Lei Chen
Title: On the calculation of risk measures for variable annuities with guaranteed benefits
Date: August 26th, 2022
Time: 1:30PM PST
Location: Library Thesis Defence Room - LIB 2020
Abstract
With the development of the life insurance industries, different types of life insurance products in addition to the traditional ones had been well developed. A typical and well-known life insurance product is the variable annuity with different types of guaranteed benefit riders, which provides policyholders a high rate of investment return with downside risk protections. Two typical distortion risk measures, VaR (value at risk) and CTE (conditional tail expectation), are widely used to manage insurer’s future liabilities for avoiding insolvency. In this project, we consider variable annuities with certain types of guaranteed benefits and various asset price processes and focus on the calculation of the two risk measures of insurer’s net and gross liabilities at the maturity date. Specifically, we consider two riders, guaranteed minimum death benefit (GMDB) and guaranteed minimum maturity benefit (GMMB), and assume that the logarithm of underlying asset returns follows a Cauchy or a skewed normal distribution. Analytical expressions of VaR and CTE for insurer’s future liabilities are obtained, and numerical calculation algorithms are proposed. Comparisons of the calculated risk measure results with these under the normal distribution are also presented.
Keywords: Variable annuity with guaranteed benefits; Risk measures; Cauchy distribution; Skew-normal distribution