Bending the Curve: How Curve Methodology Transforms ECL Assessment in Stress Testing

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Accurate estimation of credit risk has become a cornerstone of prudent financial management. For banks and financial institutions, the transition from incurred loss models to forward-looking frameworks like IFRS 9 and CECL underscores the need for dynamic risk measurement tools. At the heart of these frameworks lies the concept of Expected Credit Loss (ECL), a measure sensitive to both borrower-specific factors and macroeconomic conditions.

Traditional ECL models often rely on static assumptions, overlooking the time-varying nature of risk. Curve Methodology is an advanced approach for assessing ECL – especially under financial stress scenarios. By modeling Prepayment Probability (PP), Probability of Default (PD), Loss Given Default (LGD), and Exposure at Default (EAD) as time-dependent curves, we can achieve greater accuracy and responsiveness in stress testing exercises.

What Is Curve Methodology?

Curve methodology refers to modeling risk parameters such as PP, PD, LGD, EAD and other components as continuous or time-dependent functions, rather than static values, reflecting their evolution over the life of a financial product. These "curves" are built using historical data, econometric models, and macroeconomic scenario inputs, allowing practitioners to evaluate how credit risk evolves across different time horizons and under varying conditions.

Significance of Curve Methodology Under IFRS 9 and Stress Testing

IFRS 9 requires entities to estimate ECL using forward-looking information and consider multiple scenarios, including adverse ones. Stress testing frameworks – especially those mandated by regulators like the European Central Bank (ECB) or Federal Reserve – rely on dynamic modeling of credit risk under extreme but plausible macroeconomic conditions. Curve methodology enables institutions to meet both mandates more robustly.

Traditional models often use static assumptions, estimating ECL at a single point in time without capturing future variability. Curve methodology remedies this by revealing how risk evolves, enabling analysts to conduct stress testing across multiple future horizons.

During macroeconomic stress, for instance, the PD curve steepens as defaults are expected to occur earlier. LGD may increase due to declining collateral values, while EAD could grow due to increased drawdowns. This time-sensitive modeling is particularly effective when layered with macroeconomic shocks.

Fundamentals of ECL Modeling

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Where:

PD_t (Probability of default at time t): The likelihood that a borrower will default within the time horizon t.
LGD_t (Loss given default at time t): The proportion of exposure that is expected to be lost once a default has occurred, expressed as a percentage of EAD.
EAD_t (Exposure at default at time t): The total credit exposure at the time of default, often derived from the unpaid principal balance and contingent credit lines.
PP_t (Prepayment probability at time t): The total credit exposure at the time of default, often derived from the unpaid principal balance and contingent credit lines.
ShockFactor_t Economic scenario adjustment at time t – Simulates macroeconomic impacts on PP, PD, LGD, and EAD curves.

Consider a 5-year loan portfolio with 100 customers. Let’s assume that the observed defaults over the 5-year period is as follows:

Year 1: 1 customers default ⇒PD₁=0.01
Year 2: 2 customers default ⇒PD₂=0.02
Year 3: 3 customers default ⇒PD₃=0.03
Year 4: 2 customers default ⇒PD₄=0.02
Year 5: 1 customers default ⇒PD₅=0.01

These values plotted against time form a PD curve. Similar curves can be constructed for PP, LGD and EAD using historical patterns, contractual terms, and behavioral data.

Adjusting Curves with Shock Factors

Curve techniques allow dynamic adjustment of PD, LGD, and EAD via Shock Factors (ShockFactor_t) derived from macroeconomic forecasts. ShockFactor_t represents the cumulative effect of adverse economic conditions. Suppose the baseline PD for Year 3 is 0.03. Under a recession scenario with a shock factor of 1.5, the stressed PD becomes:

This adjustment can be applied similarly to LGD and EAD. If the LGD increases from 70% to 80% under stress and EAD increases due to drawn credit lines, the ECL calculation reflects the more severe outcome.

And, by summing across all years, analysts generate a full lifetime expected loss profile.

