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2018 | OriginalPaper | Buchkapitel

6. A Regulatory Perspective

verfasst von : David Jamieson Bolder

Erschienen in: Credit-Risk Modelling

Verlag: Springer International Publishing

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Abstract

Quantitative analysts seek to construct useful models to assess the magnitude of credit risk in their portfolios and inform associated management decisions. Regulators, in a slightly alternative context, perform a similar task. They face, however, a rather different set of constraints and objectives. Regulators, in fact, use standardized models to promote fairness, a level playing field, monitor the solvency of individual entities, and enhance overall economic stability. Much can be learned from the regulatory perspective; indeed, actions and trends in the regulatory field are an important diagnostic for internal modellers. To underscore this point, this chapter focuses principally on the widely used internal-ratings-based (IRB) approach proposed by the Basel Committee on Banking Supervision. Closer inspection reveals that this approach is founded on a portfolio-invariant version of the Gaussian threshold model. Portfolio invariance implies that the risk of the portfolio is independent of the overall portfolio structure and depends only on the characteristics of the individual exposures. Expedient rather than realistic, this choice reduces the computational and system burden on regulated organizations, but ignores concentration risk. After applying the IRB approach to our portfolio example, we then carefully explore Gordy (2003, Journal of Financial Intermediation, 12, 199–232)’s granularity adjustment, which was proposed to address this shortcoming.

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Vorheriges Kapitel The Genesis of Credit-Risk Modelling

Nächstes Kapitel Risk Attribution

In the interests of full disclosure, the author was employed, although not involved with the BCBS, by the BIS from 2008 to 2016.

For most of our previous and subsequent analysis, we assume that γ _n ≡ 1 and thus it is equivalent to work exclusively with c _n.

Or, at least, it makes an important contribution to this relationship. Recall, from Chap. 4, that the state-variable correlation is equivalent \(\rho _{nm}=\sqrt {\rho _n\rho _m}\) in the one-factor threshold model for two arbitrary obligors n and m.

Practically, however, it should be stressed that the correlation function in the IRB setting only influences the conditional default probability used in the risk-capital coefficient computations. There is no notion of an underlying correlation matrix for all issuers given the principle of portfolio invariance.

The actual values of ρ ⁻, ρ ⁺ and h were, presumably, determined through a combination of empirical work, calibration and compromise.

This is easily verified,

https://static-content.springer.com/image/chp%3A10.1007%2F978-3-319-94688-7_6/MediaObjects/458636_1_En_6_Equ16_HTML.png

(6.16)

See, for example, Zaccone (2015) for more detail on these techniques.

See, for example, Bolder (2015, Chapter 11) for a more detailed discussion of this technique in the market-risk setting.

Moreover, any work involving this assumption—such as the Standard & Poor’s credit-rating agency’s risk-adjusted capital ratio employed in assessing firm’s credit ratings—also inherits this potential shortcoming. There is, therefore, general interest in its implications.

A rigorous and axiomatic treatment is found in Gordy (2003).

For more on sector-concentration risk, the reader is referred to Lütkebohmert (2008, Chapter 11).

Rau-Bredow (2004) also addresses this tricky issue in substantial detail.

This is specialized to the Gaussian threshold setting, but in any one-factor setting this behaviour is prevalent. The systematic factor may be, of course, monotonically increasing in G. The key is that, in all one-factor models, default loss is a monotonic function of the systematic factor; the direction of this relationship does not create any loss of generality.

See Billingsley (1995, Chapter 2) for more colour on the change-of-variables technique. Torell (2013) does this in a slightly different, but essentially, equivalent manner.

See S&P (2010, 2011, 2012) for more detail on this widely discussed ratio.

This value is determined using equation 6.11 with an average unconditional default probability of 0.01.

Practically, for small values of λ _n(S), the random variable X _n basically only takes two values: 0 and 1. The \(\mathbb {P}(X_n>1)\) is vanishingly small.

If, for example, ω _n = 0, then it reduces to an independent-default Poisson model.

In the shape-rate parameterization, which we used in Chap. 3, the density has a slightly different form. In this case, we assume that \(S\sim \varGamma \left (a,a\right )\). Ultimately, there is no difference in the final results; we used the shape-scale parametrization to maximize comparability with the Gordy and Lütkebohmert (2007, 2013) development.

See, for example, S&P (2010, Paragraphs 148–151).

See Casella and Berger (1990, Chapter 3) or Johnson et al. (1997, Chapter 17) for more information on the gamma distribution.

Recall that the monotonicity of conditional default probabilities runs in opposite directions for the CreditRisk+ and threshold methodologies. Thus, q _1−α(G) is equivalent to q _α(S) where G and S denote the standard-normal and gamma distributed systematic state variables, respectively.

a, in principle, also describes the expectation of S, but this has been set to unity.

