Chapter 4: Modeling Green Credit Risk: Scoring, Default Probability, and Loss Given Default

In 2021 a credit officer at a provincial commercial bank in Jiangsu reviewed a RMB 400 million term loan application from a mid-sized steel mill. The mill wanted to retrofit two blast furnaces with waste-heat recovery and install a dust-suppression system that would bring particulate emissions below the provincial cap. Leverage stood at 68%, interest coverage at 2.4×, five-year revenue CAGR at 6%. The legacy scorecard placed the borrower in the lower half of the acceptable band, priced at roughly 5.8%, approved with a covenant package. Nothing on the form asked about the retrofit. The officer's own view, that the retrofit would cut the mill's exposure to environmental shutdown orders and lower its energy bill by an estimated RMB 60 million a year, had no line item to live in.

That is the gap this chapter addresses. Chapter 3 argued that environmental performance can be measured and folded into a rating framework. The question here is narrower: once you have those measurements, how do you turn them into the three numbers a credit risk model needs—a score, a probability of default (PD), and a loss given default (LGD)? There is no single model. There is a construction sequence, and each stage carries its own assumptions, its own data problems, its own failure modes.

Section 4.1 builds scorecards that include environmental variables. Section 4.2 estimates default probabilities using logit and survival models. Section 4.3 addresses loss given default and recovery, where environmental risk enters through collateral value and through the timing of enforcement. One discipline runs through all three: every model discussed must be runnable by a bank risk team with data it can plausibly obtain, not only by a quant desk with a Bloomberg terminal and a decade of clean internal history.

4.1 Data-Driven Scoring for Green Firms: Building Scorecards with Environmental Variables

4.1.1 What a Scorecard Does, and What It Cannot Do

A credit scorecard maps observable borrower characteristics to a rank-ordering of creditworthiness. It is not a PD model, though it feeds one. The distinction matters because scorecards are often judged by the wrong criterion. A scorecard that ranks borrowers correctly but whose scores do not map monotonically to default frequency is still useful for approval decisions (accept/reject, price tier) but misleading if plugged directly into an expected-loss calculation.

Two construction philosophies dominate practice. The statistical scorecard is built by logistic regression or discriminant analysis on a historical sample of defaulted and non-defaulted borrowers, with variables selected for statistical power and stability. The expert scorecard assigns weights to factors a credit committee believes are predictive, calibrated loosely against observed default experience where available. Most banks use a hybrid: a statistical core for the financial variables, expert weights for qualitative and sector-specific factors.

Green firms strain both approaches. The statistical approach needs a default history long enough to contain green borrowers who defaulted, and that history is thin. The expert approach needs a defensible theory of how environmental performance transmits to default risk, and that theory is younger than the data. Neither problem is fatal. Both require the modeler to be explicit about what the scorecard is estimating and how much confidence to place in each block of variables.

4.1.2 The Variable Menu

Table 4-1 lists the variable families a green scorecard can draw on, organized by the four categories used throughout this book: financial, environmental performance, environmental risk exposure, and governance/transition capacity. The table is deliberately over-inclusive. No scorecard should use all of these variables; the menu exists so that a modeling team can select a parsimonious set with a rationale.

Table 4-1: Candidate Variable Families for a Green Corporate Scorecard

The menu reveals a design tension. Environmental performance variables (carbon intensity, energy intensity) are continuous and comparable within a sector but not across sectors. A cement plant at 0.85 tCO₂e per tonne of clinker and a software firm at 0.02 tCO₂e per RMB 10k revenue are not on the same scale, and forcing them onto one is a category error. Environmental risk exposure variables (sector sensitivity, proximity) are categorical and comparable across sectors but coarse. Transition capacity variables are ordinal and depend on manual judgment.

The practical resolution is sector-segmented scorecards with a shared financial core. The financial block is estimated once on the full portfolio; the environmental block is estimated within sector segments where the variables are commensurable. Retail scorecards have been segmented by product for decades; green scorecard design frequently neglects the same discipline, and the temptation is to build one "green score" for all borrowers.

4.1.3 Constructing the Environmental Block

Consider a bank building the environmental block for its manufacturing portfolio. The first decision is whether to use a points-based scoring system or a probability-of-default regression. Points-based systems assign points to variable bins and sum them; they are transparent, easy to explain to loan officers, and easy to audit. Regression-based systems estimate coefficients that maximize the fit to observed defaults; they are statistically efficient but opaque and require a default sample.

For green variables, the points-based approach has a decisive practical advantage: the default sample is too small to estimate stable coefficients for variables that were not collected historically. A bank that began collecting carbon intensity data in 2022 cannot estimate its coefficient on a 2015–2020 default sample. It can, however, assign points based on sector benchmarks and expert judgment, then validate the points system against whatever default experience accumulates.

A workable points scheme for the environmental block has three sub-blocks, each scored 0–100, then weighted.

Sub-block A: Environmental performance (weight 40%). Points are awarded on a curve relative to sector benchmark. A firm at or below the sector's 25th percentile of carbon intensity scores 100; at the median, 60; at the 75th percentile, 20; above the 90th percentile, 0. The curve is set by the bank's sector research team and revised annually. Energy intensity is scored the same way and averaged with carbon intensity.

