Hong-Chih Huang

An Optimal Product Mix for Hedging Longevity Risk in Life Insurance Companies: The Immunization Theory Approach

This article investigates the natural hedging strategy to deal with longevity risks for life insurance companies. We propose an immunization model that incorporates a stochastic mortality dynamic to calculate the optimal life insurance–annuity product mix ratio to hedge against longevity risks. We model the dynamic of the changes in future mortality using the well-known Lee–Carter model and discuss the model risk issue by comparing the results between the Lee–Carter and Cairns–Blake–Dowd models. On the basis of the mortality experience and insurance products in the United States, we demonstrate that the proposed model can lead to an optimal product mix and effectively reduce longevity risks for life insurance companies.

Mortality Modeling with Non‐Gaussian Innovations and Applications to the Valuation of Longevity Swaps

This article provides an iterative fitting algorithm to generate maximum likelihood estimates under the Cox regression model and employs non‐Gaussian distributions - the jump diffusion (JD), variance gamma (VG), and normal inverse Gaussian (NIG) distributions - to model the error terms of the Renshaw and Haberman () (RH) model. In terms of mean absolute percentage error, the RH model with non‐Gaussian innovations provides better mortality projections, using 1900–2009 mortality data from England and Wales, France, and Italy. Finally, the lower hedge costs of longevity swaps according to the RH model with non‐Gaussian innovations are not only based on the lower swap curves implied by the best prediction model, but also in terms of the fatter tails of the unexpected losses it generates.

Optimal Multiperiod Asset Allocation: Matching Assets to Liabilities in a Discrete Model

Investment and risk control are becoming increasingly important for financial institutions. Asset allocation provides a fundamental investing principle to manage the risk and return trade-off in financial markets. This article proposes a general formulation of a first approximation of multiperiod asset allocation modeling for institutions that invest to meet the target payment structures of a long-term liability. By addressing the shortcomings of both single-period models and the single-point forecast of the mean variance approach, this article derives explicit formulae for optimal asset allocations, taking into account possible future realizations in a multiperiod discrete time model.

Valuation and Hedging of Limited Price Indexed Liabilities

This paper considers the market or economic valuation and the hedging of Limited Price Indexed (LPI) liabilities. This involves finding optimal static and dynamic hedging strategies which minimise the riskiness of the investment portfolio relative to the liability.

On the valuation of reverse mortgage insurance

This article presents a closed-form formula for calculating the loan-to-value (LTV) ratio in an adjusted-rate reverse mortgage (RM) with a lump sum payment. Previous literatures consider the pricing of RM in a constant interest rate assumption and price it on fixed-rate loans. This paper successfully considers the dynamic of interest rate and the adjustable-rate RM simultaneously. This paper also considers the housing price shock into the valuation model. Assuming that house prices follow a jump diffusion process with a stochastic interest rate and that the loan interest rate is adjusted instantaneously according to the short rate, we demonstrate that the LTV ratio is independent of the term structure of interest rates. This argument holds even when housing prices follow a general process: an exponential Lévy process. In addition, the HECM (Home Equity Conversion Mortgage) program may be not sustainable, especially for a higher level of housing price volatility. Finally, when the loan interest rate is adjusted periodically according to the LIBOR rate, our finding reveals that the LTV ratio is insensitive to the parameters characterizing the CIR model.

An Empirical Study of Mortality Models in Taiwan

There has been a significant increase in the life expectancies of the Taiwanese population after the end of Second World War. Like in many developed countries, due to the prolonging life expectancy and lower fertility rates, the aging population has now become a major policy concern in Taiwan. The search for feasible methods for modeling the future mortality changes has become a popular issue in Taiwan. The Lee-Carter (LC) model, the reduction factor (RF) model and the age-period-cohort (APC) model are three frequently used methods for modeling future mortality dynamics. In this paper, we introduce these three models and discuss their respective pros and cons. We carry out an empirical study using these models based on Taiwan mortality experience. In addition, we make a comparison analysis of different models with different mortality experience in Japan, England and Wales, and the US.

THE VALUATION OF LIFETIME HEALTH INSURANCE POLICIES WITH LIMITED COVERAGE

In adopting a traditional actuarial view, insurance companies often use expected values to determine the premiums for lifetime health insurance policies with limited coverage, which can lead to serious overpricing problems when the coverage limit is not very low or very high. To address this overpricing problem, this article provides analytical solutions for fair premiums of lifetime health insurance policies with limited coverage. Using internal data provided by insurance companies, this article describes the relationship between the level of limited coverage and excess premiums. The premium difference between a practical pricing method and a proposed pricing model creates a humped curve; the maximum excess premium ratio reaches nearly 20 percent for limited coverage for younger insured people.

The Valuation of Lifetime Health Insurance Policies with Limited Coverage

In adopting a traditional actuarial view, insurance companies often use expected values to determine the premiums for lifetime health insurance policies with limited coverage, which can lead to serious overpricing problems when the coverage limit is not very low or very high. To address this overpricing problem, this article provides analytical solutions for fair premiums of lifetime health insurance policies with limited coverage. Using internal data provided by insurance companies, this article describes the relationship between the level of limited coverage and excess premiums. The premium difference between a practical pricing method and a proposed pricing model creates a humped curve; the maximum excess premium ratio reaches nearly 20 percent for limited coverage for younger insured people.

The Application of Reverse Mortgages in Aging Society

Due to the low mortality rates and decreased fertility, as well as the subsequent increased aging problems, insufficient pensions have become a worldwide serious issue. In addition to traditional resources, such as public and private pensions, commercial annuities, individual savings and investments, reverse mortgages provide a new resource option for retirement. We investigate the application of reverse mortgages to retirement and analyze the risk for both governments and financial institutions of issuing reverse mortgage products. Numerical results show that gender, age, loan rate, the return of house price, and the maximum loan amount have significant impact on the risk of issuing reverse mortgages. These factors are very sensitive to the loss distributions of reverse mortgages, therefore risk management is a crucial means for governments and financial institutions to control the risk of reverse mortgages to avoid huge losses.