Confidence interval - Ch11

Hi everyone,

Calculating the 95% confidence interval for the lognormal distribution of a share price S(t) I thought that the approach is to find a number a such that P(S_0 - a <= S_t <= S_0 +a) = 0.95. I realized that it is not possible to find such an a easily (without some computer technics). Then checking the approach in the study material I saw that in fact the confidence interval is transitioned to the normal distribution, i.e. we are in fact looking for b such that P(log(S_0) - b <= log(S_t) <= log(S_0) +b)=0.95. This is computable using the actuarial tables and it makes intuitive sense as well (as the lognormal distribution is driven in fact somehow by the underlying normal distribution - and that we are trying to estimate the mean and not the population...). However, It raises a question that how do we generally define the confidence intervals. I am sure that this is covered somewhere else (maybe CS1, CS2?), but I have not sat those exams yet. Could anybody give me a comprehensive definition?

Thanks in advance.

 

This is found in CT3 and presumably CS1. Confidence intervals looks at the middle 95% of values. That is, given the distribution of a random variable, we can find the 2.5th and 97.5th percentiles and can then say that those two figures are the bounds for the 95% confidence interval (the random variable has 95% probability to land within the interval).