I am struggling to prove left and right quantile relationship:
Right quantile (0.95) (x) = -left quantile (1-0.95) (-x)
I tried to prove with probability manipulations but struggle to get correct result.
Could you please help?
I am struggling to prove that for a normally distributed loss RV introducing stochastic volatility (\sigma_1 with probability 0.5 and \sigma_2 with probability 0.5) would make kurtosis bigger than 3 (fat tails).
Can someone help?
If we are given Loss RV as :
How to prove that kurtosis is 3?
Additionally if Volatility is stochastic:
How to prove that the distribution is fat tailed (kurtosis is greater than 3) assuming and are independent?
If .the logistic distribution is defined as it corresponding quantile function:
How can I show that q is strictly increasing and compute logistic distribution function and it's density function?
How to compute VaR and ES of r.v. with logistic distribution?
Thank you for your help