Doubly truncated moment risk measures for elliptical distributions

TL;DR

This paper introduces doubly truncated moment measures for elliptical distributions, providing explicit formulas and applications to financial stock return data, enhancing risk assessment methods.

Contribution

It defines and derives explicit formulas for doubly truncated moments, skewness, and kurtosis for elliptical distributions, including practical financial data applications.

Findings

Explicit formulas for DTM, DTS, DTK for key elliptical distributions.

Application to stock return data from financial industry segments.

Enhanced tools for risk measurement in finance.

Abstract

In this paper, we define doubly truncated moment (DTM), doubly truncated skewness (DTS) and kurtosis (DTK). We derive DTM formulae for elliptical family, with emphasis on normal, student-$t$, logistic, Laplace and Pearson type VII distributions. We also present explicit formulas of the DTE (doubly truncated expectation), DTV (doubly truncated variance), DTS and DTK for those distributions. As illustrative example, DTEs, DTVs, DTSs and DTKs of three industry segments' (Banks, Insurance, Financial and Credit Service) stock return in London stock exchange are discussed.