Reverse Sensitivity Analysis for Risk Modelling

Pesenti, Silvana M.

doi:10.3390/risks10070141

Cited by 9 publications

(6 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As future work, it is expected to generalize the proposed methodology to Distortion Risk Measure and Coherent Distortion Risk Measure, such as those investigated in Wang et al (2020) and Pesenti (2022). Among other possible extensions of our paper, one could introduce new risk indicators as the high-order TCE risk measure studied in Faroni et al (2022).…”

Section: Discussionmentioning

confidence: 91%

“…In this case, the well-studied Wasserstein metric supports the method and provides fundamental connections for the rising concept of barycenter, in the sense of Agueh and Carlier (2011); this is considered seminal for a number of generalizations and applications (see, e.g., Bigot et al (2018), Álvarez Esteban et al (2018), Le Gouic and Loubes (2017), and the references therein). The Wasserstein metric has notably enriched the risk management literature (see, e.g., Feng and Erik (2018), Wang et al (2020), Pesenti (2022), and Liu and Liu (2022)).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Multi-Variate Risk Measures under Wasserstein Barycenter

Serna

Loubes

Caro-Lopera

2022

Risks

View full text Add to dashboard Cite

When the uni-variate risk measure analysis is generalized into the multi-variate setting, many complex theoretical and applied problems arise, and therefore the mathematical models used for risk quantification usually present model risk. As a result, regulators have started to require that the internal models used by financial institutions are more precise. For this task, we propose a novel multi-variate risk measure, based on the notion of the Wasserstein barycenter. The proposed approach robustly characterizes the company’s exposure, filtering the partial information available from individual sources into an aggregate risk measure, providing an easily computable estimation of the total risk incurred. The new approach allows effective computation of Wasserstein barycenter risk measures in any location–scatter family, including the Gaussian case. In such cases, the Wasserstein barycenter Value-at-Risk belongs to the same family, thus it is characterized just by its mean and deviation. It is important to highlight that the proposed risk measure is expressed in closed analytic forms which facilitate its use in day-to-day risk management. The performance of the new multi-variate risk measures is illustrated in United States market indices of high volatility during the global financial crisis (2008) and during the COVID-19 pandemic situation, showing that the proposed approach provides the best forecasts of risk measures not only for “normal periods”, but also for periods of high volatility.

show abstract

Section: Discussionmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Multi-Variate Risk Measures under Wasserstein Barycenter

Serna

Loubes

Caro-Lopera

2022

Risks

View full text Add to dashboard Cite

show abstract

“…In this work, we quantify the distance between the alternative distribution function and the reference distribution via the Wasserstein distance of order 2. The Wasserstein distance has been widely applied to model distributional uncertainty in financial contexts (see, e.g., Bartl et al, 2020, Chen & Xie, 2021, and Pflug & Wozabal, 2007, and as a distance from reference model (see e.g., Pesenti, 2022 andPesenti &Jaimungal, 2023).…”

Section: Introductionmentioning

confidence: 99%

Robust distortion risk measures

Bernard

Pesenti

Vanduffel

2023

Mathematical Finance

Self Cite

View full text Add to dashboard Cite

The robustness of risk measures to changes in underlying loss distributions (distributional uncertainty) is of crucial importance in making well‐informed decisions. In this paper, we quantify, for the class of distortion risk measures with an absolutely continuous distortion function, its robustness to distributional uncertainty by deriving its largest (smallest) value when the underlying loss distribution has a known mean and variance and, furthermore, lies within a ball—specified through the Wasserstein distance—around a reference distribution. We employ the technique of isotonic projections to provide for these distortion risk measures a complete characterization of sharp bounds on their value, and we obtain quasi‐explicit bounds in the case of Value‐at‐Risk and Range‐Value‐at‐Risk. We extend our results to account for uncertainty in the first two moments and provide applications to portfolio optimization and to model risk assessment.

show abstract

“…In a discrete and static setting, Cambou and Filipović (2017) use the f -divergence to incorporate constraints on events, which they term "views", while Makam, Millossovich, and Tsanakas (2021) consider the χ 2divergence and a constraint on the expected value of a risk factor. For general but static models, Pesenti, Millossovich, and Tsanakas (2019) and Pesenti (2022) consider stresses defined via changes in risk measures such as Value-at-Risk (VaR), distortion risk measures, and expected utilities, using the Kullback-Leibler (KL) and the Wasserstein distance, respectively. This work generalizes the reverse stress testing approach to a dynamic setting.…”

Section: Introductionmentioning

confidence: 99%

Stressing Dynamic Loss Models

Emma¹,

Pesenti²,

Jaimungal³

2022

Preprint

View full text Add to dashboard Cite

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 the state space. 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? Moreover, for general constraints, we provide a simulation algorithm to simulate sample paths under the stressed measure.

show abstract

Reverse Sensitivity Analysis for Risk Modelling

Cited by 9 publications

References 38 publications

Multi-Variate Risk Measures under Wasserstein Barycenter

Multi-Variate Risk Measures under Wasserstein Barycenter

Robust distortion risk measures

Stressing Dynamic Loss Models

Contact Info

Product

Resources

About