Sharon S. Yang

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.

Reserving, Pricing and Hedging For Policies with Guaranteed Annuity Options

In this paper we consider reserving and pricing methodologies for a pensions-type contract with a simple form of guaranteed annuity option. We consider only unit-linked contracts, but our methodologies and, to some extent, our numerical results would apply also to with-profits contracts.

Pricing Survivor Derivatives with Cohort Mortality Dependence Under the Lee–Carter Framework

This article introduces cohort mortality dependence in mortality modeling. We extend the classical Lee–Carter model to incorporate cohort mortality dependence by considering mortality correlations for a cohort of people born in the same year. The pattern of cohort mortality dependence is demonstrated on the basis of U.S. mortality experience. We study the effect of cohort mortality dependence on the pricing of survivor derivatives. For this purpose, a survivor floor is introduced. To understand the difference between a survivor floor and other survivor securities, the valuation formulas for survivor swaps and survivor floors are all derived in detail and the effects of cohort mortality dependence on pricing survivor derivatives are investigated numerically.

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.

Pricing and Implementation of Longevity Bonds in Taiwan

As the population ages and the deterioration of pension funds continue, hedging longevity risk is becoming increasingly important in Taiwan. This article analyzes the potential market for issuing longevity bonds to hedge against the longevity risk in Taiwan. Many recent studies have suggested that longevity bond can serve as an effective risk management tool to mitigate the longevity risks. Following the design of the longevity bond proposed by Denuit, Devolder and Godernaiaux (2007), we make an illustration of pricing longevity bond using Lee-Carter model on the basis of the mortality experience in Taiwan. Our results show that the risk premium for issuing a longevity bond in Taiwan is lower than that in the United State. However, in order to measure the longevity risk more precisely and to overcome the potential problems of issuing longevity bonds in Taiwan, the quality of mortality data should be improved and more regulations need to be amended in the near future.

Analytic option pricing and risk measures under a regime-switching generalized hyperbolic model with an application to equity-linked insurance

Option pricing and managing equity linked insurance (ELI) require the proper modeling of stock return dynamics. Due to the long duration nature of equity-linked insurance products, a stock return model must be able to deal simultaneously with the preceding stylized facts and the impact of market structure changes. In response, this article proposes stock return dynamics that combine Lévy processes in a regime-switching framework. We focus on a non-Gaussian, generalized hyperbolic distribution. We use the most popular linked equity of ELIs, the S&P 500 index, as an example. The empirical study verifies that the proposed regime-switching generalized hyperbolic (RSGH) model gives the best fit to data. In investigating the effects of stock return modeling on pricing and risk management for financial contracts, we derive the characteristic function, embedded option price, and risk measure of equity-linked insurance analytically. More importantly, we demonstrate that the regime-switching generalized hyperbolic (RSGH) model is realistic and can meet the stylistic facts of stock returns, which in turn can be employed in option pricing and risk management decisions.

Detecting and modelling the jump risk of CO2 emission allowances and their impact on the valuation of option on futures contracts

Modelling CO2 emission allowance prices is important for pricing CO2 emission allowance linked assets in the emissions trading scheme (ETS). Some statistical properties of CO2 emission allowance prices have been discovered in the literature ignoring price jumps. By employing real data from the ETS, this research first detects the jump risk using a jump test and then verifies jump effects in modelling CO2 emission allowance prices by comparing the in-sample and out-of-sample model performance. We suggest a model which can capture the statistical properties of autocorrelation, volatility clustering and jump effects is more appropriate for modelling CO2 emission allowance prices. We establish a general framework for pricing CO2 emission allowance options on futures contracts with these properties and find that the jump risk significantly affects the value of the CO2 emission allowance option on futures contracts. More importantly, we demonstrate that the dynamic jump ARMA–GARCH model can provide more accurate valuations of the CO2 emission allowance options on futures than other models in terms of pricing error.

The Valuation of Temperature Derivatives: The Case for Taiwan

This research focuses on the temperature risk and attempts to investigate which distribution is most appropriate for capturing the Taiwans temperature dynamics. We adopt the Campbell and Diebold (2005) model to describe the temperature characteristics and examine a variety of distributions. We find that the standard Gumbel distribution provides the best fit for both in-sample and out-of-sample performance. Further, we extend Cao and Weis (2004) approach to obtain the valuation framework for HDD and CDD contracts. Finally, we observe that the effects of different distributions on the value of the temperature derivatives are very significant.

Analysis of the Efficient Frontier for Life Settlements in the Presence of Longevity Risk

This study attempts to analyze the effect of portfolio selection when life settlements, which are considered to have zero or low correlation with traditional investment instruments, are taken into account. We utilize the efficient frontier to assess the investment performance of a portfolio that includes three assets, namely, stocks, bonds, and life settlements. Because mortality plays an important role in determining the prices of life settlements, we consider a stochastic mortality model in our pricing framework to reflect longevity risk. The impacts of age effect, mortality improvement, and transaction costs on life settlements and investment performance are investigated numerically.

Valuation of Rate of Return Guarantees under a Defined Contribution Pension Plan Considering the Choice of Retirement Age

This paper studies the valuation of the rate of return guarantee under a DC pension plan considering the choice of retirement age. In this setting, the rate of return guarantee can be referred to as the American option. We carry out a simulation study using the Least Squares Monte Carlo (LSM) approach proposed by Longstaff and Schwartz (2001) to calculate the value of the rate of return guarantee. We also compare the results with the case where the retirement age is fixed. We illustrate the valuation of the rate of return guarantee for the new Labor Pension Plan in Taiwan. The numerical analysis demonstrates that the guarantee value is lower with early retirement but higher with late retirement. The effect of the retirementage on the value of the rate return guarantee is significant. Key words: Pension plan, defined contribution, rate of return guarantees, American options.