19) While the general market risk portion is always derived from value-at-risk model estimates, the specific risk figures may be based on a risk measurement model or may be calculated using standardized regulatory weights.
Empirical work to date presents somewhat conflicting evidence of the accuracy of the value-at-risk models that underlie the market risk capital requirements.
Unlike value-at-risk models
, which are run on a daily basis to assess the market risk in banks' trading activities, credit risk models are run less frequently.
Given the inherent limitations of value-at-risk models
, Rahl agreed with Sabatacakis that stress testing and scenario analysis are key to rounding out the picture of a portfolio's risk.
The introduction of the higher scaling factor for banks experiencing five or more exceptions is based on a simple statistical technique that calculates the probability that an accurate value-at-risk model would generate a given number of exceptions during a year of trading days.
Thus, an accurate value-at-risk model will produce more than five exceptions over a 250-day trading period 4.
Of course, the consequences, of such a shortfall in performance depend on the particular circumstances in which the value-at-risk model
is being used.
Although a substantial literature has examined the statistical and economic meaning of Value-at-Risk models
, this article is the first to provide a detailed analysis of the performance of models actually in use.
The fact that value-at-risk models
were among the first statistical risk models developed reflects the high-frequency and largely continuous nature of market risk and its management,(26) the mark-to-market environment in which most trading activities occur, and the resultant ease of modeling (normality has often been assumed) and availability of comparatively long historical data series around which to calibrate the models.
These advances are the outgrowth of both academic research efforts and financial institutions' day-to-day experience with value-at-risk models