This is a bit time consuming, but the idea is to create fair conditions for the experiment.

To put Algorithm 6.10 into context and for more information on the practical implementation of the CreditRisk+ model, please see Chap. 3.

Billingsley, P. (1995). Probability and measure (3rd edn.). Third Avenue, New York, NY: Wiley.

BIS. (2001). The internal ratings-based approach. Technical report. Bank for International Settlements.

BIS. (2004). International convergence of capital measurement and capital standards: A revised framework. Technical report. Bank for International Settlements.

BIS. (2005). An explanatory note on the Basel II IRB risk weight functions. Technical report. Bank for International Settlements.

BIS. (2006b). Studies on credit risk concentration. Technical report. Bank for International Settlements.

Bolder, D. J. (2015). Fixed income portfolio analytics: A practical guide to implementing, monitoring and understanding fixed-income portfolios. Heidelberg, Germany: Springer.CrossRef

Casella, G., & Berger, R. L. (1990). Statistical inference. Belmont, CA: Duxbury Press.

Emmer, S., & Tasche, D. (2005). Calculating credit risk capital charges with the one-factor model. Technical report. Deutsche Bundesbank.

Gordy, M. B. (2002). A risk-factor model foundation for ratings-based bank capital rules. Board of Governors of the Federal Reserve System.

Gordy, M. B. (2003). A risk-factor model foundation for ratings-based bank capital rules. Journal of Financial Intermediation, 12, 199–232.CrossRef

Gordy, M. B., & Lütkebohmert, E. (2007). Granularity Adjustment for Basel II. Deutsche Bundesbank, Banking and Financial Studies, No 01–2007.

Gordy, M. B., & Lütkebohmert, E. (2013). Granularity adjustment for regulatory capital assessment. University of Freiburg.

Gourieroux, C., Laurent, J., & Scaillet, O. (2000). Sensitivity analysis of values at risk. Journal of Empirical Finance, 7(3–4), 225–245.CrossRef

Gundlach, M., & Lehrbass, F. (2004). CreditRisk+ in the banking industry (1st edn.). Berlin: Springer-Verlag.CrossRef

Johnson, N. L., Kotz, S., & Balakrishnan, N. (1997). Continuous univariate distributions: volume 2. New York, NY: John Wiley & Sons. Wiley series in probability and statistics.

Lütkebohmert, E. (2008). Concentration risk in credit portfolios. Berlin: Springer-Verlag.

Martin, R. J., & Wilde, T. (2002). Unsystematic credit risk. Risk, 123–128.

Merton, R. (1974). On the pricing of corporate debt: The risk structure of interest rates. Journal of Finance, 29, 449–470.

Rau-Bredow, H. (2004). Value-at-risk, expected shortfall, and marginal risk contribution. In G. Szegö (Ed.), Risk measures for the 21st century. John Wiley & Sons.

Sharpe, W. F. (1963). A simplified model for portfolio analysis. Management Science, 9(2), 277–293.CrossRef

Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. The Journal of Finance, 19(3), 425–442.

S&P. (2010). Bank capital methodology and assumptions. Technical report. Standard & Poor’s Global Inc.

S&P. (2011). General criteria: Principles of credit ratings. Technical report. Standard & Poor’s Global Inc.

S&P. (2012). Multilateral lending institutions and other supranational institutions ratings methodology. Technical report. Standard & Poor’s Global Inc.

Torell, B. (2013). Name concentration risk and pillar 2 compliance: The granularity adjustment. Technical report. Royal Institute of Technology, Stockholm, Sweden.

Vasicek, O. A. (1987). Probability of loss on loan distribution. KMV Corporation.

Vasicek, O. A. (1991). Limiting loan loss probability distribution. KMV Corporation.

Vasicek, O. A. (2002). The distribution of loan portfolio value. Risk, (12), 160–162.

Wilde, T. (1997). CreditRisk+: A credit risk management framework. Credit Suisse First Boston.

Yago, K. (2013). The financial history of the Bank for international settlements. London: Routledge, Taylor & Francis Group.CrossRef

Zaccone, G. (2015). Python parallel programming cookbook. Birmingham, UK: Packt Publishing.

Titel: A Regulatory Perspective
verfasst von: David Jamieson Bolder
Verlag: Springer International Publishing
Buch: Credit-Risk Modelling
Print ISBN: 978-3-319-94687-0

Electronic ISBN: 978-3-319-94688-7

Copyright-Jahr: 2018
DOI: https://doi.org/10.1007/978-3-319-94688-7_6