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Logistic Regression for Default Risk and Bank Capital

Article Quant Q&A · Author: BCLC
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Summary

The document discusses practical use of logistic regression to estimate probability of default (PD), especially for retail credit such as consumer loans and credit cards. It contrasts those settings with low-default portfolios, including government bonds, where too few observed defaults can make logit estimates unreliable or infeasible.

The response argues that banks may benefit from more accurate PD estimates because they inform regulatory capital requirements. It recommends comparing logistic regression with probit and neural network models, assessing both capital needs and the effect on lending capacity. However, it offers no case study or measured implementation result: the author says the empirical evidence is limited and the topic remains debated. The proposed financial benefit is therefore a rationale to investigate, not proof that a particular model saved money. Model approval, validation, and supervisory requirements also constrain whether estimated capital reductions can be realized.

Key ideas

  • Logistic regression is commonly applied to retail credit default estimation.
  • Low-default portfolios may not contain enough events for reliable logit estimation.
  • PD estimates contribute to bank regulatory capital calculations.
  • Model comparisons should consider capital impact alongside predictive performance.
  • The document supplies a proposed economic rationale, not evidence from an implemented case.

Tags

StatisticsRisk managementMachine learning
Full text
# Actually benefiting from logistic regression to estimate probability of default


# Actually benefiting from logistic regression to estimate probability of default












Does anyone know any events where using logistic regression to estimate probability of default has led to a bank, financial institution, government or anything really to benefit in practice?

I see a lot of journals, papers and theses on logistic regression used to estimate PD. Some develop models, and some validate. But how many actually prove beneficial in practice?

Motivation: For a mathematical finance project, I have to convince a bank, financial institution or government to even entertain the idea of using probabilities of default coming from logistic regression. Theoretical justifications or predictions won't do. It has to be good effects that actually come from using the PDs. Like, model was implemented then it turned out great (Never mind The Black Swan for now).

The project is already complete but utterly pointless outside a bookshelf for future research if the bank/FI/govt doesn't choose to implement it.

I am looking for not necessarily a journal, paper or thesis. It could be a news or magazine article or something, anything really.

## Answer by Quantopik (score 5, accepted)

https://quant.stackexchange.com/a/16669

Firstly, the use of the logit models to estimate the PDs is particularly appreciated in some credit industries, as, for instance, the credit retail one. The logit model predicts pretty well the PD on loans, consumer credit, credit cards, ... and all concerns the retail consumer world.

Mainly, those listed are the principal sub-industries in the credit business where the logit model works fine.

In the others, the logit model does not work. The most famous case is the PD estimate of low-default-portfolios, in which there are so fews defaults that's impossible to estimate the probability of default by using a logit model; the government bond portfolios are an example of those ones.

Secondly, I suggest to look at the benefits of those kinds of model in terms of money saved by the bank; as you probably know, generally a bank has to estimate the probability of default about own credit exposures in order to be able to set aside the right quantity of money to satisfy capital requirements according to the Basel III treaty.

As more the PD estimates about the bank credit exposures are accurate, as more the bank saves money (required capital).

This is the main reason the bank wants to estimate properly PD, EAD, LGD,... because, in this way, by showing to the Supervisor it can develop a model correctly and in a better way than the model suggested by the regulators, the bank can set aside less money in terms of capital requirements and, so, to invest money in the business.

Now, in order to show to the bank why it should use those kind of model, you should estimate the different models suggested by the literature:

- Logistic model;

- Probit model;

- Neural networks;

and compare them to see which model allows you, at the same time, to save money in terms of capital requirements and make money in terms of business. In fact, the money you set aside for the capital requirements cannot be used by the banks for business (the bank cannot use that money to issue, for example, a loan).

Thirdly, there is no articles, papers or something like this on which you can base your answer for the project work, because this topic is relatively new and the academic literature is still debatable about that. I suggest to provide your own (reasonable) considerations about the issue.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.