scholarly journals Risk Model Validation: An Intraday VaR and ES Approach Using the Multiplicative Component GARCH

Risks ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 10
Author(s):  
Ravi Summinga-Sonagadu ◽  
Jason Narsoo
Keyword(s):  
Loss Function ◽  
Value At Risk ◽  
Garch Model ◽  
Innovation Process ◽  
Expected Shortfall ◽  
Error Distribution ◽  
Garch Models ◽  
Intraday Data ◽  
Distributional Assumptions ◽  
T Distribution

In this paper, we employ 99% intraday value-at-risk (VaR) and intraday expected shortfall (ES) as risk metrics to assess the competency of the Multiplicative Component Generalised Autoregressive Heteroskedasticity (MC-GARCH) models based on the 1-min EUR/USD exchange rate returns. Five distributional assumptions for the innovation process are used to analyse their effects on the modelling and forecasting performance. The high-frequency volatility models were validated in terms of in-sample fit based on various statistical and graphical tests. A more rigorous validation procedure involves testing the predictive power of the models. Therefore, three backtesting procedures were used for the VaR, namely, the Kupiec’s test, a duration-based backtest, and an asymmetric VaR loss function. Similarly, three backtests were employed for the ES: a regression-based backtesting procedure, the Exceedance Residual backtest and the V-Tests. The validation results show that non-normal distributions are best suited for both model fitting and forecasting. The MC-GARCH(1,1) model under the Generalised Error Distribution (GED) innovation assumption gave the best fit to the intraday data and gave the best results for the ES forecasts. However, the asymmetric Skewed Student’s-t distribution for the innovation process provided the best results for the VaR forecasts. This paper presents the results of the first empirical study (to the best of the authors’ knowledge) in: (1) forecasting the intraday Expected Shortfall (ES) under different distributional assumptions for the MC-GARCH model; (2) assessing the MC-GARCH model under the Generalised Error Distribution (GED) innovation; (3) evaluating and ranking the VaR predictability of the MC-GARCH models using an asymmetric loss function.

scholarly journals Previsão de value-at-risk e expected shortfall para mercados emergentes usando modelos FIGARCH

2015 ◽  
Vol 13 (3) ◽  
pp. 394
Author(s):  
Alex Sandro Monteiro De Moraes ◽  
Antonio Carlos Figueiredo Pinto ◽  
Marcelo Cabus Klotzle
Keyword(s):  
At Risk ◽  
Long Memory ◽  
Value At Risk ◽  
Expected Shortfall ◽  
Error Distribution ◽  
Memory Models ◽  
Garch Models ◽  
Daily Data ◽  
Short Memory ◽  
Forecasting Volatility

This paper compares the performance of long-memory models (FIGARCH) with short-memory models (GARCH) in forecasting volatility for calculating value-at-risk (VaR) and expected shortfall (ES) for multiple periods ahead for six emerging markets stock indices. We used daily data from 1999 to 2014 and an adaptation of the Monte Carlo simulation to estimate VaR and ES forecasts for multiple steps ahead (1, 10 and 20 days ), using FIGARCH and GARCH models for four errors distributions. The results suggest that, in general, the FIGARCH models improve the accuracy of forecasts for longer horizons; that the error distribution used may influence the decision about the best model; and that only for FIGARCH models the occurrence of underestimation of the true VaR is less frequent with increasing time horizon. However, the results suggest that rolling sampled estimated FIGARCH parameters change less smoothly over time compared to the GARCH models.

Dependency between Risks and the Insurer’s Economic Capital: A Copula-based GARCH Model

2017 ◽  
Vol 11 (1) ◽  
Author(s):  
Jeungbo Shim ◽  
Seung-Hwan Lee
Keyword(s):  
Value At Risk ◽  
Heavy Tails ◽  
Garch Model ◽  
Joint Modeling ◽  
Market Risk ◽  
Capital Requirements ◽  
Economic Capital ◽  
Series Data ◽  
Dependence Structure ◽  
T Distribution

