Sensitivities-based method and expected shortfall for market risk under FRTB: its impact on options risk capital


  • Carlos Alexander Grajales Universidad de Antioquia, Medellín, Colombia
  • Santiago Medina Hurtado Universidad Nacional de Colombia, Medellín, Colombia


Fundamental Review of the Trading Book (FRTB), Sensitivities-based method, Expected shortfall



This paper measures different market risk impacts on options portfolios under the new Fundamental Review of the Trading Book (FRTB) regulation, issued in Basel and coming into effect in 2023.


This paper first suggests an algorithm for implementing the FRTB standardised approach via the sensitivities-based method to estimate a portfolio's risk capital and presents an illustration applied to an option position. Second, it proposes a methodology to estimate the expected shortfall in options portfolios from the FRTB internal models approach. In this regard, an application is developed to measure expected shortfall (ES) and value at risk (VaR) impacts under FRTB versus conventional VaR in a currency option position by considering stress scenarios from the 2007–9 and 2020–1 crises and back-testing procedures.


The suggested algorithm satisfactorily captures impacts via the sensitivities-based method, and higher risk capital demands are expected for emerging economies. Also, the planned FRTB methodology to measure ES and VaR is appropriate; in particular, historical metrics perform well. Astonishingly, their revealed impacts are more significant under the 2020–1 pandemic crisis than the 2007–9 financial crisis.


The proposals developed weave a communication bridge between the standardised and internal approaches of FRTB regulation, which can be scaled up technologically and institutionally.



Download data is not yet available.


Artzner, P., Delbaen, F., Eber, J.-M. and Heath, D. (1999), “Coherent measures of risk”, Mathematical Finance, Vol. 9 No. 3, pp. 203-228.

BCBS (1996), “Supervisory framework for the use of ‘Backtesting’ in conjunction with the internal models approach to market risk capital requirements”, available at:

BCBS (2006), “Basel II: international convergence of capital measurement and capital standards: a revised framework – comprehensive version”, available at:

BCBS (2011), “Revisions to the Basel II market risk framework”, available at:

BCBS (2019), “Explanatory note on the minimum capital requirements for market risk”, available at:

BIS (2019), “Minimum capital requirements for market risk”, available at:

Chen, S.X. (2008), “Nonparametric estimation of expected shortfall”, Journal of Financial Econometrics, Vol. 6 No. 1, pp. 87-107.

Christoffersen, P.F. (1998), “Evaluating interval forecasts”, International Economic Review, Vol. 39 No. 4, pp. 841-862.

Christoffersen, P. (2012), Elements of Financial Risk Management, 2nd ed., Academic Press - Elsevier, doi: 10.1016/C2009-0-22827-3.

Colletaz, G., Hurlin, C. and Pérignon, C. (2013), “The Risk Map: a new tool for validating risk models”, Journal of Banking and Finance, Vol. 37 No. 10, pp. 3843-3854.

Daníelsson, J. and Zigrand, J.-P. (2006), “On time-scaling of risk and the square-root-of-time rule”, Journal of Banking and Finance, Vol. 30 No. 10, pp. 2701-2713.

Deng, K. and Qiu, J. (2021), “Backtesting expected shortfall and beyond”, Quantitative Finance, Vol. 21 No. 7, pp. 1109-1125.

Embrechts, P., Liu, H. and Wang, R. (2018), “Quantile-based risk sharing”, Operations Research, Vol. 66 No. 4, pp. 936-949.

Embrechts, P., Liu, H., Mao, T. and Wang, R. (2020), “Quantile-based risk sharing with heterogeneous beliefs”, Mathematical Programming, Vol. 181 No. 2, pp. 319-347.

Haas, M. (2001), New Methods in Backtesting, Financial Engineering Research Center Caesar, Bonn.

Hull, J. (2018), Risk Management and Financial Institutions, 5th ed., Wiley Finance, Hoboken, NJ.

Kliemann, L. and Sanders, P. (2016), Algorithm Engineering – Selected Results and Surveys, Springer.

Kratz, M., Lok, Y.H. and McNeil, A.J. (2018), “Multinomial VaR backtests: a simple implicit approach to backtesting expected shortfall”, Journal of Banking and Finance, Vol. 88, pp. 393-407.

