Abstract
When estimating the risk of a financial position with empirical data or Monte Carlo simulations via a tail-dependent law invariant risk measure such as the Conditional Value-at-Risk (CVaR), it is important to ensure the robustness of the plug-in estimator particularly when the data contain noise. Krätschmer et al. [Comparative and qualitative robustness for law invariant risk measures. Financ. Stoch., 2014, 18, 271–295.] propose a new framework to examine the qualitative robustness of such estimators for the tail-dependent law invariant risk measures on Orlicz spaces, which is a step further from an earlier work by Cont et al. [Robustness and sensitivity analysis of risk measurement procedures. Quant. Finance, 2010, 10, 593–606] for studying the robustness of risk measurement procedures. In this paper, we follow this stream of research to propose a quantitative approach for verifying the statistical robustness of tail-dependent law invariant risk measures. A distinct feature of our approach is that we use the Fortet–Mourier metric to quantify variation of the true underlying probability measure in the analysis of the discrepancy between the law of the plug-in estimator of the risk measure based on the true data and the one based on perturbed data. This approach enables us to derive an explicit error bound for the discrepancy when the risk functional is Lipschitz continuous over a class of admissible sets. Moreover, the newly introduced notion of Lipschitz continuity allows us to examine the degree of robustness for tail-dependent risk measures. Finally, we apply our quantitative approach to some well-known risk measures to illustrate our results and give an example of the tightness of the proposed error bound.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.