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Stressing Dynamic Loss Models

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  • Emma Kroell
  • Silvana M. Pesenti
  • Sebastian Jaimungal

Abstract

Stress testing, and in particular, reverse stress testing, is a prominent exercise in risk management practice. Reverse stress testing, in contrast to (forward) stress testing, aims to find an alternative but plausible model such that under that alternative model, specific adverse stresses (i.e. constraints) are satisfied. Here, we propose a reverse stress testing framework for dynamic models. Specifically, we consider a compound Poisson process over a finite time horizon and stresses composed of expected values of functions applied to the process at the terminal time. We then define the stressed model as the probability measure under which the process satisfies the constraints and which minimizes the Kullback-Leibler divergence to the reference compound Poisson model. We solve this optimization problem, prove existence and uniqueness of the stressed probability measure, and provide a characterization of the Radon-Nikodym derivative from the reference model to the stressed model. We find that under the stressed measure, the intensity and the severity distribution of the process depend on time and state. We illustrate the dynamic stress testing by considering stresses on VaR and both VaR and CVaR jointly and provide illustrations of how the stochastic process is altered under these stresses. We generalize the framework to multivariate compound Poisson processes and stresses at times other than the terminal time. We illustrate the applicability of our framework by considering ``what if'' scenarios, where we answer the question: What is the severity of a stress on a portfolio component at an earlier time such that the aggregate portfolio exceeds a risk threshold at the terminal time? Furthermore, for general constraints, we propose an algorithm to simulate sample paths under the stressed measure, thus allowing to compare the effects of stresses on the dynamics of the process.

Suggested Citation

  • Emma Kroell & Silvana M. Pesenti & Sebastian Jaimungal, 2022. "Stressing Dynamic Loss Models," Papers 2211.03221, arXiv.org, revised Oct 2023.
  • Handle: RePEc:arx:papers:2211.03221
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    References listed on IDEAS

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    1. Paul Glasserman & Chulmin Kang & Wanmo Kang, 2015. "Stress scenario selection by empirical likelihood," Quantitative Finance, Taylor & Francis Journals, vol. 15(1), pages 25-41, January.
    2. Bellotti, Tony & Crook, Jonathan, 2013. "Forecasting and stress testing credit card default using dynamic models," International Journal of Forecasting, Elsevier, vol. 29(4), pages 563-574.
    3. Douglas Bonett & Thomas Wright, 2000. "Sample size requirements for estimating pearson, kendall and spearman correlations," Psychometrika, Springer;The Psychometric Society, vol. 65(1), pages 23-28, March.
    4. Pesenti, Silvana M. & Millossovich, Pietro & Tsanakas, Andreas, 2019. "Reverse sensitivity testing: What does it take to break the model?," European Journal of Operational Research, Elsevier, vol. 274(2), pages 654-670.
    5. Breuer, Thomas & Jandačka, Martin & Mencía, Javier & Summer, Martin, 2012. "A systematic approach to multi-period stress testing of portfolio credit risk," Journal of Banking & Finance, Elsevier, vol. 36(2), pages 332-340.
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