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Risk Drivers Revealed: Quantile Regression and Insolvency

Risk Drivers Revealed: Quantile Regression and Insolvency,Donald Leggett,ASA MAAA

Risk Drivers Revealed: Quantile Regression and Insolvency  
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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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