Default modelling in an age of agility

June 2024
4 min read

We explore how the Bayesian Gaussian Process Classifier (GPC) injects much needed agility and interpretability into default modelling.

In brief:

  • Prevailing uncertainty in geopolitical, economic and regulatory environments demands a more dynamic approach to default modelling.
  • Traditional methods such as logistic regression fail to address the non-linear characteristics of credit risk.
  • Score-based models can be cumbersome to calibrate with expertise and can lack the insight of human wisdom.
  • Machine learning lacks the interpretability expected in a world where transparency is paramount.
  • Using the Bayesian Gaussian Process Classifier defines lending parameters in a more holistic way, sharpening a bank’s ability to approve creditworthy borrowers and reject proposals from counterparties that are at a high risk of default.

Historically high levels of economic volatility, persistent geopolitical unrest, a fast-evolving regulatory environment – a perpetual stream of disruption is highlighting the limitations and vulnerabilities in many credit risk approaches. In an era where uncertainty persists, predicting risk of default is becoming increasingly complex, and banks are increasingly seeking a modelling approach that incorporates more flexibility, interpretability, and efficiency.

While logistic regression remains the market standard, the evolution of the digital treasury is arming risk managers with a more varied toolkit of methodologies, including those powered by machine learning. This article focuses on the Bayesian Gaussian Process Classifier (GPC) and the merits it offers compared to machine learning, score-based models, and logistic regression.

A non-parametric alternative to logistic regression

The days of approaching credit risk in a linear, one-dimensional fashion are numbered. In today’s fast paced and uncertain world, to remain resilient to rising credit risk, banks have no choice other than to consider all directions at once. With the GPC approach, the linear combination of explanatory variables is replaced by a function, which is iteratively updated by applying Bayes’ rule (see Bayesian Classification With Gaussian Processes for further detail).

For default modelling, a multivariate Gaussian distribution is used, hence forsaking linearity. This allows the GPC to parallel machine learning (ML) methodologies, specifically in terms of flexibility to incorporate a variety of data types and variables and capability to capture complex patterns hidden within financial datasets.

A model enriched by expert wisdom

Another way GPC shows similar characteristics to machine learning is in how it loosens the rigid assumptions that are characteristic of many traditional approaches, including logistic regression and score-based models. To explain, one example is the score-based Corporate Rating Model (CRM) developed by Zanders. This is the go-to model of Zanders to assess the creditworthiness of corporate counterparties. However, calibrating this model and embedding the opinion of Zanders’ corporate rating experts is a time-consuming task. The GPC approach streamlines this process significantly, delivering both greater cost- and time-efficiencies. The incorporation of prior beliefs via Bayesian inference permits the integration of expert knowledge into the model, allowing it to reflect predetermined views on the importance of certain variables. As a result, the efficiency gains achieved through the GPC approach don’t come at the cost of expert wisdom.

Enabling explainable lending decisions

As well as our go-to CRM, Zanders also houses machine learning approaches to default modelling. Although this generates successful outcomes, with machine learning, the rationale behind a credit decision is not explicitly explained. In today’s volatile environment, an unexplainable solution can fall short of stakeholder and regulator expectations – they increasingly want to understand the reasoning behind lending decisions at a forensic level. 

Unlike the often ‘black-box’ nature of ML models, with GPC, the path to a decision or solution is both transparent and explainable. Firstly, the GPC model’s hyperparameters provide insights into the relevance and interplay of explanatory variables with the predicted outcome. In addition, the Bayesian framework sheds light on the uncertainty surrounding each hyperparameter. This offers a posterior distribution that quantifies confidence in these parameter estimates. This aspect adds substantial risk assessment value, contrary to the typical point estimate outputs from score-based models or deterministic ML predictions. In short, an essential advantage of the GPC over other approaches is its ability to generate outcomes that withstand the scrutiny of stakeholders and regulators.

A more holistic approach to probability of default modelling

In summary, if risk managers are to tackle the mounting complexity of evaluating probability of default, they need to approach it non-linearly and in a way that’s explainable at every level of the process. This is throwing the spotlight onto more holistic approaches, such as the Gaussian Process Classifier. Using this methodology allows for the incorporation of expert intuition as an additional layer to empirical evidence. It is transparent and accelerates calibration without forsaking performance. This presents an approach that not only incorporates the full complexity of credit risk but also adheres to the demands for model interpretability within the financial sector.

Are you interested in how you could use GPC to enhance your approach to default modelling? Contact Kyle Gartner for more information.


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