Interactive Exploration

Climate-Extended
Vasicek Model

How much additional capital should banks hold once physical climate risk is accounted for?

This dashboard implements a climate extension of the Vasicek framework, following BIS Working Paper No. 1274 (Pozdyshev, Lobanov & Ilinsky, July 2025). The extension replaces the standard normal with a mixture that assigns probability q to a discrete climate shock, raising both the probability of default and the loss given default. The resulting model nests the Basel IRB formula as a special case, produces closed-form portfolio loss distributions, and quantifies the capital banks currently underhold against climate-exposed portfolios.

The Classic Vasicek Model

The Vasicek model is the basis of the Basel II/III Internal Ratings-Based approach. Every borrower in a portfolio shares exposure to a common systematic factor $S$ , and carries their own idiosyncratic risk $\ arepsilon_i$ .

The asset return of borrower $i$ is modeled as a weighted sum of these two independent standard normal draws:

Z_i = \sqrt{\rho} \cdot S + \sqrt{1-\rho} \cdot \varepsilon_i

(1)

The parameter $\rho$ is the asset correlation: it measures how tightly borrower fortunes move with the broader economy. When $\rho$ is high, borrowers default together; when it is low, each firm’s fate is its own.

Default occurs whenever the asset value falls below a critical threshold $C^*$ , which is pinned to the unconditional probability of default:

\ ext{Default} \iff Z_i < C^* = \Phi^{-1}(P_D^0)

(2)

The framework is tractable because of conditional independence: once we fix the systematic factor $S$ , all borrowers default independently. Setting $S = -y$ (so that positive $y$ represents economic stress), the conditional probability of default becomes:

P_D(\text{default} \mid S = -y) = \Phi\left(\frac{\sqrt{\rho} \cdot y + \Phi^{-1}(P_D^0)}{\sqrt{1-\rho}}\right)

(3)

Equation 3 is the core input to the Basel II/III IRB capital charge. At the 99.9% regulatory confidence level, this conditional PD, combined with LGD and a maturity adjustment, determines how much capital a bank must hold. The conditional PD itself requires only two inputs: the unconditional PD and the asset correlation.

The chart below plots how the conditional default rate changes with the state of the economy. The x-axis is the systematic factor $S$ : positive values are good times, negative values are recessions. Try pushing the asset correlation slider up to see how tightly coupled defaults become in a downturn, or raise the unconditional PD to model a lower-quality borrower pool.

Unconditional PD

Asset correlation

Conditional PD vs. the systematic factor. The steep rise on the left shows how quickly defaults concentrate in tail scenarios. At $S = -3$ (a roughly 0.1% probability event), default rates can exceed 50% for correlated portfolios.

Introducing Climate Risk

The classical Vasicek model assumes normally distributed asset returns. A flood, drought, or wildfire is a discrete event that the normal distribution has no mechanism to represent: concentrated damage with a well-defined probability, not a smooth tail realization.

The chart below shows what this looks like for individual borrowers. Gray paths are baseline asset returns driven by Brownian motion. When a climate event strikes (the red dashed line), affected paths drop by $\alpha$ . The marginal distribution on the right shows the resulting shift in terminal returns: more mass below the default threshold.

Damage intensity α

Climate probability q

The BIS framework introduces a binary climate shock: with probability $q$ , a climate event occurs and shifts the default threshold by a damage parameter $\hat{\alpha}$ . The unconditional probability of default becomes a mixture:

P_D = (1-q) \cdot \Phi(C^*) + q \cdot \Phi(C^* + \hat{\alpha})

(4)

The paper calls this the q-deformed normal: a two-component distribution that preserves Vasicek tractability while thickening the left tail where credit losses originate:

\Phi_{q,\hat{\alpha}}(x) \equiv (1-q) \cdot \Phi(x) + q \cdot \Phi(x + \hat{\alpha})

(5)

The constraint is self-consistency. A bank’s observed unconditional PD already embeds whatever climate risk the market prices in. Call this observed probability $P_D$ . The latent PD that would prevail without any climate effect is $P_D^0$ . The two are linked through the q-deformed inverse:

\Phi^{-1}(P_D^0) = \Phi_{q,\hat{\alpha}}^{-1}(P_D)

(6)

Given $P_D^0$ , $P_D$ , and an estimate of $q$ , this condition pins $\hat{\alpha}$ uniquely. When the observed PD contains no climate signal ( $P_D^0 = P_D$ ), $\hat{\alpha}$ must instead be calibrated from physical damage models.

