Tail Conditional Moments for Location-Scale Mixture of Elliptical Distributions

Abstract

We present the general results on the univariate tail conditional moments for a location-scale mixture of elliptical distributions. Examples include the location-scale mixture of normal, location-scale mixture of Student’s t, location-scale mixture of logistic, and location-scale mixture of Laplace distributions. More specifically, we give the tail variance, the tail conditional skewness, and the tail conditional kurtosis of generalised hyperbolic distribution and Student–GIG mixture distribution. We give an illustrative example, which discusses the TCE, TV, TCS and TCK of three stocks, including Amazon, Google and Apple.

Keywords

• tail conditional moment
• location-scale mixture
• elliptical distribution
• tail variance
• tail conditional skewness
• tail conditonal kurtosis