The Valuation of a Guaranteed Minimum Maturity Benefit under a Regime-Switching Framework

Abstract

Global insurance markets have become more sophisticated in recent times in response to the evolving needs of populations that tend to live longer. Policy holders desire the benefits of longevity/mortality protection while taking advantage of investment growth opportunities in equity markets. As a result, insurers incorporate payment guarantees in new insurance products, known as equity-linked contracts, whose values are dependent on prices of risky assets. A guaranteed minimum maturity benefit (GMMB) is now common in many equity-linked contracts. We develop an integrated pricing framework for a GMMB focusing on segregated fund contracts. More specifically, we construct hidden Markov models (HMMs) for a stock index, interest rate, and mortality rate. The dependence between these risk factors is characterized explicitly. We assume that the stock index follows a Markov-modulated geometric Brownian motion and the interest and mortality rates have Markov-modulated affine dynamics. A series of measure changes is employed to obtain a semi-closed-form solution for the GMMB price. A Fourier transform method is applied to numerically approximate the prices more efficiently. Recursive HMM filtering is used in our model calibration. Numerical investigations in our article demonstrate the accuracy of GMMB prices and an extensive analysis is included to systematically examine how risk factors affect the value of a GMMB.

ACKNOWLEDGMENTS

R. Mamon expresses his sincere appreciation for the hospitality of the Division of Physical Sciences and Mathematics, University of the Philippines Visayas, where certain parts of the draft of this article were formulated and written during an academic visit both as an Adjunct Professor and as a DOST-PCIEERD Balik Scientist for the Philippine government.

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Additional information

Funding

This work is supported by the Natural Sciences and Engineering Research Council of Canada through R. Mamon’s Discovery Grant (RGPIN-2017-04235).