The gray fill below is the standard normal (no climate risk). The red fill is the climate-shifted component, weighted by $q$ . The dark line is the resulting mixture. Watch the left tail as you increase $q$ : this is where credit losses live, and the climate extension thickens it substantially. Try pushing $q$ past 20% or raising $\alpha$ above 0.5 to see how the distribution deforms under extreme assumptions.

Climate probability q

Damage intensity alpha

The q-deformed normal distribution (dark line) as a mixture of the standard normal (gray) and the climate-shifted component (red). The parameter $\hat{\alpha} = \alpha / \sigma$ = 0.8 controls the shift magnitude.

Default and Recovery

Climate risk amplifies credit losses through two channels: the probability of default and the loss given default both rise.

Channel 1: PD increases. The climate event shifts the asset return distribution leftward, pushing more borrowers below the default threshold. Without climate risk, the conditional PD given systematic stress $y$ is:

\Phi\left(\frac{1}{\sqrt{1-\rho}}\left(\sqrt{\rho} \cdot y + \Phi^{-1}(P_D^0)\right)\right)

(7)

With the climate damage parameter, the conditional PD acquires an additional shift inside the normal CDF. This is the climate-adjusted version:

\Phi\left(\frac{1}{\sqrt{1-\rho}}\left(\sqrt{\rho} \cdot y + \Phi^{-1}(P_D^0)\right) + \frac{\hat{\alpha}}{\sqrt{1-\rho}}\right)

(8)

The term $\hat{\alpha} / \sqrt{1-\rho}$ amplifies the damage: when asset correlation is high, the denominator shrinks and the effective shift grows larger. Climate risk and systematic risk are complements.

Channel 2: LGD increases. When a climate event destroys collateral (a flood devastating a mortgaged property, for instance), the bank recovers less. The paper models this as an exponential damage function:

LGD_1 = LGD_0 + (1 - e^{-\alpha})(1 - LGD_0)

(15)

The expression $1 - e^{-\alpha}$ maps the damage intensity to the fraction of previously recoverable value that is destroyed. When $\alpha$ is small, the damage is approximately linear; as $\alpha$ grows, the function saturates as recovery approaches zero.

For

\alpha = 0.20

and

LGD_0 = 10\%

, the climate-adjusted LGD is 26.3%, a 2.6x multiple. Because expected loss is PD × LGD, both corrections compound in the final number.

Unconditional PD

Climate probability q

Damage intensity α

Baseline LGD

PD (baseline)

2.0%

PD (climate)

2.10%

LGD (baseline)

45%

LGD (climate)

59.3%

The gray dot is the baseline position; the red dot is the climate-adjusted outcome. The arrow crosses EL contours diagonally — both PD and LGD shift, and expected loss rises faster than either channel alone would suggest.

Portfolio Loss Distribution

For an infinitely granular portfolio (the ASRF assumption underlying Basel's IRB framework), the portfolio loss CDF has a closed form.

Let $L$ denote a target loss level. Because defaults in the baseline and climate-shocked regimes carry different severities, we normalise by the respective LGDs:

\Theta_0 = \frac{L}{\text{LGD}_0}, \quad \Theta_1 = \frac{L}{\text{LGD}_1} = \Theta_0 \cdot \frac{\text{LGD}_0}{\text{LGD}_1}

(13)

$\Theta_0$ is the fraction of the portfolio that must default under normal severities to reach loss $L$ ; $\Theta_1$ is the corresponding fraction under elevated climate-shock severities. Since $\text{LGD}_1 > \text{LGD}_0$ , fewer defaults are needed to breach the same loss level when a climate event strikes.

The portfolio loss CDF decomposes into a weighted sum over the two regimes:

\begin{aligned} P(\text{Loss} < L) ={} & q \cdot \Phi\!\left(\frac{\sqrt{1-\rho}\,\Phi^{-1}(\Theta_1) - \Phi^{-1}(P_D^0)}{\sqrt{\rho}} - \frac{\hat{\alpha}}{\sqrt{\rho}}\right) \\ & + (1-q) \cdot \Phi\!\left(\frac{\sqrt{1-\rho}\,\Phi^{-1}(\Theta_0) - \Phi^{-1}(P_D^0)}{\sqrt{\rho}}\right) \end{aligned}

(14)

Reduction to Vasicek. When

q = 0

\hat{\alpha} = 0

, the climate term drops out and the expression reduces to the standard Vasicek loss distribution.