Sub-block B: Environmental risk exposure (weight 35%). Sector sensitivity is a fixed score: green sectors (renewables, environmental services) 100; transition sectors (steel, cement, chemicals) 40; brown sectors (coal mining, thermal power without retrofit plans) 0. Proximity to sensitive areas and penalty history are deductions from a base of 100: each recorded penalty in the past three years deducts 15 points, capped at 45; proximity to a protected area or water source deducts 20.

Sub-block C: Transition capacity (weight 25%). Here the scoring shifts from exposure to the borrower's ability to adapt. Green capex ratio is scored on a curve: above 30% of total capex scores 100; 10–30% scores 60; below 10% scores 20. Transition plan quality is scored 1–5 by manual review, multiplied by 20. Certification adds 10 points, capped at 100.

The composite environmental score \(E\) is then:

with \(E \in [0, 100]\). A firm with \(E = 80\) is a strong environmental performer; \(E = 30\) is a laggard.

The weights are the most contestable element. Why 40/35/25 rather than 50/30/20 or equal weights? The honest answer is that the weights should reflect the relative predictive power of each sub-block for default, and that power is unknown at the outset. The weights above are a prior, set so that no single sub-block dominates and so that a firm cannot score well on performance alone while carrying catastrophic exposure. They should be re-estimated once default data permit. A bank that treats these weights as immutable is not modeling; it is decorating.

4.1.4 Combining Financial and Environmental Blocks

The composite score \(S\) combines the financial score \(F\) and the environmental score \(E\):

The parameter \(\alpha\) controls how much weight the environmental block carries. Three regimes are worth distinguishing.

Regime 1: Environmental as a tiebreaker (\(\alpha = 0.85\)). The environmental block shifts the composite score by at most 15 points. This is appropriate when the bank has low confidence in the environmental data and wants the scorecard to remain anchored on financial fundamentals. It is also the regime most likely to be adopted in the first year of a green scorecard, because it minimizes disruption to existing approval patterns.

Regime 2: Environmental as a material factor (\(\alpha = 0.65\)). The environmental block can move a borrower across a rating grade boundary. A firm with a strong financial profile but poor environmental performance can be downgraded from, say, BBB to BB. This regime requires that the environmental data be audited or third-party verified, because the stakes of mismeasurement are now grade-level.

Regime 3: Environmental as a co-equal factor (\(\alpha = 0.50\)). The environmental block carries the same weight as the financial block. This is defensible only for sectors where environmental risk is the dominant driver of default—thermal power in a carbon-constrained market, for instance—and only when the environmental data meet the same evidentiary standard as audited financials. I have not seen a bank adopt \(\alpha = 0.50\) across a diversified portfolio, and I would be skeptical of one that did.

The choice of \(\alpha\) is a governance decision, not a statistical one. It encodes the bank's belief about how much environmental performance matters relative to financial performance, and it should be set by the risk committee with explicit reasoning, not inherited from a vendor's default configuration.

4.1.5 Validation and the Small-Sample Problem

A scorecard is only as good as its validation. The standard tools are the Gini coefficient, the Kolmogorov–Smirnov statistic, and the population stability index. Each requires a sample of defaults.

For green scorecards, the default sample is the binding constraint. Suppose a bank has 2,000 corporate borrowers, of which 300 are classified as green or transition firms. Over a five-year window, the expected number of defaults in that sub-portfolio, at a 1.5% annual default rate, is roughly 22. Twenty-two defaults is enough to estimate a Gini coefficient with a confidence interval wide enough to be almost uninformative. It is not enough to validate a segmented scorecard with a dozen variables.

Pooling across banks is the most practical response. Industry consortia—in China, the provincial banking associations have begun assembling green credit default databases—can accumulate samples that no single bank can. The obstacle is data-sharing incentives: banks regard default data as competitively sensitive, and the legal frameworks for sharing are uneven. A second option validates the environmental block's incremental contribution on the full portfolio rather than on the green sub-portfolio alone. If the full-portfolio scorecard has a Gini of 0.55 and the version without environmental variables has a Gini of 0.53, the environmental block adds 0.02. Whether that increment is statistically significant depends on the sample size, and with 22 defaults it usually is not. The increment is suggestive, not conclusive. A bank can also run out-of-time and out-of-sample tests on the environmental block alone, treating the block's score as a ranking device and checking whether high-\(E\) firms have lower subsequent penalty rates, lower shutdown incidence, and lower default rates than low-\(E\) firms, without claiming a precise coefficient. This is weaker than a full validation but stronger than nothing, and it is what most banks can actually do in the first three years.

4.1.6 A Note on Data Provenance

The scorecard is only as good as the data feeding it, and green data has a provenance problem that financial data does not. Audited financials have a defined evidentiary standard: a licensed auditor, a prescribed format, a liability regime for misstatement. Environmental data has no comparable standard in most jurisdictions. Carbon intensity may come from a continuous emissions monitoring system (CEMS), from an annual report, from a third-party verification body, or from an estimate based on fuel input. These sources are not interchangeable.

A scorecard that treats all carbon intensity figures as equally reliable will be gamed. A firm that wants a better score has an incentive to report the lowest defensible number, and the lowest defensible number depends on the measurement method. The modeler's response should be a data-quality tier assigned to each environmental variable, with the score discounted when the tier is low. A simple scheme: tier 1 (third-party verified, CEMS-based) receives the full score; tier 2 (self-reported, audited process) receives 80% of the score; tier 3 (self-reported, unaudited) receives 60%; tier 4 (estimated from sector averages) receives 40%. The discounts are judgmental, but they make the data-quality problem visible in the score rather than hidden in the assumption.

