Whats the difference between a confidence level and a confidence interval?
Pet peeve coming up. While VaR is an estimate of a percentile of the loss distribution, it is commonly referred to as a confidence level. This is because we say, we are 99% confident that the loss will not exceed $XX. It’s more exact to refer to VaR as a percentile estimate. Because VaR is a statistical estimate, it is an uncertain amount itself, and that uncertainty can be encapsulated in a statistical concept called a confidence interval – I am 95% sure that the VaR actually lies between $AA and $BB. It’s too confusing to talk about a confidence interval around a confidence level.
