DOI : https://doi.org/10.18517/ijaseit.15.3.20197

Advancing Risk Management with GAS-1F: Value at Risk and Expected Shortfall Estimation

Fevi Novkaniza (1), Irene Patricia Wibowo (2), Rahmat Al Kafi (3)
(1) Department of Mathematics, Universitas Indonesia, Depok, Jawa Barat, Indonesia
(2) Department of Mathematics, Universitas Indonesia, Depok, Jawa Barat, Indonesia
(3) Department of Mathematics, Universitas Indonesia, Depok, Jawa Barat, Indonesia
Fulltext View | Download
How to cite (IJASEIT) :
[1]
F. Novkaniza, I. P. Wibowo, and R. Al Kafi, “Advancing Risk Management with GAS-1F: Value at Risk and Expected Shortfall Estimation”, Int. J. Adv. Sci. Eng. Inf. Technol., vol. 15, no. 3, pp. 887–893, Jun. 2025.
Citation Format :
Value at Risk (VaR) and Expected Shortfall (ES) are critical metrics for quantifying financial risk. VaR estimates the maximum potential loss within a specific timeframe, while ES captures the average loss that exceeds the VaR threshold. Accurate estimation of these risk measures is vital for financial institutions; however, traditional methods often falter in addressing the dynamic volatility of financial data. This study explores the One-Factor Generalized Autoregressive Score (GAS-1F) semiparametric model, a novel approach that incorporates elicitability into its score function to circumvent distributional assumptions. Elicitability guarantees alignment between the estimated loss function and the true underlying risk measure. The GAS-1F model excels as a two-tiered, semiparametric framework for estimating VaR and ES. By applying this model to historical data from the S&P 500 index, we demonstrate its effectiveness in estimating these risk metrics. The model operates in two stages: first, it estimates the volatility of the data, reflecting the extent of price fluctuations. This estimated volatility is then utilized to calculate VaR and ES for each data point, generating a time series of daily values that offer a comprehensive view of potential risks investors face. The Diebold-Mariano test reveals that the GAS-1F model achieves superior accuracy compared to the widely used GARCH parametric model in estimating VaR and ES for stock prices. This enhanced accuracy can significantly benefit financial institutions, providing informed risk management decisions and valuable insights for short-term investors, particularly day traders, by facilitating more effective risk management strategies.

P. Owusu Junior and I. Alagidede, "Risks in emerging markets equities: Time-varying versus spatial risk analysis," Physica A, Stat. Mech. Appl., vol. 542, p. 123474, 2020, doi:10.1016/j.physa.2019.123474.

L. Merlo, L. Petrella, and V. Raponi, "Forecasting VaR and ES using a joint quantile regression and its implications in portfolio allocation," J. Bank. Financ., vol. 133, p. 106248, 2021, doi:10.1016/j.jbankfin.2021.106248.

J. W. Taylor, "Forecasting Value at Risk and expected shortfall using a model with a dynamic omega ratio," J. Bank. Financ., vol. 140, p. 106519, 2022, doi: 10.1016/j.jbankfin.2022.106519.

A. Naimoli, "The information content of sentiment indices in forecasting Value at Risk and Expected Shortfall: A Complete Realized Exponential GARCH-X approach," Int. Econ., vol. 176, p. 100459, 2023, doi: 10.1016/j.inteco.2023.100459.

E. Lazar, J. Pan, and S. Wang, "On the estimation of Value-at-Risk and Expected Shortfall at extreme levels," J. Commodity Markets, vol. 34, p. 100391, 2024, doi: 10.1016/j.jcomm.2024.100391.

P. Mahisi and B. Usman, "The Effect of Basel III Liquidity, Credit Risk, and Market Risk on the Profitability of Commercial Banks in Indonesia," Indones. Interdiscip. J. Sharia Econ., vol. 7, no. 2, pp. 1–15, Jun. 2024.

R. Rockafellar and S. Uryasev, "Optimization of Conditional Value-At-Risk," J. Risk, vol. 2, pp. 21–42, Oct. 2000, doi:10.21314/jor.2000.038.

M. M. Manguzvane and S. B. Ngobese, "A Component Expected Shortfall Approach to Systemic Risk: An Application in the South African Financial Industry," Int. J. Financ. Stud., vol. 11, no. 4, pp. 1–20, 2023, doi: 10.3390/ijfs11040146.

M. Barczy, F. K. Nedényi, and L. Sütő, "Probability equivalent level of Value at Risk and higher-order Expected Shortfalls," Insur. Math. Econ., vol. 108, pp. 107–128, 2023, doi:10.1016/j.insmatheco.2022.11.004.

L. Catania and A. Luati, "Quasi maximum likelihood estimation of Value at Risk and Expected Shortfall," Econom. Stat., vol. 33, pp. 23-34, Jan. 2025, doi: 10.1016/j.ecosta.2021.08.003.

Z. De Khoo, K. H. Ng, Y. B. Koh, and K. H. Ng, "Forecasting volatility of stock indices: Improved GARCH-type models through combined weighted volatility measure and weighted volatility indicators," N. Amer. J. Econ. Finance, vol. 71, p. 102112, 2024, doi:10.1016/j.najef.2024.102112.

R. V. Ivanov, "On the Stochastic Volatility in the Generalized Black-Scholes-Merton Model," Risks, vol. 11, no. 6, pp. 1–20, 2023, doi:10.3390/risks11060111.

S. Song and H. Li, "A method for predicting VaR by aggregating generalized distributions driven by the dynamic conditional score," Quart. Rev. Econ. Finance, vol. 88, pp. 203–214, 2023, doi:10.1016/j.qref.2023.01.006.