Kupiec, P. (1995), “Techniques for verifying the accuracy of risk management models”, Journal of Derivatives, Vol. 3, pp. 73-84.

Laurent, J.-P., Sestier, M. and Thomas, S. (2016), “Trading book and credit risk: how fundamental is the Basel review?”, Journal of Banking and Finance, Vol. 73, pp. 211-223.

Majumder, M.T.H. and Li, X. (2018), “Bank risk and performance in an emerging market setting: the case of Bangladesh”, Journal of Economics, Finance and Administrative Science, Vol. 23 No. 46, pp. 199-229, doi: 10.1108/JEFAS-07-2017-0084.

McNeil, A.J., Frey, R. and Embrechts, P. (2005), Quantitative Risk Management: Concepts, Techniques, and Tools, Princeton University Press, Princeton, NJ.

Menéndez, S.C. and Hassani, B.K. (2021), “Expected shortfall reliability—added value of traditional statistics and advanced artificial intelligence for market risk measurement purposes”, Mathematics, Vol. 9 No. 17, doi: 10.3390/math9172142.

Nadarajah, S., Zhang, B. and Chan, S. (2014), “Estimation methods for expected shortfall”, Quantitative Finance, Vol. 14 No. 2, pp. 271-291.

Nieto, M.R. and Ruiz, E. (2016), “Frontiers in VaR forecasting and backtesting”, International Journal of Forecasting, Vol. 32 No. 2, pp. 475-501.

Orgeldinger, J. (2018), “Recent issues in the implementation of the new Basel minimum capital requirements for market risk”, Emerging Science Journal, Vol. 2 No. 2, pp. 65-77.

Patton, A.J., Ziegel, J.F. and Chen, R. (2019), “Dynamic semiparametric models for expected shortfall (and Value-at-Risk)”, Journal of Econometrics, Vol. 211 No. 2, pp. 388-413.

Pederzoli, C. and Torricelli, C. (2021), “An assessment of the fundamental review of the trading book: the capital requirement impact on a stylised financial portfolio”, International Journal of Banking, Accounting and Finance, Vol. 12 No. 4, pp. 389-403.

Porretta, P. and Agnese, P. (2021), “The fundamental review of trading book: new standard approach and risk management impacts”, Journal of Risk Management in Financial Institutions, Vol. 14 No. 2, pp. 209-219.

Rockafellar, R. and Uryasev, S. (2000), “Optimization of conditional value-at-risk”, The Journal of Risk, Vol. 2 No. 3, pp. 21-41.

Rockafellar, R. and Uryasev, S. (2002), “Conditional value-at-risk for general loss distributions”, Journal of Banking and Finance, Vol. 26 No. 7, pp. 1443-1471.

Rockafellar, R. and Uryasev, S. (2013), “The fundamental risk quadrangle in risk management, optimization and statistical estimation”, Surveys in Operations Research and Management Science, Vol. 18 Nos 1-2, pp. 33-53.

Scaillet, O. (2004), “Nonparametric estimation and sensitivity analysis of expected shortfall”, Mathematical Finance, Vol. 14 No. 1, pp. 115-129.

Serrano Bautista, R. and Núñez Mora, J.A. (2021), “Value-at-risk predictive performance: a comparison between the CaViaR and GARCH models for the MILA and ASEAN-5 stock markets”, Journal of Economics, Finance and Administrative Science, Vol. 26 No. 52, pp. 197-221, doi: 10.1108/JEFAS-03-2021-0009.

Valerio Roncagliolo, F.C. and Villamonte Blas, R.N. (2022), “Impact of financial stress in advanced and emerging economies”, Journal of Economics, Finance and Administrative Science, Vol. 27 No. 53, pp. 68-85, doi: 10.1108/JEFAS-05-2021-0063.




How to Cite

Grajales, C. A., & Medina Hurtado, S. (2023). Sensitivities-based method and expected shortfall for market risk under FRTB: its impact on options risk capital. Journal of Economics, Finance and Administrative Science, 28(55), 96–115. Retrieved from



Special section: Business Economics from Iberoamerica - Part 1