Goodness-of-Fit of Logistic Regression of the Default Rate on GDP Growth Rate and on CDX Indices
Under the Basel II and Basel III agreements, the probability of default (PD) is a key parameter used in calculating expected credit loss (ECL), which is typically defined as: PD <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><sema...
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MDPI AG
2021-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/16/1930 |
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| author | Kuang-Hua Hu Shih-Kuei Lin Yung-Kang Ching Ming-Chin Hung |
| author_facet | Kuang-Hua Hu Shih-Kuei Lin Yung-Kang Ching Ming-Chin Hung |
| author_sort | Kuang-Hua Hu |
| collection | DOAJ |
| description | Under the Basel II and Basel III agreements, the probability of default (PD) is a key parameter used in calculating expected credit loss (ECL), which is typically defined as: PD <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>×</mo></semantics></math></inline-formula> Loss Given Default <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>×</mo></semantics></math></inline-formula> Exposure at Default. In practice or in regulatory requirements, gross domestic product (GDP) has been adopted in the PD estimation model. Due to the problem of excessive fluctuation and highly volatile ECL estimation, models that produce satisfactory PD and thus ECL estimations in the context of existing risk management techniques are lacking. In this study, we explore the usage of the credit default swap index (CDX), a market’s expectation of future PD, as a predictor of the default rate (DR). By comparing the goodness-of-fit of logistic regression, several conclusions are drawn. Firstly, in general, GDP has considerable explanatory power for the default rate which is consistent with current models in practice. Secondly, although both GDP and CDX fit the DR well for rating B class, CDX has a significantly better fit of DR for ratings [A, Baa, Ba]. Thirdly, compared with low-rated companies, the relationship between the DR and GDP is relatively weak for rating A. This phenomenon implies that, in addition to using macroeconomic variables and firm-specific explanatory variables in the PD estimation model, high-rated companies exhibit a greater need to use market supplemental information, such as CDX, to capture the changes in the DR. |
| first_indexed | 2024-03-10T08:36:59Z |
| format | Article |
| id | doaj.art-5630f8c437554139b0cb8ae4b4cdc606 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T08:36:59Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-5630f8c437554139b0cb8ae4b4cdc6062023-11-22T08:34:02ZengMDPI AGMathematics2227-73902021-08-01916193010.3390/math9161930Goodness-of-Fit of Logistic Regression of the Default Rate on GDP Growth Rate and on CDX IndicesKuang-Hua Hu0Shih-Kuei Lin1Yung-Kang Ching2Ming-Chin Hung3Finance and Accounting Research Center, School of Accounting, Nanfang College, Guangzhou 510970, ChinaDepartment of Money and Banking, National Chengchi University, Taipei 116, TaiwanRisk Management Department, China Development Financial Holding, Taipei 105, TaiwanDepartment of Financial Engineering and Actuarial Mathematics, Soochow University, Taipei 100, TaiwanUnder the Basel II and Basel III agreements, the probability of default (PD) is a key parameter used in calculating expected credit loss (ECL), which is typically defined as: PD <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>×</mo></semantics></math></inline-formula> Loss Given Default <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>×</mo></semantics></math></inline-formula> Exposure at Default. In practice or in regulatory requirements, gross domestic product (GDP) has been adopted in the PD estimation model. Due to the problem of excessive fluctuation and highly volatile ECL estimation, models that produce satisfactory PD and thus ECL estimations in the context of existing risk management techniques are lacking. In this study, we explore the usage of the credit default swap index (CDX), a market’s expectation of future PD, as a predictor of the default rate (DR). By comparing the goodness-of-fit of logistic regression, several conclusions are drawn. Firstly, in general, GDP has considerable explanatory power for the default rate which is consistent with current models in practice. Secondly, although both GDP and CDX fit the DR well for rating B class, CDX has a significantly better fit of DR for ratings [A, Baa, Ba]. Thirdly, compared with low-rated companies, the relationship between the DR and GDP is relatively weak for rating A. This phenomenon implies that, in addition to using macroeconomic variables and firm-specific explanatory variables in the PD estimation model, high-rated companies exhibit a greater need to use market supplemental information, such as CDX, to capture the changes in the DR.https://www.mdpi.com/2227-7390/9/16/1930credit default swap indexexpected credit lossGDPgoodness-of-fitprobability of defaultrisk measures |
| spellingShingle | Kuang-Hua Hu Shih-Kuei Lin Yung-Kang Ching Ming-Chin Hung Goodness-of-Fit of Logistic Regression of the Default Rate on GDP Growth Rate and on CDX Indices Mathematics credit default swap index expected credit loss GDP goodness-of-fit probability of default risk measures |
| title | Goodness-of-Fit of Logistic Regression of the Default Rate on GDP Growth Rate and on CDX Indices |
| title_full | Goodness-of-Fit of Logistic Regression of the Default Rate on GDP Growth Rate and on CDX Indices |
| title_fullStr | Goodness-of-Fit of Logistic Regression of the Default Rate on GDP Growth Rate and on CDX Indices |
| title_full_unstemmed | Goodness-of-Fit of Logistic Regression of the Default Rate on GDP Growth Rate and on CDX Indices |
| title_short | Goodness-of-Fit of Logistic Regression of the Default Rate on GDP Growth Rate and on CDX Indices |
| title_sort | goodness of fit of logistic regression of the default rate on gdp growth rate and on cdx indices |
| topic | credit default swap index expected credit loss GDP goodness-of-fit probability of default risk measures |
| url | https://www.mdpi.com/2227-7390/9/16/1930 |
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