4.2 Estimating Probability of Default: Logit and Survival Models for Green Borrowers

4.2.1 From Score to PD

The scorecard produces a rank. The PD model produces a number. The bridge between them is a calibration: a mapping from score bands to observed default frequencies.

The simplest calibration is a historical default table. If borrowers in score band 5 (on a 10-band scale) defaulted at a rate of 1.8% per year over the observation window, then the PD assigned to band 5 is 1.8%, adjusted for the current point in the cycle. This is the approach used by the rating agencies, whose transition and default tables—the Fitch global corporate finance average one-year and five-year transition rates, for instance—are the industry's reference calibration.

The problem for green borrowers is that the historical default table was estimated on a population that did not include environmental variables. A green firm's score band reflects its environmental performance, but the band's historical default rate reflects the average firm in that band, most of which were not scored on environmental performance. The calibration is therefore biased, and the direction of the bias depends on whether environmental performance is already correlated with the financial variables in the score. If green firms tend to be younger and more leveraged (a common pattern in capital-intensive clean technology), their financial scores already capture part of the risk, and the environmental block adds less than it appears to. If green firms tend to be established industrial firms with retrofit capex, their financial scores may understate the transition risk, and the environmental block adds more.

The clean solution is to estimate the PD model directly on a sample that includes environmental variables, rather than calibrating a score. That brings us to logit and survival models.

4.2.2 The Logit Model

The standard PD model in credit risk is the logistic regression. Let \(y_i = 1\) if borrower \(i\) defaults within the horizon (typically one year) and \(y_i = 0\) otherwise. The model specifies:

where \(\mathbf{x}_i\) is the vector of borrower characteristics and \(\boldsymbol{\beta}\) is the coefficient vector. The log-odds are linear in the covariates:

The model is estimated by maximum likelihood. Its appeal is interpretability: a coefficient \(\beta_k\) means that a one-unit increase in \(x_k\) raises the log-odds of default by \(\beta_k\), holding other variables constant. For a green scorecard, the coefficient on carbon intensity tells you how much a unit of carbon intensity raises default odds, conditional on the financial variables.

The logit model's limitation is the same as the scorecard's: it needs defaults. With 22 defaults in a 300-firm green sub-portfolio, the maximum likelihood estimates of a dozen coefficients will be unstable, and the standard errors will be wide. The model will fit the sample and may not generalize.

Variable reduction is the cheapest fix: enter the composite environmental score \(E\) as a single covariate instead of a dozen environmental variables. This reduces the degrees of freedom consumed by the environmental block from twelve to one. The cost is that the model cannot distinguish which environmental sub-block drives the effect, but for PD estimation that distinction is often secondary to getting a stable estimate of the overall effect. When even that single coefficient is unstable, ridge or lasso regularization adds a penalty to the likelihood, shrinking coefficients toward zero and reducing variance at the cost of bias. A ridge penalty on the environmental coefficient is a reasonable compromise: it keeps the financial coefficients (estimated on a larger sample) relatively unshrunk while stabilizing the environmental coefficient. If the bank has sector-level default data, even without firm-level environmental data, a hierarchical model offers a third route: firm-level coefficients are drawn from a sector-level distribution estimated on more data, and the firm-level coefficients are shrunk toward the sector mean. This is the Bayesian analogue of the pooling strategy discussed in section 4.1.5.

A practical specification for a green PD logit, using the composite score approach, is:

where Lev is leverage, Cov is interest coverage, Size is log assets, Vol is revenue volatility, \(E\) is the environmental score, and Sector is a set of sector dummies. Expected signs: \(\beta_1 > 0\), \(\beta_2 < 0\), \(\beta_3 < 0\), \(\beta_4 > 0\), \(\beta_5 < 0\). The sign and magnitude of \(\beta_5\) is the object of interest.

4.2.3 Interpreting the Environmental Coefficient

Suppose the estimated \(\beta_5\) is \(-0.018\) with a standard error of \(0.007\). The coefficient implies that a 10-point increase in the environmental score reduces the log-odds of default by 0.18, or the odds by a factor of \(\exp(-0.18) \approx 0.835\)—a 16.5% reduction in odds. At a baseline PD of 2%, this moves the PD to approximately 1.68%.

Is that a large effect? It depends on the baseline. A 16.5% reduction in odds is meaningful at the margin but small relative to the variation in financial variables: a one-standard-deviation increase in leverage might raise odds by 40% or more. The environmental score is a second-order driver of default in most sectors, not a first-order one. That is an empirical finding, not a theoretical claim, and it may change as carbon pricing tightens and environmental enforcement intensifies.

The coefficient's standard error matters as much as its point estimate. A \(\beta_5\) of \(-0.018\) with a standard error of \(0.007\) is statistically distinguishable from zero at conventional levels. A \(\beta_5\) of \(-0.018\) with a standard error of \(0.020\) is not, and the honest conclusion is that the data cannot reject the hypothesis that environmental performance has no effect on default, conditional on the financial variables. Reporting the point estimate without the standard error is the most common sin in green credit modeling papers, and it is a sin that practitioners should refuse to commit.

4.2.4 The Survival Model

The logit model estimates the probability of default within a fixed horizon. The survival model estimates the time to default, which is more informative when the horizon is uncertain and when borrowers are observed over different periods.

