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Applying Mean Field Games to Retail Banking Risk Models

Article Quant Q&A · Author: Who cares
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Summary

The document considers whether retail banking models for deposits, cards, loans, and underwriting can use ideas beyond generic econometric or machine learning methods. It distinguishes risk-neutral valuation used within financial intermediation from the real economic risks borne by people who deposit, borrow, and repay. Because depositors and borrowers may be the same population, those risks can interact in a feedback loop rather than behaving like independent claims with natural opposite-risk holders.

The proposed direction is to model how real-economy risk passes through financial intermediaries and to use mean field games to represent the interacting decisions of many agents. Stochastic control provides a framework for decision-making, while liquidity and crowding effects are identified as relevant considerations. The discussion points to existing literature and alternative data as useful resources, but it is a conceptual roadmap rather than a specified model, empirical study, or tested underwriting method. It gives no evidence that one approach outperforms current retail models.

Key ideas

  • Risk-neutral valuation in financial intermediation differs from modeling household and business credit risk.
  • Depositors and borrowers can belong to the same population, creating linked risks and feedback effects.
  • Mean field games can represent strategic or controlled behavior across a large crowd of agents.
  • Stochastic control may help frame retail decisions, including those affected by liquidity and crowding.
  • The document proposes a research direction but does not present a calibrated model or performance evidence.

Tags

Machine learningStatisticsRisk management
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# Advances in retail modelling


# Advances in retail modelling












The risk-neutral modelling framework leads to very advanced and mathematically rich approach to contingent claims modelling. However, in my experience, retail modelling in Banks is done using generic econometric and AI/ML models. By retail modelling I mean in particular the credit risk models (deposits, cards, loans) and also the decision models (underwriting). All of it lacks the mathematical richness and the economic incisiveness of the no-arbitrage/risk-neutral framework. I have not found even academic attention given to this space.

Is this area of finance condemned to off-the-shelf lack of imagination data science modelling?

## Answer by lehalle (score 2, accepted)

https://quant.stackexchange.com/a/77010

There is a big different between the financial intermediation (that can use a risk-neutral approach to prevent too large misalignment of valuations that would be due to disparities of risk aversions), and the connection between the "real economy" (economic and business risk on people who make deposits, get loans and reimburse them --or not--) and the financial risk.

The natural approach would be to propagate the same "real risk" to the financial system until it reaches another "external agent" (I mean: external to the network of financial intermediaries).

Start by figuring out who (outside of the financial system) would have the exact opposite risk than people making deposits? Typically transforming deposits in loans is the step "maturity transformation" of a "Banking 101" course. If you have a look at Bologna, Pierluigi. Banks’ maturity transformation: risk, reward, and policy (International Monetary Fund, 2018), you will see that there is a rich literature on the topic. If you would have natural buyers of this risk, you could start to write a risk-neutral view on maturity transformation. The paradoxal aspect is that the user of loans are for a large part the same people who are making the deposits.

On the one hand you make a deposit, on the other hand someone else (or even yourself), get a loan. And of course: conditionally to the fact you want you money back, you (or someone else) will have difficulties to pay the interests of your (or her) loan... There is a closed loop there, and if you want to have a mathematical glance, you should have a look at Mean Field Games. It is the beginning of this family of models that can endogenize stochastic control performed by a crowd of agents (see Cardaliaguet, Pierre. Notes on mean field games. Technical report, 2010 for a gentle introduction).

Stochastic control is standard the way to manage decision taking in a risk-neutral environment, hence if you want to consider liquidity (or crowding effects), MFG is your theory.

For details on financial intermediation that is meant to be an introduction for future MFG users, you can have a look at Financial markets in practice, by L and Raboun 2022.

Last but not least alternative data can help to model retail behaviour, or at least to observe the outcome of these Mean Field Games, see part III of Machine Learning and Data Sciences for Financial Markets - A Guide to Contemporary Practices, Edited by Capponi and L (2023).

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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