Climate transition risk in the yield curve and in corporate credit spreads

This project projects the US Treasury yield curve and sector credit spreads to 2100 under the Shared Socioeconomic Pathways (SSP). It asks how much of the climate-transition repricing of corporate debt runs through the risk-free curve and how much through credit spreads.

Capstone project of the Executive Master Quantitative Methods for Climate Risk, École Polytechnique. This is version 2, a full rebuild of the original notebooks: see the changelog for the audit of v0.1 and what changed. The original version is tagged v0.1-capstone.

Key findings

Numbers come from results/README.md, generated by the pipeline.

1. The socio-economic pathway matters far more for the risk-free curve than climate policy.
   • By 2050 the expected 10-year yield ranges from 2.1% (SSP3) to 4.8% (SSP5), against 3.7% in the reference pathway.
   • The 1.5°C policy within SSP2 (SSP2-1.9) moves it by +10 bp in 2030 and −8 bp in 2050. Carbon pricing lifts short rates while the carbon bill catches up with the pathway's level, and slightly lower growth lowers r*.
2. Pricing the transition today widens oil & gas spreads; utilities can gain.
   • Under SSP2-1.9 the 10-year climate spread is +59 bp for oil & gas producers: 19–159 bp across the plausible range of the asset-to-output elasticity.
   • It is −7 bp for utilities, whose low-carbon business grows with electrification.
   • It is −2 bp for the low-carbon control group, a pure risk-free (drift) effect.
   • The utility result depends on the integrated assessment model: +59 bp under IMAGE (SSP1-1.9) and +7 bp under REMIND (SSP5-1.9).
3. Waiting is expensive. If the same transition is priced only in 2035, the oil & gas 10-year climate spread is 129 bp; if only in 2050, 222 bp. This is the "climate Minsky moment" of Battiston & Monasterolo.
4. The yield-curve channel matters for every issuer, and its sign depends on the central bank.
   • At revelation the 10-year Treasury yield reprices by +6 bp. This uses the expectations hypothesis, consistently with the projections.
   • That costs a 10-year bond 0.6%: about one tenth of the loss on an oil & gas bond (−6.4%), enough to cancel the small credit gain of utilities (+0.1% in total), and the whole loss on low-carbon bonds (−0.45% in total, as the higher drift lowers their default risk).
   • If the central bank looks through carbon-price inflation, the repricing is −4.5 bp instead; if the carbon bill catches up with the pathway by 2040 rather than 2050, +16 bp.
5. Portfolio tail risk. For an equally weighted portfolio of 65 issuers over five years, the 99% Expected Shortfall rises from 23.9% to 26.1% of notional under SSP2-1.9. This uses physical PDs and a t-copula calibrated on CDS co-movements (ν = 14.4). The relative increase, 9–13%, holds across dependence specifications, including the Basel IRB benchmark (12.5% → 14.2%).

Every assumption behind these numbers (θ, κ, χ, σ_A, the harmonisation convergence year) is varied one at a time in the sensitivity tables.

More figures (fit diagnostics, backtest, fan chart, delayed revelation, IAM uncertainty, portfolio) are in results/figures/.

Method

flowchart LR
    subgraph Rates["Risk-free curve"]
        GSW["GSW zero curves<br/>1986–2026"] --> NS["Nelson–Siegel<br/>one λ"]
        HLW["r* (HLW) + π* (Cleveland Fed)"] --> SE["Shifting-endpoint<br/>VAR(1)"]
        NS --> SE
        SSP["SSP scenarios<br/>(IIASA)"] --> END["Scenario endpoint<br/>growth → r*, carbon price → short rate"]
        SE --> MC["Monte Carlo to 2100"]
        END --> MC
    end
    subgraph Credit["Credit"]
        CDS["CDS 1–10y<br/>2015–2019"] --> BOOT["Hazard bootstrap<br/>Merton σ_A"]
        SSP --> BM["Battiston–Monasterolo<br/>sector output shock"]
        BOOT --> CS["Climate spreads"]
        BM --> CS
    end
    MC --> BV["Bond repricing:<br/>risk-free vs credit"]
    CS --> BV
    CDS --> COP["t-copula<br/>(Kendall τ, ν by ML)"]
    CS --> PF["Portfolio VaR / ES"]
    COP --> PF

Loading

Risk-free curve.