The workhorse is the Cox proportional hazards model. Let \(T\) be the time to default, and let \(h(t \mid \mathbf{x})\) be the hazard rate—the instantaneous probability of default at time \(t\), conditional on survival to \(t\). The Cox model specifies:

where \(h_0(t)\) is an unspecified baseline hazard and \(\boldsymbol{\beta}\) is the coefficient vector. The model is semiparametric: the baseline hazard is left free, and the coefficients are estimated by partial likelihood, which compares the covariate values of borrowers who default at time \(t\) with those of borrowers still at risk at \(t\).

The survival model's advantage for green borrowers is that it handles censoring naturally. A borrower who has not defaulted by the end of the observation window is censored, not treated as a non-default. This matters for green firms because many are young: a five-year-old clean technology firm observed over a three-year window may not have had time to default, and treating it as a confirmed non-default biases the estimated default rate downward. The survival model uses the information that the firm survived three years without assuming it will survive forever.

The proportional hazards assumption—that the effect of covariates is constant over time—is the model's main limitation. For green firms, the assumption is questionable. A firm with a strong environmental score may have a lower hazard early in its life (when environmental compliance is a barrier to entry) and a similar hazard later (when competitors have caught up). If the effect of environmental performance varies with firm age, the proportional hazards assumption is violated, and the model should be extended to allow time-varying coefficients or stratified by age cohort.

A practical specification for a green survival model:

with Age included because firm age is a strong predictor of default and is correlated with environmental performance (younger firms are more likely to be green, and more likely to default). Omitting Age would confound the environmental effect with the age effect.

4.2.5 The Macroeconomic Dimension

Both the logit and the survival model as specified above are conditional on borrower characteristics and ignore the macroeconomic environment. Default rates are strongly cyclical, and a model that ignores the cycle will misestimate PD in both booms and busts.

The standard remedy is to include macroeconomic variables in the model, or to estimate a through-the-cycle PD and apply a point-in-time adjustment. The through-the-cycle approach is more common in regulatory capital calculations; the point-in-time approach is more common in pricing and portfolio management.

For green borrowers, the macroeconomic dimension has a specific twist: environmental policy is itself a macroeconomic variable. A carbon price, an emissions trading scheme, or a tightening of discharge standards changes the default risk of every firm in the affected sectors, and the change is not captured by GDP or interest rates. A green PD model should include a policy variable—the carbon price, the stringency of environmental enforcement, or a composite policy index—either as a covariate or as a conditioning variable in the through-the-cycle estimation.

The CreditPortfolioView approach, developed by Wilson and adapted by McKinsey, offers a template. It requires three steps: (1) identify \(n\) macroeconomic variables \(X_i\) that follow an autoregressive process, (2) compute sector indices \(Y_s\) from the macroeconomic variables, and (3) transform \(Y_s\) into a default rate \(DR_s \in [0,1]\) via a logit-like link:

where \(Y_s\) approaches \(+\infty\) as the sector condition improves and \(-\infty\) as it deteriorates. The extension for green borrowers is to add an environmental policy variable to the macroeconomic vector, so that the sector index reflects both the business cycle and the policy cycle.

I am not aware of a published CreditPortfolioView implementation that includes an environmental policy variable. The extension is conceptually straightforward and empirically untested. That combination—straightforward and untested—is exactly the kind of thing a bank should pilot on a small portfolio before adopting, and exactly the kind of thing a vendor will sell as a finished product.

4.2.6 The Merton Alternative

The structural approach to PD, derived from Merton's 1974 model, treats equity as a call option on the firm's assets with strike price equal to the face value of debt. Default occurs when the asset value falls below the debt threshold at maturity. The model yields a distance-to-default measure:

where \(V\) is asset value, \(D\) is the default threshold, \(\mu\) is the expected asset return, \(\sigma\) is asset volatility, and \(T\) is the horizon. The PD is then \(\Phi(-DD)\), where \(\Phi\) is the standard normal cumulative distribution.

The structural approach has one advantage over the logit: it does not need a default sample, only equity prices and balance sheet data. For green firms, many of which are young and have no default history, this is a real attraction. Moody's Analytics EDF (Expected Default Frequency) is the most widely used commercial implementation.

The disadvantage is that the structural model requires traded equity and a stable relationship between asset value and equity value. Most green borrowers in emerging markets are unlisted. For listed firms, the model's PD estimates are sensitive to the asset volatility estimate, which is itself noisy for small-cap firms. And the model has no natural way to incorporate environmental variables except through their effect on expected asset returns and volatility—a channel that is real but indirect.

A hybrid approach is worth considering: use the structural model to generate a market-implied PD for listed green firms, then calibrate the logit model's environmental coefficient so that the logit PD matches the structural PD on average for the listed subsample. This uses the market data where it exists to discipline the accounting-based model where it does not. The calibration is only as good as the overlap between the listed and unlisted populations, which is a strong assumption. It is, however, better than assuming the two populations are identical without checking.

4.2.7 A Worked Example

To make the estimation concrete, consider a simplified portfolio of 500 manufacturing firms, of which 120 are classified as transition-sector firms with environmental scores. Suppose the bank observes 18 defaults over a three-year window. The logit model is estimated with five covariates: leverage, coverage, log assets, revenue volatility, and the environmental score \(E\).

The estimated coefficients (illustrative, not from a specific dataset) are:

At a baseline PD of 2.0% (the sample average for the transition sector), a 10-point increase in \(E\) reduces PD by about 0.2 percentage points, or 10% of the baseline. The effect is statistically significant at the 5% level (t = 2.33) but economically modest.