The chart below shows the portfolio loss density under both models. The gray fill is the standard Vasicek distribution; the red fill is the climate-extended version. The dashed vertical lines mark the 99.9th percentile VaR, the loss level that is exceeded with probability 0.1%. The gap between VaR₀ and VaR₁ is capital that Basel does not require banks to hold. Try pushing the damage intensity slider past 0.5 or setting a low LGD to see the capital gap grow rapidly.

PD₀

Climate prob q

Severity α

Correlation ρ

LGD₀

VaR 99.9% Baseline

7.93%

Standard Vasicek

VaR 99.9% Climate

9.09%

Climate-extended

Expected Loss Baseline

0.900%

PD₀ × LGD₀

Expected Loss Climate

0.948%

Blended PD × LGD

Portfolio loss probability density. Dashed lines mark the 99.9th percentile VaR under each model.

The Basel Gap

The Basel IRB framework sets capital requirements using the standard Vasicek model ( $q = 0$ ), ignoring climate-driven shifts in both default probability and loss severity.

Under the Basel IRB approach, the capital charge for a given exposure is:

K_{\text{Basel}} = \text{LGD} \cdot \left[\Phi\!\left(\frac{\Phi^{-1}(PD) + \sqrt{\rho}\cdot\Phi^{-1}(0.999)}{\sqrt{1-\rho}}\right) - PD\right] \cdot MA

(20)

where $MA$ is the maturity adjustment. The climate-extended model modifies the capital charge in two ways. First, the conditional default probability draws on the q-deformed distribution rather than the standard normal, which raises the default rate during climate events. Second, a climate multiplier scales the unexpected loss to reflect higher severity:

\text{RWA}_{\text{model}} = \text{Multiplier} \cdot \text{LGD}_0 \cdot \left[C_V(Q) - P_D\right] \cdot \left(1 + (1-e^{-\alpha}) \cdot q \cdot \frac{1-\text{LGD}_0}{\text{LGD}_0}\right)

(21)

The bracketed factor is the climate multiplier. It amplifies the capital requirement in proportion to the probability of a climate shock ( $q$ ), the damage intensity ( $1 - e^{-\alpha}$ ), and the ratio of recoverable to impaired value ( $(1 - \text{LGD}_0)/\text{LGD}_0$ ). For well-collateralised exposures with low baseline LGD, the multiplier can be large: the denominator $\text{LGD}_0$ is small while the numerator $1 - \text{LGD}_0$ is large.

For high quality loan portfolios with low baseline PD and LGD, risk weighted assets can rise by as much as 20% once climate corrections are applied. Basel does not currently require banks to hold capital against this gap.

The paired bars below compare Basel’s capital charge (gray) with the climate-extended model (red) across a range of climate probabilities. The gap between the bars is capital that banks are not currently required to hold. Try lowering LGD₀ toward 10% to see the climate multiplier grow sharply for well-secured exposures, or push damage intensity past 0.5 for extreme scenarios.

PD₀

Severity α

Correlation ρ

LGD₀

Capital requirements under Basel IRB vs. climate-extended ASRF, by climate event probability. Gap reaches +21.2% at q = 30%.

q	Basel K	Climate K	Gap
2%	7.03%	7.13%	+1.4%
5%	7.03%	7.27%	+3.4%
8%	7.03%	7.42%	+5.5%
10%	7.03%	7.52%	+6.9%
15%	7.03%	7.76%	+10.4%
20%	7.03%	8.01%	+13.9%
25%	7.03%	8.27%	+17.6%
30%	7.03%	8.53%	+21.2%

Monte Carlo Verification

The analytical results above rely on the ASRF assumption: an infinitely granular, homogeneous portfolio where every obligor carries identical risk parameters. Real portfolios satisfy none of these. Monte Carlo simulation lets us check the closed-form results and measure how far finite, heterogeneous portfolios deviate from the ASRF tail loss estimate.

We construct a five-sector portfolio, each segment with different credit characteristics and climate exposures. Agriculture and Energy carry the highest climate probabilities and damage intensities; Services and Real Estate carry the lowest. In each simulation run, a single systematic factor $S \sim \mathcal{N}(0,1)$ drives correlated defaults across all sectors, while idiosyncratic shocks $\varepsilon_i$ generate obligor-level randomness.