AbstractCopulas can be a useful tool to capture heavy-tailed dependence between risks in estimating economic capital. This paper provides a procedure of combining copula with GARCH model to construct a multivariate distribution. The copula-based GARCH model using a skewed student’s t-distribution controls for the issues of skewness, heavy tails, volatility clustering and conditional dependencies contained in the financial time series data. Using the sample of U.S. property liability insurance industry, we perform Monte Carlo simulation to estimate the insurer’s economic capital measured by Value-at-Risk (VaR) and Expected Shortfall (ES). The result indicates that the choice of dependence structure and business mix between asset classes and liability lines has a significant impact on the resulting capital requirements and diversification benefits. We find the incremental diversification benefit in terms of a reduction in the total capital requirement from the joint modeling of underwriting risk and market risk compared to the modeling of market risk only.

High-frequency analysis, Model Validation and Intraday risk metrics

2019 ◽  
Author(s):  
Ravi Summinga-Sonagadu
Keyword(s):  
Model Validation ◽  
Internal Control ◽  
High Frequency ◽  
Insurance Industry ◽  
Garch Model ◽  
Capital Requirements ◽  
Garch Models ◽  
Analysis Model ◽  
Error Distributions ◽  
Distributional Assumptions

https://www.mdpi.com/2227-9091/7/1/10 Background Despite the growing amount of research in the field of high frequency financial data analysis, few studies have focused on model validation and high-frequency risk measures. This study contributes to the literature in the following ways: A rigorous model validation, both in terms of in-sample fit and out-sample performance for the MC-GARCH model under five error distributions is provided. Statistical and graphical tests are conducted to validate the models. One component of the MC-GARCH model is the daily variance forecast. For this purpose, the GARCH(1,1) and EGARCH(1,1) under the five error distributions are compared and the best model among the 10 GARCH models is used to forecast the daily variance. The modelling and forecasting performance of the MC-GARCH model under different distributional assumptions is assessed in this study. The 99% intraday VaR is forecasted and three backtesting procedures are used. This is the first study to assess the VaR predictive ability of the MC-GARCH models by using an asymmetric VaR loss function. This is the first study to forecast the intraday expected shortfall under different distributional assumptions for the MC-GARCH model. Again, three backtests are used including the recently proposed ES regression backtest. Due to the high importance of risk management, the results of this study may contribute in many fields. This study is highly relevant to the banking industry since banks are required to calculate risk metrics on a daily basis for internal control purposes and for determining their capital requirements. Risk measurement is also essential to the insurance industry from the pricing of insurance contracts to determining the Solvency Capital Requirement (SCR) and therefore the results of this study might be useful. Any other organisation having an exposure to some kind of financial risk might benefit from this study. 

Can Lognormal, Weibull or Gamma Distributions Improve the EWS-GARCH Value-at-Risk Forecasts?

2016 ◽  
Vol 63 (3) ◽  
pp. 329-350
Author(s):  
Marcin Chlebus
Keyword(s):  
At Risk ◽  
Loss Function ◽  
Value At Risk ◽  
Empirical Distribution ◽  
Garch Models ◽  
Quadratic Loss ◽  
Empirical Distributions ◽  
Basel Committee ◽  
Gamma Distributions

In the study, two-step EWS-GARCH models to forecast Value-at-Risk are analysed. The following models were considered: the EWS-GARCH models with lognormal, Weibull or Gamma distributions as a distributions in a state of turbulence, and with GARCH(1,1) or GARCH(1,1) with the amendment to empirical distribution of random error models as models used in a state of tranquillity. The evaluation of the quality of the Value-at-Risk forecasts was based on the Value-at-Risk forecasts adequacy (the excess ratio, the Kupiec test, the Christoffersen test, the asymptotic test of unconditional coverage and the backtesting criteria defined by the Basel Committee) and the analysis of loss func-tions (the Lopez quadratic loss function, the Abad & Benito absolute loss function, the 3rd version of Caporin loss function and the function of excessive costs). Obtained results show that the EWS-GARCH models with lognormal, Weibull or Gamma distributions may compete with EWS-GARCH models with exponential and empirical distributions. The EWS-GARCH model with lognormal, Weibull or Gamma distributions are relatively less conservative, but using them is less expensive than using the other EWS-GARCH models.

