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Keywords
(9)
Conditional Quantile
Extreme Value
Interest Rate
Multivariate Regression
Quantile Regression
Robust Regression
Term Structure
Ordinary Least Squares Regression
Region of Interest
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Risk Drivers Revealed: Quantile Regression and Insolvency
Risk Drivers Revealed: Quantile Regression and Insolvency,Donald Leggett,ASA MAAA
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Risk Drivers Revealed: Quantile Regression and Insolvency
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Donald Leggett
,
ASA MAAA
Most stochastic corporate models examine only resultant output (specif ically the surplus), and thereby divorce the model results from key input model assumptions, such as the
term structure
of interest rates. A simple relationship of the economic rate scenarios to the surplus could be a multi variate regression. However, one drawback of using
ordinary least squares regression
(OLSR) is that the regression is on the mean of the surplus results. With insolvency we are concerned with the tail of the distribution of surplus results (i.e., relatively infrequent extreme values) or where the surplus is neg ative, which may be far from the mean. The second drawback to
multivariate regression
is that it is very sensitive to outliers. The values of the associated coefficients are severely distorted when an extreme outlier is used within the regression. Koenker and Basset (13) resolve both of these difficulties when they introduce
Quantile Regression
(QR). As the name implies, QR allows one to conduct a regression on specific conditional quantiles. These specific conditional quantiles can be chosen so that they are located near the region of interest. Also, QR is a
robust regression
method t.hat reduces or removes the influence of outhers on the regression coefficients. We will use QR to determine the location in time and the impact of specific risk drivers.
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References
(5)
An Empirical Quantile Function for Linear Models with iid Errors
(
Citations: 65
)
Gilbert Bassett Jr
,
Roger Koenker
Journal:
Journal of The American Statistical Association  J AMER STATIST ASSN
, vol. 77, no. 378, pp. 407415, 1982
Recent Advances in Quantile Regression Models
(
Citations: 71
)
M. Buchinsky
Published in 1998.
Multivariate analysis: methods and applications
(
Citations: 723
)
W. Dillon
,
M. Goldstein
Published in 1984.
Numerical Recipes in Pascal
(
Citations: 266
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B. P. Flannery
,
S. A. Teukolsky
,
W. T. Vetterling
Published in 1987.
A Quantile Regression Approach to Estimating the Distribution of Multiperiod Returns
(
Citations: 20
)
James W Taylor
Journal:
Journal of Derivatives  J DERIV
, vol. 7, no. 1, pp. 6478, 1999