Sector	Weight	PD₀	LGD₀	q	α
Agriculture	15%	2.5%	45%	8%	0.30
Real Estate	25%	1.5%	35%	6%	0.25
Manufacturing	20%	1.8%	40%	4%	0.20
Services	25%	1.0%	30%	3%	0.15
Energy	15%	2.0%	50%	10%	0.35

With 1,000 obligors across five sectors, simulated tail losses exceed the ASRF prediction. This is the finite granularity effect: the ASRF formula assumes away the concentration that finite portfolios retain.

Simulation will begin when this section scrolls into view.

Illustrative Example

The paper’s Annex 1 calibrates the framework to a real loan. Consider an investment-grade borrower secured by commercial real estate in Mobile, Alabama, a city on the Gulf Coast where S&P’s climate analytics estimate a 3% annual probability of a major hurricane making landfall.

That 3% figure (Category 3 or higher) is 76% above the long-term historical average of 1.7%. At the 95th-percentile confidence level, the probability rises to 4.8%.

Start with the borrower

The borrower is BBB-rated, with an unconditional PD of $P_D^0 = 0.3\%$ . The loan is well-secured, with an LGD of 10%. The Basel asset correlation is $\rho = 22.3\%$ , and we use an implied volatility of $\sigma = 30\%$ for high-quality US equities.

PD (baseline)

0.30%

LGD (baseline)

10%

Correlation

22.3%

Volatility

30%

Introduce climate risk

The climate event probability is $q = 3\%$ (from S&P). To calibrate the model, we need either an observed climate-adjusted $P_D$ or a physical damage estimate $\alpha$ . The paper’s Annex 1 takes the second route: physical damage models give $\alpha = 0.174$ , which with $\sigma = 30\%$ yields $\hat{\alpha} = \alpha / \sigma = 0.58$ . The damage factor $e^{-\alpha} = 0.84$ implies a 16% reduction in asset value upon a climate event.

q (hurricane)

3.0%

Damage param.

0.58

α̂ via self-consistency

Asset impact

−16%

exp(−α) = 0.84

Adjust default probability

Climate risk lifts the unconditional PD from 0.30% to 0.336%, a 12.1% increase.

PD (baseline)

0.300%

PD (climate)

0.336%

+12.1%

Adjust loss given default

The second channel hits recovery. The climate-adjusted LGD rises from 10% to 24.4%, an increase of 14.4 percentage points. When a hurricane destroys collateral, recovery plummets.

LGD (baseline)

10.0%

LGD (climate)

24.4%

+14.4pp

Compute conditional VaR

At the 99.9% confidence level, the conditional value-at-risk ( $C_V(Q)$ ) rises from 7.19% to 7.61%, an increase of 5.8%.

CV(Q) baseline

7.19%

CV(Q) climate

7.61%

+5.8%

Capital impact: the bottom line

Combining both channels, the unexpected loss (the capital charge banks must hold) rises from 0.689% to 0.758% using the model’s internal LGD, a relative increase of 10.1%. If we instead use an external LGD estimate of 40% (reflecting more severe collateral damage), the increase rises to 15.0%.

UL (baseline)

0.69%

UL (climate, int. LGD)

0.76%

+10.1%

UL (climate, LGD=40%)

0.79%

+15.0%

Higher probability scenario: $q = 4.8\%$

At the 95th percentile estimate for hurricane probability, the capital gap widens. Unexpected loss increases by 21.2% with internal LGD, rising to 27.9% with an external LGD of 40%.

4.8%

PD (climate)

0.388%

+29.3%

UL increase (int.)

+21.2%

UL increase (ext.)

+27.9%

In this calibration, RWA understatement reaches 8–20% at current hurricane probabilities, depending on LGD assumptions. That is under today’s climate, not under any warming scenario.

Maturity & Granularity

The preceding sections compare raw unexpected losses, $\ ext{UL} = \ ext{LGD} \cdot (C_V(Q) - P_D)$ , where $C_V(Q)$ is the conditional default rate at confidence level $Q$ . The actual Basel capital charge adds a maturity adjustment that scales UL by a factor depending on PD and maturity $M$ .