The modest effect is itself informative. It suggests that, in this portfolio, environmental performance is not a dominant driver of default—financial leverage and revenue volatility are. That does not mean the environmental score is useless; it means the scorecard should not over-weight it, and the pricing benefit for green firms should be calibrated to the actual risk reduction, not to a policy target.

4.3 Loss Given Default and Recovery: Collateral and Environmental Risk Factors

4.3.1 The Third Parameter

Expected loss on a credit exposure is the product of three parameters:

where EAD is exposure at default. The first two sections of this chapter addressed PD. This section addresses LGD, the fraction of exposure that is not recovered in the event of default.

LGD is often treated as a constant by sector—40% for senior secured corporate loans, 60% for subordinated, 75% for unsecured—and this treatment is adequate for portfolio-level capital calculations. It is inadequate for green lending, for two reasons. First, the collateral that secures green loans is often environmentally specific: a waste-heat recovery system, a solar array, a wastewater treatment plant. The value of that collateral in default depends on environmental factors that a generic LGD assumption ignores. Second, the enforcement process for green loans can be slowed or accelerated by environmental regulation, which changes the recovery timing and, through discounting, the recovery value.

4.3.2 The Components of LGD

LGD can be decomposed into three components:

where \(R_{\text{collateral}}\) is the recovery from collateral liquidation, \(R_{\text{other}}\) is recovery from other sources (guarantees, unsecured claims), and \(C_{\text{enforcement}}\) is the cost of enforcement (legal fees, administrative costs, and the time value of money during the recovery period).

For green loans, each component has an environmental dimension.

Collateral value. A loan secured by a blast furnace waste-heat recovery system has collateral whose value depends on the system's operating condition and on the market for second-hand industrial equipment. If the system is integrated into the furnace and cannot be removed without damage, its liquidation value is close to zero. If it is a modular unit, its value depends on whether there is a buyer—and the buyer pool for used environmental equipment is thin. The collateral's value is also affected by environmental regulation: a system that meets current emission standards may be obsolete if standards tighten, and a system that is grandfathered under current standards may lose its value if the grandfathering is revoked.

Enforcement cost and timing. Environmental liabilities can delay enforcement. If the defaulted firm has contaminated a site, the site must be remediated before the collateral can be sold, and the remediation cost is a senior claim on the estate in many jurisdictions. The U.S. Superfund legislation of the early 1980s is the canonical example: it made firms liable for environmental pollution and prompted banks to guard against credit risk arising from potential environmental contamination, which is often cited as the start of green finance. For LGD modeling, the lesson is that environmental liability reaches past the borrower to the lender's recovery.

Guarantees. Green loans are often supported by guarantees—government credit guarantees for green projects, insurance wrappers, or corporate guarantees from a parent. The value of the guarantee depends on the guarantor's creditworthiness, which is itself affected by environmental exposure. A guarantee from a parent company in a brown sector is worth less than a guarantee from a parent in a green sector, even if the two parents have the same standalone credit rating, because the brown parent's rating is more likely to be downgraded in a transition scenario.

4.3.3 Modeling LGD: The Standard Approaches

Three approaches to LGD modeling are in common use.

The workout approach. LGD is estimated from historical workout data: for each defaulted loan, the present value of recoveries is divided by the exposure at default. The estimate is the average across the sample. This is the most direct approach and the most data-hungry. For green loans, the workout sample is small, and the workouts that exist may not be representative. My conjecture, which I cannot yet support with a published dataset, is that the first green loans to default will cluster in sectors where the green label was thinnest—steel retrofits that were relabeled rather than redesigned, chemical firms with a single certified product line, and building materials firms whose "green" designation rested on a product category rather than a process change. If that conjecture holds, early workout data will overstate LGD for genuinely green loans.

The market approach. LGD is inferred from market prices of defaulted debt. If a defaulted bond trades at 35 cents on the dollar, the implied LGD is 65%. The market approach is fast and forward-looking but requires a liquid market for defaulted debt, which most green loans do not have.

The structural approach. LGD is modeled as a function of the firm's asset value at default and the seniority of the claim. In the Merton framework, the recovery rate on debt is:

where \(V_T\) is the asset value at maturity and \(D\) is the face value of debt. The structural approach is elegant but requires assumptions about the distribution of asset values at default that are hard to validate.

For green lending, the practical approach is a hybrid: use the workout approach where data exist, supplement with the market approach for listed firms, and use a structural model to generate a prior for new loan types. The prior is then updated as workout data accumulate—a Bayesian updating process that is more honest about uncertainty than a point estimate.

4.3.4 The Environmental Adjustment to LGD

The core modeling question is how to adjust LGD for environmental factors. I propose a three-factor adjustment, applied multiplicatively to a base LGD:

where each \(\delta\) is a sector- and loan-specific adjustment.

Collateral adjustment \(\delta_{\text{collateral}}\). Positive if the collateral is environmentally specific and illiquid (adds to LGD); negative if the collateral is a standardized, liquid green asset (reduces LGD). A loan secured by a modular solar array has a negative adjustment because the array can be removed and resold. A loan secured by an integrated waste-heat system has a positive adjustment because the system cannot be separated from the furnace.

Enforcement adjustment \(\delta_{\text{enforcement}}\). Positive if the borrower's operations carry environmental liabilities that could delay or reduce recovery. A loan to a chemical firm with a history of soil contamination carries a positive adjustment. A loan to a firm with a clean environmental record carries a zero or slightly negative adjustment.

