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Integrating Stress Scenarios into Risk Quantification Models

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Abstract

We enhance the method of integrating scenarios proposed in Ergashev (J Financ Serv Res 41(3):145–161, 2012) into risk models. In particular, we provide additional theoretical insights of the method with focus on stress testing Value-at-Risk models. We extend the application of the method, which is originally proposed for scenario analysis in the operational risk context, to market and credit risks. We provide detailed application guidance of the method for market, credit, and operational risks. The method (i) ensures that a stressed model produces a higher risk estimate than the model based on historical data only and (ii) does not require assumptions on stressed loss distributions, thereby simplifying the scenario generation process.

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Notes

  1. We note that the scenario definition we use in the credit risk application is different from the one we use in the market and operational risks applications. Also, in the credit risk application, we stress a default rate model rather than a VaR model. For the sake of simplicity, we describe our approach using a VaR model and a scenario definition in terms of losses.

  2. Throughout the paper, we work with loss distributions to make sure that the approach is applied to the various risk areas in the same manner. For example, we treat a negative return on a portfolio as being a loss. Under this convention negative losses correspond to gains (i.e., positive returns).

  3. Stress testing is a well-known concept; however, its methodology is at the early stage of development. Crouhy et al. (2001), among many others, describe various methods of stress testing.

  4. See Basel Committee on Banking Supervision (2009).

  5. In addition to this regulatory document, there are several risk-specific regulatory documents related to stress testing requirements. For example, Final Rule (2007) requires that mandatory financial institutions incorporate scenario analysis into their operational risk assessment and quantification systems; Supervisory and regulation letter SR 10-1 (2010) provides a general guidance on stress testing interest rate risk through a wide range of yield curve scenarios.

  6. For example, consider the risk measured with the 99.9th percentile of the VaR. Augmenting the risk model with a scenario in which the loss range falls below the 99.9th percentile might actually lower the original VaR estimate. This case might occur due to the redistribution of the loss probability mass in favor of the loss range falling below the 99.9th percentile.

  7. Under a low level of the current short-term interest rate many historical year-over-year yield curve changes produce negative interest rates. These yield curve changes are economically implausible under the current yield curve environment; and therefore, we exclude them from the distribution. We also exclude year-over-year yield changes that imply negative forward rates.

  8. We do not assume a scenario with a steep yield curve where the 30-year interest rate considerably increases because rather than increase in losses, it would imply a substantial increase in interest income due to the assumed structure of the balance sheet. According to our stress testing approach, this scenario would not affect the tail of the loss distribution, and therefore would not impact the VaR estimates.

  9. While our approach seems similar to that of Boudoukh et al. (1995), it is conceptually different from that study. Boudoukh et al. (1995) suggest applying a risk measure to a random variable X in order to obtain robust risk estimates. We use expert opinion on X to adjust the estimate of the loss distribution Z and calculate a risk measure based on the adjusted loss distribution Z.

  10. Without going into the details, we note that it is also possible to stress both severity and frequency distributions simultaneously.

  11. Im et al. (2012) propose supplementing the PH survival model with a time-dependent component that captures changes in the macroeconomic and regulatory environment. Given that this model requires knowledge of the future path of the latent time-dependent component, we do not use it for the purpose of stressing future credit default rates.

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Authors and Affiliations

  1. The Federal Reserve Bank of Richmond, 530 East Trade Street, Charlotte, NC, 28202, USA

    Azamat Abdymomunov & Sharon Blei

  2. The Office of the Comptroller of the Currency, 400 7th Street SW, Washington, DC, 20024, USA

    Bakhodir Ergashev

Authors
  1. Azamat Abdymomunov
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  2. Sharon Blei
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  3. Bakhodir Ergashev
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Correspondence to Azamat Abdymomunov.

Additional information

The views expressed in this paper are those of the authors and do not necessarily reflect the position of the Federal Reserve Bank of Richmond, the Federal Reserve System, or the Office of the Comptroller of the Currency. We thank Marshal Auron, Jeremy Caldwell, Kevin Littler, Konstantin Pavlikov, Evan Sekeris, and Nathan Suwalski for helpful comments and suggestions. All remaining errors are our own.

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Abdymomunov, A., Blei, S. & Ergashev, B. Integrating Stress Scenarios into Risk Quantification Models. J Financ Serv Res 47, 57–79 (2015). https://doi.org/10.1007/s10693-014-0194-6

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  • DOI: https://doi.org/10.1007/s10693-014-0194-6

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