Paper: arXiv 2510.15934

Authors: Daniela I. Flores-Silva, Miguel A. Sordo, Alfonso Suárez-Llorens

Abstract

We extend the “probability-equivalent level of VaR and CoVaR” (PELCoV) methodology to accommodate bivariate risks modeled by a Student-t copula, relaxing the strong dependence assumptions of earlier approaches and enhancing the framework’s ability to capture tail dependence and asymmetric co-movements. While the theoretical results are developed in a static setting, we implement them dynamically to track evolving risk spillovers over time. We illustrate the practical relevance of our approach through an application to the foreign exchange market, monitoring the USD/GBP exchange rate with the USD/EUR series as an auxiliary early warning indicator over the period 1999-2024. Our results highlight the potential of the extended PELCoV framework to detect early signs of risk underestimation during periods of financial stress.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper extends the probability-equivalent level of VaR and CoVaR (PELCoV) framework to bivariate Student-t copulas, overcoming limitations of strict stochastic monotonicity assumptions. The mathematical formulation is sound, and the theoretical model is implemented dynamically on FX market data (USD/GBP and USD/EUR) over a 25-year period to assess systemic risk spillovers.

Research Flowchart

  flowchart TD
    A[Research Goal: Extend PELCoV framework to Student-t copulas for FX risk monitoring] --> B[Data Inputs: Daily USD/GBP & USD/EUR FX rates 1999-2024]
    B --> C[Methodology: Model bivariate tail dependence via Student-t copula]
    C --> D[Computational Process: Dynamic rolling-window estimation of VaR & CoVaR]
    D --> E[Outcomes: Early detection of risk underestimation during financial stress]

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