scholarly journals Jump Aggregation, Volatility Prediction, and Nonlinear Estimation of Banks’ Sustainability Risk

2020 ◽  
Vol 12 (21) ◽  
pp. 8849
Author(s):  
Zhouwei Wang ◽  
Qicheng Zhao ◽  
Min Zhu ◽  
Tao Pang
Keyword(s):  
Quantile Regression ◽  
Stock Prices ◽  
Value At Risk ◽  
Stock Price ◽  
Garch Model ◽  
Jump Diffusion ◽  
Support Vector ◽  
Garch Models ◽  
Bank Stock ◽  
Better Than

Extreme financial events usually lead to sharp jumps in stock prices and volatilities. In addition, jump clustering and stock price correlations contribute to the risk amplification acceleration mechanism during the crisis. In this paper, four Jump-GARCH models are used to forecast the jump diffusion volatility, which is used as the risk factor. The linear and asymmetric nonlinear effects are considered, and the value at risk of banks is estimated by support vector quantile regression. There are three main findings. First, in terms of the volatility process of bank stock price, the Jump Diffusion GARCH model is better than the Continuous Diffusion GARCH model, and the discrete jump volatility is significant. Secondly, due to the difference of the sensitivity of abnormal information shock, the jump behavior of bank stock price is heterogeneous. Moreover, CJ-GARCH models are suitable for most banks, while ARJI-R2-GARCH models are more suitable for small and medium sized banks. Thirdly, based on the jump diffusion volatility information, the performance of the support vector quantile regression is better than that of the parametric quantile regression and nonparametric quantile regression.

scholarly journals VALUE-AT-RISK AND EXPECTED SHORTFALL FOR LINEAR PORTFOLIOS WITH ELLIPTICALLY DISTRIBUTED RISK FACTORS

2005 ◽  
Vol 08 (05) ◽  
pp. 537-551 ◽  
Author(s):  
JULES SADEFO KAMDEM
Keyword(s):  
Risk Factors ◽  
At Risk ◽  
Value At Risk ◽  
Expected Shortfall ◽  
Multivariate T Distribution ◽  
T Distribution ◽  
Multivariate T ◽  
Normally Distributed

In this paper, we generalize the parametric Δ-VaR method from portfolios with normally distributed risk factors to portfolios with elliptically distributed ones. We treat both the expected shortfall and the Value-at-Risk of such portfolios. Special attention is given to the particular case of a multivariate t-distribution.

scholarly journals PENERAPAN METODEEXPECTED SHORTFALLPADA PENGUKURAN RISIKO INVESTASI SAHAM DENGAN VOLATILITAS MODEL GARCH

2019 ◽  
Vol 8 (1) ◽  
pp. 184-193
Author(s):  
Nurul Fitria Fitria Rizani ◽  
Mustafid Mustafid ◽  
Suparti Suparti
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Stock Price ◽  
Garch Model ◽  
Expected Shortfall ◽  
Conditional Heteroskedasticity ◽  
Investment Risk ◽  
Stock Investment ◽  
Autoregressive Conditional Heteroskedasticity ◽  
High Volatility

One of the methods that can be used to measure stock investment risk is Expected Shortfall (ES). ES is an expectation of risk size which value is greater than Value at Risk (VaR), ES has characteristics of sub-additive and convex. The Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model is used to model stock data that has high volatility. Calculating ES is done with data that shows deviations from normality using Cornish-Fisher's expansion. This researchapplies the ES at the closing stock price of PT Astra International Tbk. (ASII), PT Bank Negara Indonesia (Persero) Tbk. (BBNI), and PT Indocement Tunggal Prakarsa Tbk. (INTP) for the period of 11 February 2013 - 31 March 2019. Based on the volatility of GARCH (1,1) analysis, we find ES calculation for each stock by 95% level  confidence. The ES for ASII shares is 4.1%, greater than the VaR value which isonly 2.64%.The ES for BBNI shares is 4.38%, greater than it’s VaR value which is only 2,86%. The ES for INTP shares is 6.22%, which is also greater than it’s VaR value which is only3,99%. The greather of VaR then Thegreather of ES obtained.Keywords: Expected Shortfall, Value at Risk, GARCH

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