Using Tukey's g and h family of distributions to calculate value-at-risk and conditional value-at-risk

Generally, when calculating value-at-risk (VaR), little importance is attached to extreme losses because they do not adequately reflect the skewness and kurtosis of the distribution. Moreover, assuming normality in VaR tends to overestimate the VaR values for upper percentiles, while it underestimates VaR for the lower percentiles of values that correspond to more extreme events. We propose to use Tukey's g and h family of distributions for calculating VaR and conditional value-at-risk (CVaR), as this distribution is able to take skewness and kurtosis into account. We also calculate an explicit formula for CVaR using the Cornish-Fisher approximation. An illustrative example is presented to compare our model with other models.