• Factors. Nelson–Siegel factors are estimated with one decay parameter (Diebold & Li, 2006), on Gürkaynak–Sack–Wright zero-coupon yields.
• Dynamics. The level is split into the nominal natural rate i* = r* + π* and a stationary cycle modelled by a VAR(1) (Bauer & Rudebusch, 2020).
• Scenario channel. Each scenario moves the endpoint through two channels:
  • its growth differential with the reference pathway, at the HLW elasticity θ = 1.113;
  • its carbon-price inflation impulse on the short rate, through the Taylor principle.
• Expectations hypothesis. Scenario effects enter yields as an expectations-hypothesis overlay of the scenario's short-rate path, used both in the projections and in bond repricing.
• Harmonisation. All scenarios are harmonised to the September 2026 jump-off.

Credit.

• Baseline. Risk-neutral default probabilities are bootstrapped from sector-median CDS curves.
• Shock. The Battiston & Monasterolo (2020) climate-policy shock maps sector output in the policy scenario, relative to the baseline of the same IAM, into a Merton default-threshold shift. The risk-free repricing $\Delta y$ moves the same threshold: $q_P = \Phi\big(\Phi^{-1}(q_B) - [\ln(1+\xi) + T\Delta y]/(\sigma_A\sqrt T)\big)$.

Portfolio.

• Default dependence. It comes from Kendall's τ of weekly CDS changes (ρ = sin(πτ/2)), with a t-copula whose ν is estimated by pseudo-maximum likelihood.
• Measure. Losses use physical PDs (Driessen, 2005, risk-premium ratio).

Every equation, parameter and source is in docs/methodology.md.

Reproducing the results

git clone https://github.com/pancakes9798/Climate-Risk-Project.git
cd Climate-Risk-Project
uv sync                        # Python ≥ 3.11
uv run climate-risk download   # public data: GSW, HLW, Cleveland Fed, FRED
uv run climate-risk run        # → results/tables, results/figures, results/README.md

Credit data. The credit stage uses a licensed CDS panel that is not distributed (see data/README.md). Without it the pipeline runs in demo mode: a flat public Moody's Baa spread for every sector and Basel correlations. To reproduce the published results:

CLIMATE_RISK_CDS_PATH=/path/to/cds.csv uv run climate-risk run

Tests. The suite runs offline on a synthetic data root:

uv run pytest --cov=climate_risk   # offline, ≥ 95% coverage
uv run ruff check . && uv run mypy

Walkthrough. notebooks/walkthrough.ipynb walks through the pipeline step by step.

Repository layout

src/climate_risk/
├── config.py            every parameter, with its source
├── data/                readers (GSW, HLW, FRED, OWID), versioned extracts, SSP interpolation
├── term_structure/      Nelson–Siegel, VAR, shifting endpoint, projection, backtest
├── credit/              CDS loading and bootstrap, Merton, transition shock, climate spreads
├── portfolio/           copulas, loss distributions, VaR/ES
├── pipeline/            the three stages and their result tables
├── figures/             light/dark figures (CVD-validated palette)
├── report.py            results/README.md generator
└── cli.py               climate-risk {download, run, info}
data/                    processed extracts, SSP table, sector map (CDS panel never committed)
docs/methodology.md      equations, identification, calibration, limitations
results/                 tables (CSV), figures (PNG), generated summary
tests/                   unit and end-to-end tests on synthetic data

Limitations

• The SSP quantifications date from 2017 and are world-level. NGFS scenarios are the natural next step.
• The Nelson–Siegel model is not arbitrage-free. Term premia are held constant.
• The transition shock uses static business lines: no capex reallocation, and a representative utility.
• Physical risk is out of scope. PG&E, the original case study, went bankrupt in 2019 because of wildfire liabilities.

The full discussion is in docs/methodology.md §7.

References

Key sources:

• Diebold & Li (2006);
• Gürkaynak, Sack & Wright (2007);
• Bauer & Rudebusch (2020);
• Holston, Laubach & Williams (2023);
• Riahi et al. (2017);
• Battiston & Monasterolo (2020);
• Merton (1974);
• Demarta & McNeil (2005);
• Driessen (2005).

The complete list is in references/references.bib.

Citation and author

Emanuele Migliaccio, PhD candidate in Quantitative Finance, Sapienza University of Rome. The credit-spread notebook of v0.1 was co-authored with Marco Venditti. To cite this repository, see CITATION.cff. The code is released under the MIT licence; data sources keep their own terms.