Page 41 - CCFA Journal - Ninth Issue

加中金融 数学建模 Math Modeling
加中金融

In our proposed DRC IMA model, a standardized normal asset process is assumed for each obligor, and mapped to the global
indices, country (region) indices.

4 最新的发展

Merton 类型模型的最新应用之一是模拟与气候相关的转型风险。 Merton 框架用于将气候转型情景与信用风险联系起来，
信用风险由行业/部门和地理的概率概率来衡量。该模型的详细描述可以在参考文献中找到 [11].

另一个最新进展是 FRTB 中的 DRC IMA 模型。 FRTB 是巴塞尔银行监管委员会 (BCBS) 在 2008 年金融危机之后的几年里发起
的针对交易账户的基于风险的新资本要求 [12]。

DRC 捕获任何信用风险敞口的违约风险，取代巴塞尔协议 2.5 中当前的 IRC 模型。 DRC IMA 使用风险值 (VaR) 模型进行衡
量。需要一个超过一年时间范围的多因素蒙特卡罗模拟模型，模型中包含 PD 相关性和 PD/LGD 相关性。

在我们提出的 DRC IMA 模型中，假设每个债务人都有一个标准化的正常资产流程，并映射到全球指数、国家（地区）指数。

( ( )⊗ )
( )
= × + ∑ , × ( ) + ∑ , ×

( ( )⊗ ) + × [13]

Weights related to base (country(region)/industry) factors can be assigned based on revenue or discretional decisions.
Following Basel guidelines, default correlation is computed based on historical credit spreads and listed equity prices. Sector
definitions need to be based on the bank’s exposure. For a typical global bank, we can have over 10 industry sectors, one
government, and one municipal sector.

The global factor also serves the purpose of computing PD-LGD correlation. LGD is simulated via a beta distribution.

与基本（国家（地区）/行业）因素相关的权重可以根据收入或自行决定分配。

根据巴塞尔准则，违约相关性是根据历史信用利差和上市股票价格计算的。行业定义需要基于银行的风险敞口。对于一家
典型的全球银行，我们可以拥有 10 个以上的行业部门、一个政府部门和一个市政部门。

全局因子还用于计算 PD-LGD 相关性。 LGD 是通过 beta 分布模拟的。

References
[1] Merton, R.C. “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates,” Journal of Finance, 29: 449-70 (1974)

[2] Crosbie, P., Bohn, J., “Modeling Default Risk. Modeling Methodology.” Moody’s KMV (2003)

[3] Gupton, G.M., J.P. Morgan & Co, C. C. Finger, and M. Bhatia, “CreditMetrics - Technical Document: The Benchmark for
Understanding Credit Risk,” 1997

[4] Tazhi Y., E. Wang, Z. Hu, and M. A. Clayton, “Transition Probability Matrix Methodology for Incremental Risk Charge,”, Journal of
Financial Engineering, Vol. 01, No. 01, 1450010 (2014)

[5] Albanese C. and O. Chen, “Implied migration rates from credit barrier models,” Journal of Banking & Finance, vol 30, 607-626
(2006)

[6] Hull, J., I. Nelken, and A. White, “Merton’s model, Credit Risk, and Volatility Skews”, Journal of Credit Risk, Vol 1, No. 1, 3-27
(2005)

[7] Moody’s Investors Service, “Default Trends -Global, December 2021 Default Report,” January 2022

[8] International Accounting Standards Board (IASB), “IFRS 9 Financial instruments. International Accounting Standards Board.”
(2014), https://www.ifrs.org/issued-standards/list-of-standards/ifrs-9-financial-instruments/

[9] Yang, B. H, “Point-in-time” Probability of Default Term Structure Models for Multiperiod Scenario Loss Projection,” Journal of
Risk Model Validation, Vol 11, No. 1, 73-94 (2017)

[10] Vasicek, O. “Loan Portfolio Value,” Risk (December 2002), 160-62

[11] Huang, H., E. Wang, H. Huang, and Y. Wang, “An Analytical VaR Approach for Credit Portfolio with Liquidity Horizon and Portfolio
Rebalancing,” Journal of Credit Risk 11(4), 1-28 (2015)

[12] Hosseini H., C Johnston, C. Logan, M. Molico, S. Shen, and M. Tremblay, “Assessing Climate-Related Financial Risk: Guide to
Implementation of Methods., Bank of Canada Technical Report (2022)

[13] Basel Committee on Banking Supervision, “Minimum capital requirements for market risk,” January (2019),
https://www.bis.org/bcbs/publ/d457.htm

CCFA JOURNAL OF FINANCE December 2022
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