The maturity adjustment

Basel’s maturity adjustment scales the capital charge by a factor that depends on both PD and the effective maturity $M$ :

MA(PD, M) = \frac{1 + (M - 2.5) \cdot b(PD)}{1 - 1.5 \cdot b(PD)}

(22)

where $b(PD) = (0.11852 - 0.05478 \cdot \ln PD)^2$ . Since $b$ is larger for lower PDs (the logarithm is more negative), the maturity adjustment is largest for high quality borrowers.

Climate risk increases the effective PD from $P_D^0$ to $P_D$ . Because the maturity factor decreases with PD, the climate model receives a slightly smaller maturity boost than the baseline. This means the maturity adjustment partially offsets the climate gap in percentage terms.

In absolute terms, the climate-adjusted charge remains higher. The percentage gap narrows slightly once maturity is included, because the baseline charge receives a larger maturity uplift.

PD₀

LGD₀

Correlation ρ

Climate prob q

Severity α

MA (baseline)

1.199

PD₀ = 2.0%

MA (climate)

1.196

PD = 2.08%

MA ratio

99.7%

Climate MA / Baseline MA

UL (raw baseline)

7.035%

UL (raw climate)

7.274%

Gap (raw)

+3.4%

Without maturity adj.

Gap (with MA)

+3.1%

With maturity adj. at M=2.5

The maturity adjustment slightly narrows the climate gap in percentage terms. For

P_D^0 = 2.0\%

, the raw gap is +3.4% but falls to +3.1% after maturity adjustment at

M = 2.5

. The effect is larger for low-PD borrowers, where the maturity factor is more sensitive to changes in PD.

The chart below shows how the full capital charge $K = \text{UL} \times MA$ varies with effective maturity under both models. At short maturities ( $M < 2.5$ ), the maturity adjustment compresses capital; at long maturities, it amplifies it. The vertical distance between the two lines is the absolute climate gap, which grows with maturity because both UL and MA scale the gap multiplicatively.

Capital charge under both models as a function of effective maturity. The absolute gap between the two lines grows with maturity.

Granularity

The ASRF framework assumes an infinitely granular portfolio, so that idiosyncratic risk diversifies away completely. Real portfolios have a finite number of obligors, and the resulting concentration adds a granularity adjustment to the capital charge (Gordy & Lütkebohmert, 2013).

For a homogeneous portfolio of $N$ equal-sized exposures, the granularity correction is proportional to the Herfindahl index $\text{HHI} = 1/N$ . As $N \to \infty$ , the correction vanishes and the ASRF formula is exact.

Climate risk interacts with granularity in two ways. First, the granularity penalty grows with tail weight, because the variance of individual loss contributions is higher. The climate-extended model therefore incurs a larger granularity penalty.

Second, climate risk is often geographically concentrated. A bank’s Gulf Coast mortgage portfolio may contain many obligors, but they all face the same hurricane. The effective number of independent exposures is smaller than the nominal count, increasing the HHI and with it the granularity correction. This is visible in the Monte Carlo results (Section 06), where simulated tail losses with 1,000 obligors across five sectors exceed the ASRF prediction.

Neither adjustment changes the main result: climate risk still requires more capital than Basel demands. The maturity adjustment compresses the percentage gap slightly; the granularity correction widens it slightly. Both effects are smaller than the double hit.

Limitations & Sensitivity

The model makes six assumptions worth spelling out, each of which can bias the capital estimates.

The ASRF assumption

The Asymptotic Single Risk Factor model assumes an infinitely granular portfolio driven by a single systematic factor. Real bank portfolios have concentration risk (large exposures to individual borrowers or sectors) and multiple correlated risk drivers. The paper inherits this from Basel’s IRB framework. The climate extension cannot be more accurate than the model it extends.

Binary climate states

The model reduces climate risk to two states: event or no event. A Category 1 hurricane is not Category 5. The paper acknowledges this and sketches a multi-state extension using vectors $\{q_i, \alpha_i\}$ of probabilities and damage intensities, but does not pursue it. The binary model assigns a single damage parameter $\alpha$ regardless of event severity: it overstates mild events and understates catastrophic ones.

Stationarity of q

The model treats the climate probability $q$ as constant, but climate probabilities are not stationary. Hurricane frequency and intensity are trending upward as sea surface temperatures rise. Today’s $q$ may understate tomorrow’s risk. For multi-year capital planning, a time-varying $q(t)$ would be more appropriate.

Independence of physical and systematic risk

The model assumes zero correlation between the physical climate factor and the systematic market factor. CAT bond returns and equity markets do show low historical correlation, which supports this. But it may not hold during compound crises: a major hurricane devastating a regional economy could trigger broader financial contagion, breaking the independence assumption exactly when it matters most.

