Analytical Calculation of Risk Measures for Variable Annuity Guaranteed Benefits

30 Pages Posted: 2 Oct 2012 Last revised: 14 Oct 2012

See all articles by Runhuan Feng

Runhuan Feng

Tsinghua University - Tsinghua University School of Economics and Management

Hans Volkmer

University of Wisconsin Milwaukee

Date Written: October 2, 2012

Abstract

With the increasing complexity of investment options in life insurance, more and more life insurers have adopted stochastic modeling methods for the assessment and management of insurance and financial risks. The most prevalent approach in market practice, Monte Carlo simulation, has been observed to be time consuming and sometimes extremely costly. In this paper we propose alternative analytical methods for the calculation of risk measures for variable annuity guaranteed benefits on a stand-alone basis. The techniques for analytical calculations are based on the study of geometric Brownian motion and its integral. Another novelty of the paper is to propose a quantitative model which assesses both market risk on the liability side and revenue risk on the asset side in the same framework from the viewpoint of risk management. As we demonstrate by numerous examples on quantile risk measure and conditional tail expectation, the methods and numerical algorithms developed in this paper appear to be both accurate and computationally efficient.

Keywords: variable annuity guaranteed benefit, Asian option, risk measures, value at risk, conditional tail expectation, geometric Brownian motion, integral of geometric Brownian motion, Hartman-Watson density, modified Bessel functions

Suggested Citation

Feng, Runhuan and Volkmer, Hans, Analytical Calculation of Risk Measures for Variable Annuity Guaranteed Benefits (October 2, 2012). Insurance: Mathematics and Economics, 51(3), 636–648, Available at SSRN: https://ssrn.com/abstract=2155930

Runhuan Feng (Contact Author)

Tsinghua University - Tsinghua University School of Economics and Management

Beijing
China

Hans Volkmer

University of Wisconsin Milwaukee ( email )

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