2009 financial crisis. The comparison is done with the use of a battery of tests which includes unconditional and conditional coverage tests, the Dynamic Quantile high-order independence test and the White (2000) empirical coverage probability and predictive quantile loss tests. The main findings of the present analysis is that the CAViaR quantile regression models and the I-CAViaR model have shown significant success in predicting the VaR measure for various periods although this performance varies over the three periods before, during and after the 2007-2009 financial crisis.

The information content of the VDAX volatility index and backtesting daily value-at-risk models

This paper examines the information content of the new VDAX volatility index to forecast daily value-at-risk (VaR) estimates and compares its VaR forecasts with the VaR forecasts of the asymmetric GARCH model of Glosten, Jagannathan and Runkle (GJR) (1993) and RiskMetrics model. The performance of the daily VaR models is evaluated both in-sample and out-of-sample using unconditional coverage, independence, and conditional coverage tests. We find that the information content of implied volatility is superior to that of historical volatility for the daily VaR forecasts of a portfolio of the DAX 30 stock index. Backtesting results suggest the following rank for our VaR models, from best to worst, GJR-GARCH(1, 1) augmented with implied volatility, implied volatility, GJR-GARCH(1, 1), and RiskMetrics. Our findings have implications for traders, risk managers and regulators.

Extreme Risk, Value-At-Risk And Expected Shortfall In The Gold Market

Extreme value theory (EVT) has been widely applied in fields such as hydrology and insurance. It is a tool used to reflect on probabilities associated with extreme, and thus rare, events. EVT is useful in modeling the impact of crashes or situations of extreme stress on investor portfolios. It describes the behavior of maxima or minima in a time series, i.e., tails of a distribution. In this paper, we propose the use of generalised Pareto distribution (GPD) to model extreme returns in the gold market. This method provides effective means of estimating tail risk measures such as Value-at-Risk (VaR) and Expected Shortfall (ES). This is confirmed by various backtesting procedures. In particular, we utilize the Kupiec unconditional coverage test and the Christoffersen conditional coverage test for VaR backtesting, while the Bootstrap test is used for ES backtesting. The results indicate that GPD is superior to the traditional Gaussian and Students t models for VaR and ES estimations.

Evaluating the accuracy of value-at-risk forecasts: New multilevel tests

We propose independence and conditional coverage tests which are aimed at evaluating the accuracy of Value-at-Risk (VaR) forecasts from the same model at different confidence levels. The proposed procedures are multilevel tests, i.e., joint tests of several quantiles corresponding to different confidence levels. In a comprehensive Monte Carlo exercise, we document the superiority of the proposed tests with respect to existing multilevel tests. In an empirical application, we illustrate the implementation of the tests using several VaR models and daily data for 15 MSCI world indices.

Out of sample value-at-risk and backtesting with the standardized pearson type-IV skewed distribution

This paper studies the efficiency of an econometric model where the volatility is modeled by a GARCH (1,1) process, and the innovations follow a standardized form of the Pearson type-IV distribution. The performance of the model is examined by in sample and out of sample testing, and the accuracy is explored by a variety of Value-at-Risk methods, the success/failure ratio, the Kupiec-LR test, the independence and conditional coverage tests of Christoffersen, the expected shortfall measures, and the dynamic quantile test of Engle and Manganelli. Overall, the proposed model is a valid and accurate model performing better than the skewed Student-t distribution, providing the financial analyst with a good candidate as an alternative distributional scheme.

IMPLEMENTING A ROBUST RISK MODEL FOR SOUTH AFRICAN EQUITY MARKETS: A PEAK‐OVER‐THRESHOLD APPROACH

AbstractThis paper implements a market risk model for the South African equity market using daily returns of the Johannesburg Stock Exchange All Share Index. Firstly, we separate positive returns from negative returns and model them using the peak‐over‐threshold (POT) method in order to compute the downside as well as upside risk measures separately. We thereafter compute the value‐at‐risk (VAR) and the expected shortfall (ES) estimates corresponding to upside and downside risks. We bootstrap these risk measures and compute their standard errors and confidence intervals (CIs) to see whether they fall inside these CIs. Secondly, we compute out‐sample forecasts of VAR estimates using the POT method and the generalised autogressive conditional heteroscedasticity process. Three backtesting methodologies are employed: the unconditional and conditional coverage tests and the counting of number of exceptions according to Basel II green zone. We find that all our VAR and ES estimates are well inside their CIs and that at lower quantiles, parametric ES estimates are equal to POT‐ES estimates, although the difference between the two is more pronounced at higher quantiles (99% or higher). Furthermore, our market risk model falls into the Basel II green zone, as it produces fewer exceptions in out‐sample space.

Evaluation of Basel III revision of quantitative standards for implementation of internal models for market risk

This paper studies revisions under Basel III for market risk which allow conservative combination of short and long period Value-at-Risks (VaRs). This is the first study that examines this issue. The performance of the combination method is evaluated through regulatory back tests, unconditional and conditional coverage tests. The combination improves performance in regulatory back tests and tests of unconditional coverage. A common trend is the superior performance of long (1000/750 day) in combination with short (190/125 days) VaR methods. The combination does not enhance conditional coverage performance. This is the first study on this topic.