LGD timing

The climate adjusted LGD assumes the physical event occurs just before loan maturity, which is the most conservative timing. If the event occurs earlier, the borrower may have time to recover or the lender may restructure. If it occurs after maturity, the loan is already repaid.

Parameter uncertainty

Both $\alpha$ and $q$ must be estimated from limited historical data and climate models with substantial uncertainty. The self consistency condition propagates these estimation errors into the final capital numbers. Small changes in inputs can produce large changes in outputs, as the sensitivity charts below show.

Calibration also has two routes. A bank can either estimate $\ ilde{\alpha}$ directly from physical damage models, or back it out from an observed climate-adjusted $P_D$ via the self-consistency condition. The two approaches may yield different values, especially when the observed PD embeds climate risk imperfectly.

Sensitivity analysis

Each line in the first chart represents a fixed damage intensity $\alpha$ , and shows how the capital gap grows as the climate probability $q$ rises. The gap is roughly linear in $q$ but highly nonlinear in $\alpha$ : doubling the damage intensity more than doubles the gap. The second chart shows the absolute VaR level under both models, with the growing wedge representing capital that Basel currently misses. Try setting a low LGD (e.g. 10%) to see how dramatically the gap widens for well-secured loans.

Unconditional PD

LGD (baseline)

Asset correlation

Climate gap by probability and severity

Each line tracks a fixed damage severity. The near-linearity in $q$ contrasts with the wide spacing between lines, showing that capital sensitivity to severity dominates.

99.9% VaR: baseline vs. climate-adjusted

Portfolio VaR at the 99.9th percentile. The growing wedge between the two lines represents unrecognized risk in the standard model.

Capital gap surface

Each cell below shows the percentage increase in required capital relative to Basel across the full $q$ - $\alpha$ parameter space. Darker red means a larger gap. Raising both probability and severity together produces gaps far larger than either dimension alone.

Severity α (%)

Climate probability q (%)

+53%

Capital gap (%) as a function of climate probability (columns) and damage severity (rows). Each cell shows the percentage increase in required capital relative to Basel IRB.

Parameter sensitivity is a first order concern. Small errors in

q

\alpha

propagate into large swings in the capital charge. Any specific calibration needs a sensitivity table alongside it.

Key Takeaways

Climate risk can be incorporated into the standard Vasicek/Basel framework through a $q$ -deformed normal distribution. The existing IRB formula handles physical climate risk without modification.

The double hit of increased PD and increased LGD creates a climate multiplier. For the paper’s calibration, this raises capital requirements by 8–20%. The amplification is nonlinear in severity: doubling $\alpha$ more than doubles the capital gap. The relationship with $q$ is closer to linear, but the two channels activate simultaneously, so combined losses exceed what either channel implies on its own.

Current Basel capital calculations underestimate climate-exposed portfolio risk. The gap grows with $q$ and $\alpha$ . For banks with concentrated exposures to physical climate hazards, the capital shortfall is already measurable at current climate probabilities, not only under future warming scenarios.

Reference

Pozdyshev, V., Lobanov, A., & Ilinsky, A. (2025). “Incorporating physical climate risks into banks’ credit risk models.” BIS Working Papers, No. 1274, July 2025. bis.org/publ/work1274.pdf

BIS Working Paper No. 1274 is a research contribution, not a regulatory proposal. Other approaches exist, including transition risk frameworks and scenario-based stress tests. The Vasicek extension is attractive because it stays in closed form and slots into the existing Basel IRB architecture without modifications.

Interactive implementation by Jona Wilke

The Classic Vasicek Model

Introducing Climate Risk

Default and Recovery

Portfolio Loss Distribution

The Basel Gap

Monte Carlo Verification

Illustrative Example

Start with the borrower

Introduce climate risk

Adjust default probability

Adjust loss given default

Compute conditional VaR

Capital impact: the bottom line

Higher probability scenario: q=4.8%q = 4.8\%q=4.8%

Maturity & Granularity

The maturity adjustment

Granularity

Limitations & Sensitivity

The ASRF assumption

Binary climate states

Stationarity of q

Independence of physical and systematic risk

LGD timing

Parameter uncertainty

Sensitivity analysis

Capital gap surface

Key Takeaways

Higher probability scenario: $q = 4.8\%$