Corporate Credit Climate Stress


Patrick Naim, risk modelling expert.
Published June, 03, 2021


In this article, we present a method for assessing the impact of climate change on a bank's corporate credit portfolio. This approach is built around 3 ideas:

This method has been designed as part of the 2020 Climate Risk Exercise of the French regulator ACPR.

Corporate Climate Sensitivity

The formalization of the climate stress on corporate credit has been proposed in particular in the UNEP-FI Initiative in 2018.

Transition costs (carbon tax) and possible disaster costs impact the firm EBITDA and therefore its market value. This stressed market value is then used as an input to Black&Scholes and Merton equations to infer a stressed PD.


Production Costs

Transition Costs

Possible Disaster Costs

Other Expenses (3)
EBITDA (4) (1)-(2)-(T)-(P)-(3)
Firm market value (5) k.(4)

Knowing in full detail the balance sheet of a firm allows to implement the method just discussed and calculate a stressed PD. However, to be applicable in full detail for all firms, this method requires a very significant data collection effort.

We believe that this effort is not justified given the available level of knowledge, and in particular taking into account the uncertainty on transition policies, and the status of models relating climate change and GDP.

This is why we present a simple, normative method, to infer PD multipliers from minimal corporate knowledge. This method allows a quick calibration of climate-related exposure for banks with large corporate portfolios.

Using Black & Scholes and Merton equations

Physical or transition stress will result in additional costs incurred by the exposed company. These costs will affect its profitability, and thus its earnings. Assuming that the market value of the firm is proportional to its profits, climate stress will therefore affect the value of the most exposed firms.

To assess the impact of climate stress on the default risk of a company, we can use the mathematical tools of the Black & Scholes equations and the Merton model.

Solving the Black & Scholes equations allows us to infer a variation in assets from a variation in market value.

Black & Scholes

Assuming that the firm's debt remains stable, the gap between assets and debt is therefore reduced. According to Merton's model, the probability of default is increased.


Systematic application

The analysis just presented is applicable for an individually identified company, since it requires knowledge of its balance sheet, market value, and sensitivity to climate risk, including its emissions and physical risk exposure.
This level of detail may not be known for all of a bank's customers, and in this case, a less granular approach may be useful.
In this respect, external climate stress scenarios generally provide estimates of the impact of transition risk or physical risk, or both, on the market value (equity) of firms in a sector, or on other quantities that can be linked to equity. This is the case of the ACPR 2020 scenarios, which provide an estimate of the impact of the climate transition on the value added of the 55 sectors of the NACE sectoral taxonomy.

The calculation process for the probability of default is as follows:

  1. The value of the Leverage, the return and the volatility of the Equity are measured.
  2. A shock is applied to the value of the Equity.
  3. The value of the Asset, its return and its volatility are inferred from the inversion of the Black-Scholes equations.
  4. The probability of default is calculated using the Merton model.


This graph can be collapsed into a graph linking the 5 inputs and the output (PD).

Simplified Abacus

The comparison between the configurations where the shock is different from 0, and those where the shock is zero, allow us to calculate PD multipliers, expressing the stress of the shock.

Moreover, since the Asset Return and risk-free Return data cannot be known in "forward-looking", we use averages by varying these variables in their definition interval. As the result of all these simplifications we obtain a three-entry abacus associating a level of Leverage and Volatility and a Level of Shock to a PD multiplier.


To make this chart even more readable, we will replace the double entry Leverage and Equity volatility by the rating.

Simplified Transition Stress

Transition risk is modelled as the ratio between priced emissions (using a reference price, for instance 2020) and earnings. It can be measured at the company level if possible, or a sector proxy can be used.
When the detailed balance sheet and market parameters of the firm as not known, we infer a range of balance sheet parameters compatible with the current credit rating and PD. This is done through the inversion of Black & Scholes and Merton equations.

This range of balance sheets is transformed in a range of stressed balance sheets, and we can infer an average stress on PD – or a distribution. For the portfolio of exposures, we can use a mix of company assessments and sector proxies.


Simplified Physical Stress

Physical risk is modelled through the increase factor of natural disasters in the regions where the company primarily operates. We consider that the current level of natural disasters is already priced into the current probability of default

Then, knowing the current probability of natural disasters to which the firm is exposed, we deduce the contribution of natural disasters to the probability of default.  Finally, we only need to stress the probability of disasters to evaluate a stressed PD.


Application to a portfolio

To apply the method to a portfolio of corporate credit exposures, we only need 3 ratings : the credit rating, the transition sensitivity rating, and the physical sensitivity rating.
Combined with the hypotheses of the climate scenario, this allows us to calculate PD multipliers for transition and physical risks.