Guarantee adjustment \(\delta_{\text{guarantee}}\). Positive if the guarantor's creditworthiness is correlated with the borrower's environmental exposure. A guarantee from a parent in the same brown sector is worth less than a guarantee from a diversified parent with green revenue.

The magnitudes are judgmental. A reasonable starting point, based on the limited workout evidence available: \(\delta_{\text{collateral}} \in [-0.10, +0.20]\), \(\delta_{\text{enforcement}} \in [0, +0.15]\), \(\delta_{\text{guarantee}} \in [0, +0.10]\). These ranges should be narrowed as data accumulate.

4.3.5 Recovery Timing and the Discount Rate

LGD is a present-value concept, and the discount rate matters. A recovery of 50% realized after five years is worth less than a recovery of 50% realized after one year. The standard formula is:

where \(r\) is the discount rate and \(t\) is the time to recovery.

For green loans, the time to recovery can be extended by environmental remediation. A site that requires remediation before sale may take two to three years longer to resolve than a comparable non-contaminated site. At a 6% discount rate, a three-year delay reduces the present value of a 50% recovery from 50% to about 42%—an eight-percentage-point increase in LGD from timing alone.

The adjustment is easy to miss in a spreadsheet because the base recovery rate looks unchangedThe modeler who ignores timing will systematically understate LGD for environmentally complex workouts, and the understatement will be largest precisely where the exposure is largest.

4.3.6 A Worked LGD Example

Consider three loans, each with an exposure at default of RMB 100 million. Loan A is secured by a standardized solar array on a leased rooftop; Loan B is secured by an integrated waste-heat recovery system; Loan C is unsecured but backed by a parent guarantee from a diversified industrial group with a brown subsidiary.

The base LGD for senior secured corporate loans in the bank's portfolio is 40%; for unsecured loans, 60%. Applying the adjustments:

The multiplicative form matters. Loan B's adjusted LGD is \(0.40 \times 1.15 \times 1.05 = 0.483\), not \(0.40 + 0.15 + 0.05 = 0.60\). The additive form overstates the adjustment when multiple factors apply, because each factor operates on a base that has already been adjusted by the others. The multiplicative form is the correct one if the adjustments are interpreted as proportional changes; the additive form is defensible only if the adjustments are interpreted as absolute percentage-point additions, which is harder to justify theoretically.

Loan A illustrates the case where environmental factors reduce LGD. The solar array is modular, has a liquid second-hand market, and carries no remediation liability. The collateral on a green loan is often more separable than the collateral on a comparable brown loan, which lowers LGD as well as PD. This is one of the underappreciated arguments for green lending, and it is also an argument that can be tested: compare the realized recovery rates on defaulted green loans secured by modular equipment against those on defaulted brown loans secured by process-integrated equipment. The comparison requires only workout data the bank already collects, and it would settle the question faster than another year of theorizing.

Loan C illustrates the correlation problem. The parent guarantee looks like a credit enhancement, but the parent's brown subsidiary exposes it to environmental liability that could impair its ability to honor the guarantee at the moment the guarantee is needed. The +5% adjustment is a rough proxy for that correlation. A more rigorous treatment would model the joint default probability of borrower and guarantor, which requires a dependence model—the subject of Chapter 5.

4.3.7 The Recovery Rating Analogue

The rating agencies have developed recovery ratings that separate the expected recovery on a specific instrument from the issuer's overall credit rating. S&P's recovery ratings, on a scale from 1+ (highest recovery) to 5 (lowest), are the most widely used. The recovery rating reflects collateral coverage, seniority, and the estimated enterprise value at default.

For green loans, a recovery rating analogue would be useful: a separate assessment of recovery prospects that captures the environmental dimensions discussed above. The analogue would have four components: collateral quality (including separability and liquidity), environmental liability exposure, guarantee quality (including correlation with the borrower), and enforcement timeline. Each component scored on a 1–5 scale, with the composite mapped to an expected recovery range.

I have not seen a bank implement such a scheme, but the logic is straightforward and the data requirements are modest. The scheme would make the environmental adjustment to LGD explicit and auditable, rather than buried in a judgmental overlay. The scoring itself would take an analyst perhaps two hours per exposure, which is affordable for a portfolio of a few hundred green loans and prohibitive for a retail book. That is the right trade-off: the exposures where environmental collateral matters are large, negotiated, and few.

4.4 Bringing the Three Models Together

4.4.1 The Expected Loss Calculation

With PD, LGD, and EAD estimated, expected loss follows:

For a green loan, each parameter carries an environmental adjustment: PD through the environmental score, LGD through the collateral and enforcement adjustments, and EAD through the drawdown behavior of the borrower. The EAD channel deserves a sentence of its own, because it is the one most often omitted. A firm in environmental distress may draw down committed lines faster than a healthy firm, raising EAD at exactly the moment when PD and LGD are also rising. The three parameters are not independent, and a model that multiplies point estimates as if they were will understate expected loss in the tail.

The portfolio-level expected loss is the sum of individual expected losses:

This sum is a first moment. It says nothing about the distribution of losses, which is what capital adequacy and stress testing require. The distribution depends on the dependence structure among borrowers—the correlation of defaults—which is the subject of Chapter 5.

