Modeling default risk charge (DRC) with intensity probability theory

Badreddine Slime; Jaspreet Singh Sahni; Badreddine Slime; Jaspreet Singh Sahni

doi:10.3934/math.2025137

AIMS Mathematics

2025, Volume 10, Issue 2: 2958-2973. doi: 10.3934/math.2025137

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Modeling default risk charge (DRC) with intensity probability theory

Badreddine Slime ^{1,2
,
,},
Jaspreet Singh Sahni ^{3
,
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1.
Applied Mathematics University of Technology of Compiègne Alliance Sorbonne University, Compiègne, France
2.
Market and Treasury Credit Risk Modeling and Analytics, Emirates National Bank of Dubai, Dubai, UAE
3.
Market and Treasury Credit Risk, Emirates National Bank of Dubai, Dubai, UAE

Received: 21 September 2024 Revised: 12 January 2025 Accepted: 17 January 2025 Published: 17 February 2025
MSC : 37M05, 46N30, 47N30, 62D05, 62E10

The latest regulation ^[1] of the fundamental review of the trading book (FRTB) proposes replacing incremental risk charge (IRC) with default risk charge (DRC). Accordingly, many studies were implemented to analyze this change and its impact. Current modeling practices test several assumptions during conception and implementation. However, these assumptions impact model output and sometimes do not reflect market behavior. Two common assumptions used in DRC modeling in the literature are: (ⅰ) the default is implemented in a structural model (e.g., the Merton model) and (ⅱ) correlations between issuers follow the Gaussian copula. Notably, the Merton model does not pick up defaults for positions with a very small probability of default or instant default. Therefore, the structural approach results in a model risk that is not conservative enough to cover the DRC risk. In this paper, we compared an intensity model (CreditRisk+) to a structural model (Merton) to assess their impact on DRC and quantify the risk generated by the first assumption.
- credit risk,
- market risk,
- fundamental review of the trading book (FRTB),
- default risk charge,
- model risk,
- mathematical finance modeling,
- statistics,
- probability
Citation: Badreddine Slime, Jaspreet Singh Sahni. Modeling default risk charge (DRC) with intensity probability theory[J]. AIMS Mathematics, 2025, 10(2): 2958-2973. doi: 10.3934/math.2025137

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Abstract

The latest regulation ^[1] of the fundamental review of the trading book (FRTB) proposes replacing incremental risk charge (IRC) with default risk charge (DRC). Accordingly, many studies were implemented to analyze this change and its impact. Current modeling practices test several assumptions during conception and implementation. However, these assumptions impact model output and sometimes do not reflect market behavior. Two common assumptions used in DRC modeling in the literature are: (ⅰ) the default is implemented in a structural model (e.g., the Merton model) and (ⅱ) correlations between issuers follow the Gaussian copula. Notably, the Merton model does not pick up defaults for positions with a very small probability of default or instant default. Therefore, the structural approach results in a model risk that is not conservative enough to cover the DRC risk. In this paper, we compared an intensity model (CreditRisk+) to a structural model (Merton) to assess their impact on DRC and quantify the risk generated by the first assumption.

References

[1]	Basel committee on banking supervision, Minimum capital requirements for market risk, 2016. Available from: https://www.bis.org/bcbs/publ/d457.htm
[2]	R. C. Merton, On the pricing of corporate debt: The risk structure of interest rates, J. Finance, 29 (1974), 449–470. https://doi.org/10.1111/j.1540-6261.1974.tb03058.x doi: 10.1111/j.1540-6261.1974.tb03058.x
[3]	T. Wilde, Credit Risk+: A credit risk management framework, Technical document, Credit Suisse First Boston, 1997. Available from: http://www.defaultrisk.com/pp_model_21.htm
[4]	J. P. Laurent, M. Sestier, S. Thomas, Trading book and credit risk: How fundamental is the basel review?, J. Banking Finance, 73 (2016), 211–223. https://doi.org/10.1016/j.jbankfin.2016.07.002 doi: 10.1016/j.jbankfin.2016.07.002
[5]	S. Wilkens, M. Predescu, Default risk charge: Modeling framework for the "Basel" risk measure, J. Risk, 19 (2017), 23–50. http://dx.doi.org/10.21314/JOR.2017.358 doi: 10.21314/JOR.2017.358
[6]	S. Wilkens, M. Predescu, Model risk in the fundamental review of the trading book: The case of the default risk charge, J. Risk Model Validation, 12 (2018), 1–26. https://dx.doi.org/10.2139/ssrn.3053426 doi: 10.2139/ssrn.3053426
[7]	A. D. Joseph, Emerging market default risk charge model, J. Risk Financ. Manag., 16 (2023), 194. https://doi.org/10.3390/jrfm16030194 doi: 10.3390/jrfm16030194
[8]	S. Mestiri, Credit scoring using machine learning and deep learning-based models, Data Sci. Finance Econ., 4 (2024), 236–248. https://doi.org/10.3934/DSFE.2024009 doi: 10.3934/DSFE.2024009
[9]	K. Pourkermani, VaR calculation by binary response models, Data Sci. Finance Econ., 4 (2024), 350–361. https://doi.org/10.3934/DSFE.2024015 doi: 10.3934/DSFE.2024015
[10]	B. Slime, Mathematical modeling of concentration risk under the default risk charge using probability and statistics theory, J. Probab. Stat., 2022. https://doi.org/10.1155/2022/3063505
[11]	M. Wu, D. Xie, The impact of ESG performance on the credit risk of listed companies in Shanghai and Shenzhen stock exchanges, Green Finance, 6 (2024), 199–218. https://doi.org/10.3934/GF.2024008 doi: 10.3934/GF.2024008
[12]	G. Orlando, M. Bufalo, H. Penikas, C. Zurlo, Modern financial engineering, In: Topics in systems engineering, World Scientific Publishing Company, 2022. https://doi.org/10.1142/12725
[13]	A. Bhattacharya, S. Kr. Biswas, A. Mandal, Credit risk evaluation: A comprehensive study, Multimed. Tools Appl., 82 (2023), 18217–18267. https://doi.org/10.1007/s11042-022-13952-3 doi: 10.1007/s11042-022-13952-3

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