Volume 10, Issue 2 -

This article examines the pricing of guaranteed annuity options (GAOs) in a stochastic volatility and interest rate model. While the pricing of these options in a stochastic volatility and interest rate model has been examined in van Haastrecht, Plat, and Pelsser (2010. Insurance: Mathematics and Economics 47:266–77), the pricing is difficult under the general stochastic volatility environment. In order to overcome these difficulties, we examined the asymptotic expansion method introduced by Kim and Kunitomo (1999. Asia-Pacific Financial Markets 6:49–70) and extended by Kim (2002. Journal of the Operations Research Society of Japan 45:404–25), and Kunitomo and Kim (2007. Japanese Economic Review 58:71–106). The asymptotic expansion method obtains a closed-form approximation formula for the price of GAOs in a general stochastic volatility environment including the Schöbel–Zhu–Hull–White model and the Heston–Hull–White model, for example. We confirm the accuracy of the asymptotic expansion methods by numerical demonstrations. The sensitivity analysis of the options price to changes in the parameters for the stochastic volatility process is also analyzed.

Recently, concerns have been raised about the systemic financial threat potentially posed by life insurers. In part, these concerns have arisen because of life insurer involvement in the sales of variable annuity products with put-like performance guarantees. Guarantees expose life insurers to the market risks of mutual funds that are directed by their policyholders. In 2007, U.S. policyholders held about $500 billion in variable annuity accounts subject to guarantees issued by insurers. In this study we examine life insurer management of the risks of these guarantees, with emphasis on management of capital buffers. We introduce actuarial/regulatory and exposure-based proxies for these risks. Surprisingly, we find a robust and paradoxical result. In the years immediately prior to the Great 2008 Recession, the assumption of additional guarantee risk was associated with reductions in capital (contradicting the finite risk hypothesis), ceteris paribus . The result survives the attempts of two regression models designed to uncover explanatory confounders. The result can inform the debate on systemic risk and capital adequacy for life insurers.

As a variety of mortality risk factors have been identified by previous studies, it is desirable that these factors are reflected in mortality (longevity) risk assessments for life insurance, individual annuities, and pension plans. In this study, an extended traditional mortality table that accommodates marital status, which is one of the important risk factors in terms of mortality, is considered. A logistic regression method is used to model the mortality of groups of people with four different marital statuses–never married, married, widowed, and divorced. The analyses are based on data regarding mortality and changes of marital status in Korea. The results of the analyses that are based on the developed mortality model suggest that the information on risk factors must be reflected in an actuarial model to improve the evaluations and monitoring of risk for the portfolios of relevant insurance products.

Long-term care insurance plays a very important role as providing a protection against financial risk of an individual when he/she becomes in a health condition incurring significant costs for long-term care. Construction of an appropriate actuarial model for long-term care is an integral part of maintaining and improving a long-term care insurance system. A model is suggested for analyzing the impact of change in score-based long-term care grading system and for estimating future cost of long-term care insurance. A spliced distribution was used to model assigned scores for long-term care insurance in Korea based on experience data. The suggested approach is quite flexible, as it allows us to adapt to possible changes in the grading system.