4.4.2 The Model Risk Inventory

Every model in this chapter carries assumptions that can fail. A disciplined modeling team maintains an inventory of those assumptions and tests them. Table 4-2 lists the principal assumptions and the tests that would falsify them.

Table 4-2: Model Risk Inventory for Green Credit Models

Each row corresponds to a way the model can be wrong, and each test is a way to find out. A bank that runs the tests and reports the results, including the failures, is doing model risk management. A bank that runs the models and reports only the fits is doing something else. The distinction is not academic: the second bank will discover its model failures through loan losses, which is the most expensive possible audit.

4.4.3 Calibration Against the Rating Scale

The PD estimates from the logit or survival model are continuous probabilities. The bank's rating scale is discrete. The mapping from PD to rating grade should be monotonic and should be recalibrated annually against the observed default experience of each grade.

For green borrowers, the calibration has a specific pitfall: if the environmental score is correlated with firm age, and firm age is correlated with default, then the PD-to-grade mapping estimated on the full portfolio will misclassify green firms. A young green firm with a strong environmental score may be assigned a better grade than its default experience warrants, because the grade's historical default rate reflects older, established firms.

The remedy is to calibrate the mapping separately for green and non-green segments, or to include age as a covariate in the PD model (as recommended in section 4.2.4). The first is simpler; the second is more efficient. Either is preferable to ignoring the problem. A bank that ignores it will find that its green book performs worse than its grades predict in the first downturn, and will then over-correct by tightening standards across the board, penalizing the good green borrowers along with the misgraded ones.

4.4.4 A Note on Regulatory Capital

The Internal Ratings-Based (IRB) approach to regulatory capital requires banks to estimate PD and LGD for each exposure and to apply the regulatory risk-weight formula. The formula is sensitive to both parameters: a 10% reduction in PD reduces capital requirements by roughly 10%, and a 10% reduction in LGD reduces them by roughly 10% as well, though the exact sensitivity depends on the exposure's maturity and the correlation assumption.

This creates an incentive to estimate green PD and LGD optimistically. A bank that can justify a lower PD for green loans frees capital for more lending. The incentive is not necessarily bad—if green loans genuinely have lower risk, capital should reflect it—but it is a reason for regulators to scrutinize green PD and LGD estimates more closely than conventional ones. The scrutiny should focus on the validation evidence, not on the point estimates.

In China, the China Banking and Insurance Regulatory Commission (CBIRC) has issued green credit statistics and evaluation rules that require banks to report green loan balances and environmental risk classifications, but the rules do not yet prescribe PD or LGD adjustments for green loans. The space between reporting and capital is where the modeling work happens, and it is currently unregulated. That is an opportunity for banks to build credible models before the rules tighten, and a risk for banks that build models designed to minimize capital rather than to measure risk. The two objectives diverge most sharply in the environmental block, where the data are soft enough that a motivated modeler can justify almost any coefficient.

4.5 Implementation: A Staged Path

4.5.1 Why Staging Matters

A bank that tries to implement all three models at once will fail. The data requirements are different, the validation timelines are different, and the organizational resistance is different. A staged path—scorecard first, PD second, LGD third—allows each model to be validated before the next is built, and allows the bank to learn from its mistakes at low cost.

The staging also reflects the dependency structure. The scorecard produces the environmental score \(E\) that the PD model uses as a covariate. The PD model produces the default probabilities that, combined with the LGD model, produce expected loss. Building out of order means building on sand.

4.5.2 Stage 1: The Scorecard (Months 1–9)

The first stage builds the environmental scorecard and integrates it with the existing financial scorecard at \(\alpha = 0.85\), the tiebreaker regime. What the bank learns in this stage is mostly about its own data. The variable menu will shrink as the team discovers which variables it can actually populate: carbon intensity may turn out to be available for 60% of the manufacturing book and 10% of the trading book, and the scorecard must handle the missing values without silently imputing them to the sector average. The data-quality tier system will reveal how much of the environmental data is self-reported and unaudited, which is usually more than the risk committee expected. And the correlation between the environmental score and the financial score will show whether the environmental block is adding information or restating it.

The stage-1 validation is necessarily weak. The bank will not have enough defaults to estimate a Gini coefficient for the environmental block. It can, however, test whether the environmental score is stable over time (population stability index), whether it is correlated with the financial score (if the correlation is too high, the environmental block adds nothing), and whether high-\(E\) firms have lower penalty rates and shutdown incidence in the subsequent year. These are leading indicators, not default evidence, but they are better than no validation. The stage fails, usefully, when the environmental score turns out to be a near-duplicate of firm size or sector—a result that is common enough that the team should test for it first.

4.5.3 Stage 2: The PD Model (Months 9–18)

The second stage estimates the logit or survival model with the environmental score as a covariate. The deliverable that matters is not the coefficient table but the calibration table mapping PD to rating grades, together with the confidence intervals around each grade's central estimate. The stage-2 challenge is the small default sample. The bank should expect wide confidence intervals and should report them. It should also run the model with and without the environmental score and compare the out-of-sample discrimination. If the environmental score adds nothing, the honest conclusion is that the data do not support its inclusion at the current sample size—not that environmental performance is irrelevant.

What typically fails in stage 2 is the survival model, not the logit. The Cox specification requires clean default dates and a censoring convention, and banks often discover that their internal records do not distinguish a default from a restructured loan that never formally defaulted. The team then has to reconstruct default dates from workout files, which takes longer than the estimation itself. The logit, which needs only a binary indicator over a fixed horizon, is more forgiving of messy records, and most banks should run it first.

