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Environmental CVA with K-Robust Wrong-Way Risk

Takayuki Sakuma

Abstract

Although climate and nature related scenario analysis is increasingly important in finance, operational implementations remain limited for translating long horizon environmental scenarios into counterparty credit risk measures used in pricing and regulatory capital. We propose an environmental valuation adjustment framework for CVA with three components: (i) a scenario to credit translation that maps environmental scenario drivers into hazard rates; (ii) nature specific tail generators that quantify model risk in scenario generation; and (iii) a distributionally robust wrong way risk bound based on Kullback Leibler (KL) divergence. We compute climate CVAs using transition scenarios and nature CVAs using biodiversity indicators. Our results show that nature CVAs can vary materially across alternative ecosystem generators, highlighting an additional source of model uncertainty.

Environmental CVA with K-Robust Wrong-Way Risk

Abstract

Although climate and nature related scenario analysis is increasingly important in finance, operational implementations remain limited for translating long horizon environmental scenarios into counterparty credit risk measures used in pricing and regulatory capital. We propose an environmental valuation adjustment framework for CVA with three components: (i) a scenario to credit translation that maps environmental scenario drivers into hazard rates; (ii) nature specific tail generators that quantify model risk in scenario generation; and (iii) a distributionally robust wrong way risk bound based on Kullback Leibler (KL) divergence. We compute climate CVAs using transition scenarios and nature CVAs using biodiversity indicators. Our results show that nature CVAs can vary materially across alternative ecosystem generators, highlighting an additional source of model uncertainty.
Paper Structure (20 sections, 43 equations, 9 figures, 10 tables)

This paper contains 20 sections, 43 equations, 9 figures, 10 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Overview and notation
  4. Independence CVA
  5. KL-robust WWR
  6. Calculation of $\varepsilon$ from market co-movements
  7. Step 1: estimate a stressed dependence target.
  8. Step 2: construct $\rho_{\mathrm{equiv}}(\varepsilon)$ and the budget $\varepsilon$.
  9. Setup and results
  10. Nature CVA
  11. Construction of hazard multiplier: Reduced-form translation
  12. Construction of hazard multiplier: Two-stage transmission layer
  13. Tail generator
  14. Data sources and scenario objects
  15. Tail generator comparison: MadingleyR vs ISIMIP
  16. ...and 5 more sections

Figures (9)

  • Figure 1: Decomposition of headline CCVA into independence CCVA and the robust $\Delta^{\text{WWR}}_s(\varepsilon)$.
  • Figure 2: Marginal distortion induced by the KL-robust worst-case reweighting. The figure compares the baseline independence measure $P$ with the worst-case reweighted measure $Q^\star$ in terms of the default-time marginal distribution and the exposure marginal summarized by the EPE profile.
  • Figure 3: Sensitivity of the robust WWR to the KL radius $\varepsilon$.
  • Figure 4: Deterministic policy stress ratios $\mathrm{SR}_s(t)$ constructed from BES-SIM PREDICTS intactness.
  • Figure 5: Tail-factor distribution at year 2050 (two-sided mode). In the benchmark, MadingleyR exhibits a substantially heavier right tail than ISIMIP.
  • ...and 4 more figures