Risk management of guaranteed minimum maturity benefits under stochastic mortality and regime-switching by Fourier space time-stepping framework

TL;DR

This paper develops a Fourier space time-stepping framework to accurately and efficiently evaluate the risks and sensitivities of guaranteed minimum maturity benefits in variable annuities under stochastic mortality and regime-switching models.

Contribution

It introduces a modified FST algorithm for net liability calculation, improving accuracy in risk assessment of GMMB under complex stochastic models.

Findings

FST algorithm provides fast, accurate solutions for GMMB liabilities.

Comparison of hedging strategies shows differences in portfolio volatility.

Modified FST algorithm yields reliable net liability estimates.

Abstract

In this paper, we adopted a net liability model which assesses both market risk on the liability side and revenue risk on the asset side for a Guaranteed Minimum Maturity Benefit (GMMB) embedded in variable annuity (VA) contracts. Numeric solutions for net liabilities, fair rate of fees and Greeks of GMMB are obtained by a more accurate and fast Fourier Space time-stepping (FST) algorithm. Monte Carlo results are provided for comparative purpose. The unhedged and three statically hedged portfolios are introduced, and their performances are assessed by comparing the short term and long term portfolio's volatility. Recently, we noticed FST algorithm can only be used to hedge the gross liability of GMMB and it leads to an incorrect result when applying FST algorithm to the net liability model. We have modified the method we used in the hedging part and obtained the reliable result now. They will be reported in near future.