On the limit of conditional Spearman’s rho under the common factor model
Under the common factor structural model of credit risk, we study a limit of a conditional Spearman’s rho coefficient. The conditioning event is that the common factor stays below a threshold and the limit is taken as the threshold tends to − ∞ . The main result is established through a relation wit...
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| Veröffentlicht in: | Extremes (Boston) 2016-03, Vol.19 (1), p.51-78 |
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| creator | Bae, Taehan Iscoe, Ian |
| description | Under the common factor structural model of credit risk, we study a limit of a conditional Spearman’s rho coefficient. The conditioning event is that the common factor stays below a threshold and the limit is taken as the threshold tends to −
∞
. The main result is established through a relation with the classical theory of regular variation. We identify the relationship between the limiting Spearman’s rho and the tail thickness of the distribution function of the common factor. In particular, a necessary condition for the limiting Spearman’s rho to be strictly less than 1, is that the inverse cumulative distribution function of the common random variable is slowly varying at zero. As an illustration, the calculation of Stress Value-at-Risk for portfolio credit losses is discussed. |
| doi_str_mv | 10.1007/s10687-015-0231-3 |
| format | Article |
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∞
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∞
. The main result is established through a relation with the classical theory of regular variation. We identify the relationship between the limiting Spearman’s rho and the tail thickness of the distribution function of the common factor. In particular, a necessary condition for the limiting Spearman’s rho to be strictly less than 1, is that the inverse cumulative distribution function of the common random variable is slowly varying at zero. 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The conditioning event is that the common factor stays below a threshold and the limit is taken as the threshold tends to −
∞
. The main result is established through a relation with the classical theory of regular variation. We identify the relationship between the limiting Spearman’s rho and the tail thickness of the distribution function of the common factor. In particular, a necessary condition for the limiting Spearman’s rho to be strictly less than 1, is that the inverse cumulative distribution function of the common random variable is slowly varying at zero. As an illustration, the calculation of Stress Value-at-Risk for portfolio credit losses is discussed.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10687-015-0231-3</doi><tpages>28</tpages></addata></record> |
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| source | Springer Nature - Complete Springer Journals; Business Source Complete |
| subjects | Civil Engineering Conditioning Constraining Credit risk Distribution functions Economics Environmental Management Finance Hydrogeology Illustrations Insurance Inverse Management Mathematical analysis Mathematical models Mathematics and Statistics Normal distribution Portfolio management Principal components analysis Quality Control Random variables Reliability Risk management Safety and Risk Statistics Statistics for Business Studies Thresholds |
| title | On the limit of conditional Spearman’s rho under the common factor model |
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