E. Tsionas and S. Kumbhakar, "Stochastic frontier models with time-varying conditional variances," Eur. J. Oper. Res., vol. 292, pp. 1–15, Oct. 2020, doi: 10.1016/j.ejor.2020.11.008.

T. Bollerslev, "On the correlation structure for the generalized autoregressive conditional heteroskedastic process," J. Time Ser. Anal., vol. 9, no. 2, pp. 121-131, Mar. 1988, doi: 10.1111/j.1467-9892.1988.tb00459.x.

P. Owusu Junior, A. K. Tiwari, G. Tweneboah, and E. Asafo-Adjei, "GAS and GARCH based value-at-risk modeling of precious metals," Resour. Policy, vol. 75, p. 102456, 2022, doi:10.1016/j.resourpol.2021.102456.

D. Bogdan, D. Ş. Maria, and I. Roxana, "A Value-at-Risk forecastability indicator in the framework of a Generalized Autoregressive Score with 'Asymmetric Laplace Distribution'," Financ. Res. Lett., vol. 45, p. 102134, 2022, doi:10.1016/j.frl.2021.102134.

D. Creal, S. J. Koopman, and A. Lucas, "Generalized Autoregressive Score Models with Applications," J. Appl. Econom., vol. 28, pp. 1–20, Oct. 2013, doi: 10.1002/jae.1279.

S. Contreras-Espinoza, C. Caamaño-Carrillo, and J. E. Contreras-Reyes, "Generalized autoregressive score models based on sinh-arcsinh distributions for time series analysis," J. Comput. Appl. Math., vol. 423, p. 114975, 2023, doi: 10.1016/j.cam.2022.114975.

M. Hallin and C. Trucíos, "Forecasting value-at-risk and expected shortfall in large portfolios: A general dynamic factor model approach," Econom. Stat., vol. 27, pp. 1–15, 2023, doi:10.1016/j.ecosta.2021.04.006.

T. Dimitriadis, T. Fissler, and J. Ziegel, "Osband's principle for identification functions," Stat. Papers, vol. 65, no. 2, pp. 1125–1132, 2024, doi: 10.1007/s00362-023-01428-x.

T. Fissler and J. Ziegel, "Higher order elicitability and Osband's principle," Ann. Statist., vol. 44, no. 4, pp. 1680–1707, Oct. 2016, doi:10.1214/16-AOS1439.

E. Lazar and X. Xue, "Forecasting risk measures using intraday data in a generalized autoregressive score framework," Int. J. Forecast., vol. 36, no. 3, pp. 1057–1072, 2020, doi:10.1016/j.ijforecast.2019.10.007.

F. Zhang, Y. Xu, and C. Fan, "Nonparametric inference of expectile-based value-at-risk for financial time series with application to risk assessment," Int. Rev. Financ. Anal., vol. 90, p. 102852, 2023, doi:10.1016/j.irfa.2023.102852.

G. Storti and C. Wang, "Nonparametric expected shortfall forecasting incorporating weighted quantiles," Int. J. Forecast., vol. 38, no. 1, pp. 224–239, 2022, doi: 10.1016/j.ijforecast.2021.04.004.

A. J. Patton, J. F. Ziegel, and R. Chen, "Dynamic semiparametric models for expected shortfall (and Value-at-Risk)," J. Econom., vol. 211, no. 2, pp. 388–413, 2019, doi: 10.1016/j.jeconom.2018.10.008.

M. Tabasi, J. M. Rose, A. Pellegrini, and T. H. Rashidi, "An empirical investigation of the distribution of travellers' willingness-to-pay: A comparison between a parametric and nonparametric approach," Transp. Policy, vol. 146, pp. 312–321, 2024, doi:10.1016/j.tranpol.2023.12.006.

A. J. Patton and K. Sheppard, "Evaluating Volatility and Correlation Forecasts," in Handbook of Financial Time Series, T. Mikosch, J.-P. Kreiß, R. A. Davis, and T. G. Andersen, Eds. Berlin, Germany: Springer, 2009, pp. 801–838, doi: 10.1007/978-3-540-71297-8_36.

N. Nolde and J. F. Ziegel, "Elicitability and backtesting: Perspectives for banking regulation," Ann. Appl. Stat., vol. 11, no. 4, pp. 1833–1874, 2017, doi: 10.1214/17-AOAS1041.

B. Zhang, F. Chen, J. Jiao, F. Pei, and W. Zhang, "Fuel cell parameter analysis and constraint optimization based on Nelder-Mead simplex algorithm considering performance degradation," Int. J. Hydrogen Energy, vol. 69, pp. 1548–1564, 2024, doi:10.1016/j.ijhydene.2024.05.105.

X. Liu, Y. Wang, W. Du, and Y. Ma, "Economic policy uncertainty, oil price volatility and stock market returns: Evidence from a nonlinear model," N. Amer. J. Econ. Finance, vol. 62, p. 101777, 2022, doi:10.1016/j.najef.2022.101777.

J. Caiado and F. Lúcio, "Stock market forecasting accuracy of asymmetric GARCH models during the COVID-19 pandemic," N. Amer. J. Econ. Finance, vol. 68, p. 101971, 2023, doi:10.1016/j.najef.2023.101971.

J. Bai, S. H. Choi, and Y. Liao, "Standard errors for panel data models with unknown clusters," J. Econom., vol. 240, no. 2, Mar. 2024, doi:10.1016/j.jeconom.2020.08.006.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Authors who publish with this journal agree to the following terms:

    1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
    2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
    3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).