4.5.4 Stage 3: The LGD Model (Months 18–30)

The third stage builds the LGD model with the environmental adjustments. Stage 3 is the slowest because workout data accumulate slowly. A green loan that defaults in year 1 may not be resolved until year 4. The bank should start collecting workout data in stage 1, even before the LGD model is built, so that the data are available when the model is ready.

What fails here is the adjustment magnitudes. The initial \(\delta\) ranges in section 4.3.4 are priors, and the first three or four green workouts will almost certainly fall outside them, because the sample is tiny and the cases that reach workout are selected for complexity. The temptation is to recalibrate the ranges on those three or four cases. The bank should resist it. A better use of the early workouts is to check the direction of each adjustment—did the integrated waste-heat system really recover less than the modular array?—and to leave the magnitudes at their priors until the sample reaches a dozen or so. The recovery rating analogue described in section 4.3.7 is the practical compromise: it imposes discipline on each workout as it arrives without pretending that four cases constitute a calibration.

4.5.5 The Feedback Loop

The three stages are not a one-time sequence. Each year, the bank should re-estimate the models on the expanded sample, re-validate the discrimination, and revise the adjustments. The revisions should be documented, with the reason for each change and the evidence that motivated it. A model that is never revised is a model that is not being validated; a model that is revised without documentation is a model that cannot be audited.

4.6 What the Models Do Not Capture

4.6.1 Transition Risk Beyond the Horizon

The models in this chapter estimate default risk over a one-year horizon. The green transition is a multi-decade process. A firm that is financially healthy today may be stranded in ten years if its assets are incompatible with a low-carbon economy. The one-year PD does not capture this.

The gap is partly addressed by the environmental score, which incorporates transition capacity (green capex ratio, transition plan quality). But the score is a point-in-time assessment, not a projection. A firm with a credible transition plan may still fail to execute it, and the model has no way to distinguish credible plans from aspirational ones except through the manual review score, which is subjective.

A more ambitious approach would model the firm's asset base under different transition scenarios and estimate the probability that the asset base becomes stranded within the loan's maturity. This is scenario analysis, not PD estimation, and it belongs in the stress-testing framework rather than the base-case model. Chapter 5 takes up the portfolio-level version of this problem.

4.6.2 Physical Risk

The models treat environmental risk primarily as transition risk—the risk that policy, technology, or market changes impair the borrower's ability to repay. Physical risk—the risk that floods, droughts, or storms damage the borrower's assets—is largely absent.

Physical risk enters the credit model through two channels: it can damage collateral (raising LGD) and it can disrupt operations (raising PD). Both channels are difficult to model at the firm level because the data on firm-specific physical exposure is sparse and the climate projections are uncertain at the spatial scale that matters for a single borrower.

The insurance literature, which Chapter 6 takes up, offers a partial solution: weather index insurance and other risk-transfer instruments can convert physical risk into a known cost (the premium), which the credit model can then treat as an expense rather than an uncertain loss. The integration of insurance into the credit model is the subject of Chapter 8.

4.6.3 The Data Quality Ceiling

The models are constrained by the data. A scorecard built on self-reported, unaudited environmental data will produce scores that are precise but not accurate. A PD model estimated on a small default sample will produce coefficients that are unbiased in expectation but highly variable. An LGD model built on a handful of workouts will produce adjustments that are plausible but unvalidated.

The constraint is not a reason to abandon the models. It is a reason to report the uncertainty honestly and to invest in data infrastructure. Chapter 12 takes up the data infrastructure question in detail. For now, the point is that the models in this chapter are only as good as the data feeding them, and the data feeding them is, in most banks, not yet good enough to support fine distinctions. A scorecard that separates borrowers into ten environmental bands is claiming a precision the underlying data cannot support; five bands is closer to honest.

4.7 Conclusion: Three Numbers, Three Sets of Assumptions

The chapter has built three models. The scorecard maps borrower characteristics to a rank. The PD model maps the rank and the environmental score to a default probability. The LGD model maps the exposure and its collateral to a recovery rate. Together they produce an expected loss that is more informative than the sector-average assumptions that most banks use today.

The models are not a solution to the green credit risk problem. They are a way of making the problem explicit. A bank that builds them will discover that its environmental data is worse than it thought, that its default sample is smaller than it needs, and that its LGD adjustments are more judgmental than it would like. Those discoveries translate into specific changes: a scorecard that drops carbon intensity for the trading book because the data are tier 3 or worse, a PD model that enters the environmental score as a single covariate because twelve coefficients cannot be estimated on 22 defaults, and an LGD schedule that leaves the adjustment ranges at their priors until the workout sample reaches a dozen cases.

A bank that does not build them will continue to price green loans as if environmental performance were irrelevant. That position is itself a model, with its own assumption—that environmental performance has no effect on default or recovery—and it is the one assumption in this chapter that has never been tested.

The next chapter takes the three numbers and asks what happens when they are aggregated across a portfolio. The answer depends on the dependence structure: the correlation of defaults among green borrowers, and between green and brown borrowers. That correlation is where the transition risk that the single-borrower models cannot capture becomes visible at the portfolio level. Estimating it requires a default history that spans both a policy tightening and a business-cycle downturn, and no Chinese bank yet has one. The first task of Chapter 5 is therefore to specify what data the correlation estimate needs, and how a bank can begin collecting it before the next tightening arrives.