Incorporating Prepayment

Prepayment probability (PP) is a behavioral factor that reflects the likelihood of early principal repayment. Since this affects the interest income stream and potentially reduces EAD, it is factored in as (1−PP) in the ECL formula, especially relevant for retail products.

PP reduces expected credit loss by lowering the exposure period. For example, a 10% annual prepayment rate (PP = 0.10) would reduce ECL by 10% each year unless default precedes prepayment.

Avoiding Conceptual Conflicts

It is crucial to distinguish between Expected and Actual credit losses. Actual losses are observed post-default, net of recoveries. ECL, however, represents a probabilistic forecast that factors in potential future defaults, recovery rates, and prepayment behavior.

Also, EAD is a measure of total credit exposure at the point of default, not the actual amount lost. LGD expresses expected loss as a percentage of EAD, reinforcing the need to model EAD accurately and separately.

Curve Methodology in SAS Stress Testing Solution

SAS Stress Testing provides a robust, transparent, and auditable environment for assessing resilience of financial institutes, and one of its key features is the Curve Methodology, which underpins the evolution of ECL components over time.

SAS Stress Testing includes the ST Curves models, namely ST Curves Common – <version number> and ST Curves – <version number>, which are designed to assess expected credit losses (ECL) under a range of stress scenarios using curve methodology.

ST Curves Common model performs credit risk analysis under standard scenarios, assuming each scenario applies to all forecast periods.

ST Curves model conducts credit risk analysis for distinct scenarios, with each scenario applicable to a single forecast period.

To support curve modeling, SAS Stress Testing Solution uses an analysis data set – often referred to as the risk factor curve data set – that contains the monthly evolution of each risk component for a portfolio or segment. This structured data format allows the curves model to process inputs efficiently and generate monthly ECL estimates that reflect the organic portfolio risk dynamics.

The sample risk factor curve data set contains the following information:

REPORTING_DT – Reporting Date
CURVE_TYPE_CD – Curve Type Code

This column includes values such as:
- LGD – Loss Given Default
- LR – Loss Ratio
- PD – Probability of Default
- PP – Prepayment Probability
SEGMENT_ID – Portfolio segment identifier
HORIZON – Forecast horizon (up to 60 months)
ENTITY_ID – Identifies the business entity
TIME_INTERVAL – Time interval in months
CURVE_RT – Curve Rate

In practice various advanced techniques can be utilized to forecast the CURVE_RT column values. Some examples include:

Survival Analysis for PD: Time-to-default models use statistical survival functions (e.g., Cox regression) to estimate default timing, ideal for modeling forward-looking PD curves.
Beta Regression for LGD: Since LGD is bounded between 0 and 1, beta regression captures its distribution more effectively than linear models.
EAD Modeling via Credit Conversion Factors (CCF): Logistic models help estimate the expected usage of undrawn credit lines, forming dynamic EAD curves.
Machine Learning Enhancements: Gradient boosting and random forest algorithms can improve predictive performance of risk curves but require explainability safeguards.

Each stress testing scenario – baseline, adverse, and severe – contains a set of macroeconomic shocks. The Stress Testing Solution applies these via shock factor values (ShockFactor_t) typically provided in the first row of each scenario input file. These shock factors modify the original curves to reflect the macroeconomic impact on risk components.

In conclusion, the curve methodology brings analytical rigor and flexibility to ECL estimation, especially under volatile conditions. By modeling PD, LGD, EAD, and PP as dynamic term structures, institutions can derive time-sensitive loss expectations that are critical for both informed risk management and regulatory stress testing.

While challenges in data, validation, and computation persist, the integration of advanced techniques like survival analysis, macroeconomic regression, and machine learning is improving forecast precision and resilience. The ability to “bend the curve” – to anticipate and model the shape of risk – is no longer optional in a landscape shaped by rapid financial, technological, and macroeconomic shifts.

Additional Information

For more information on SAS Stress Testing visit the software information page here.

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