bad luck = type I error?
- Thread starter ajsa
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Hi asja,
That's interesting. As I look at the language re: back luck...
"The third category of problems (markets moved in a fashion unanticipated by the model) should also be expected to occur at least some of the time with value-at-risk models. In particular, even an accurate model is not expected to cover 100% of trading outcomes. Some exceptions are surely the random 1% that the model can be expected not to cover. In other cases, the behaviour of the markets may shift so that previous estimates of volatility and correlation are less appropriate. No value-at-risk model will be immune from this type of problem; it is inherent in the reliance on past market behaviour as a means of gauging the risk of future market movements."
...so this refers to the yellow zone where there are 5 to 10 exceptions...and, as Basel says, "outcomes in this range (5 to 10) are plausible for both accurate and inaccurate models, although Table 1 suggests that they are generally more likely for inaccurate models than for accurate models."
...so, it is possible to commit a Type I error here (by rejecting a good model; e.g., 10.8% probability of Type I given 5 exceptions and decision to reject) or a Type II error (e.g., 12.8% probability of Type II error given 5 exceptions where decision to accept but model is only 97% accurate)
So, my interpretation of the bad luck category is: it wants to help supervisors avoid committing a Type I error; i.e., it is trying to support a scenario where luck may explain the larger-than-expected exceedences. In this sense, I guess you could argue that it "gives cover for" (may promote) a Type II error. This just illustrates they cannot both be minimized...
Hope that is some help...David
That's interesting. As I look at the language re: back luck...
"The third category of problems (markets moved in a fashion unanticipated by the model) should also be expected to occur at least some of the time with value-at-risk models. In particular, even an accurate model is not expected to cover 100% of trading outcomes. Some exceptions are surely the random 1% that the model can be expected not to cover. In other cases, the behaviour of the markets may shift so that previous estimates of volatility and correlation are less appropriate. No value-at-risk model will be immune from this type of problem; it is inherent in the reliance on past market behaviour as a means of gauging the risk of future market movements."
...so this refers to the yellow zone where there are 5 to 10 exceptions...and, as Basel says, "outcomes in this range (5 to 10) are plausible for both accurate and inaccurate models, although Table 1 suggests that they are generally more likely for inaccurate models than for accurate models."
...so, it is possible to commit a Type I error here (by rejecting a good model; e.g., 10.8% probability of Type I given 5 exceptions and decision to reject) or a Type II error (e.g., 12.8% probability of Type II error given 5 exceptions where decision to accept but model is only 97% accurate)
So, my interpretation of the bad luck category is: it wants to help supervisors avoid committing a Type I error; i.e., it is trying to support a scenario where luck may explain the larger-than-expected exceedences. In this sense, I guess you could argue that it "gives cover for" (may promote) a Type II error. This just illustrates they cannot both be minimized...
Hope that is some help...David
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