Chou-Wen Wang

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.

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.

The Effects of Macroeconomic Factors on Pricing Mortgage Insurance Contracts

Numerous empirical studies, including Abraham and Hendershott (1996), Muellbauer and Murphy (1997), Leung (2004), and Oikarinen (2009), have identified a significant relationship between housing prices and macroeconomic factors. Using a linear regression on the comovement of macroeconomic factors and housing prices, this article employs an option-pricing framework to price and hedge the fair premia of mortgage insurance (MI). Our model provides improved performance in terms of MI premium pricing, especially during periods that are characterized by high housing prices. Ignoring the impacts of macroeconomic factors on housing prices will lead to an underestimation of MI premia.

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.

Structure and Estimation of Lévy Subordinated Hierarchical Archimedean Copulas (LSHAC): Theory and Empirical Tests

Levy subordinated hierarchical Archimedean copulas (LSHAC) are flexible models in high dimensional modeling. However, there is limited literature discussing their applications, largely due to the challenges in estimating their structures and their parameters. In this paper, we propose a three-stage estimation procedure to determine the hierarchical structure and the parameters of a LSHAC. This is the first paper to empirically examine the modeling performances of LSHAC models using exchange traded funds. Simulation study demonstrates the reliability and robustness of the proposed estimation method in determining the optimal structure. Empirical analysis further shows that, compared to elliptical copulas, LSHACs have better fitting abilities as well as more accurate out-of-sample Value-at-Risk estimates with less parameters. In addition, from a financial risk management point of view, the LSHACs have the advantage of being very flexible in modeling the asymmetric tail dependence, providing more conservative estimations of the probabilities of extreme downward co-movements in the financial market.

Modeling Multi-Country Longevity Risk with Mortality Dependence: A Lévy Subordinated Hierarchical Archimedean Copulas (LSHAC) Approach

This paper proposes a new copula model known as the Levy subordinated hierarchical Archimedean copulas (LSHAC) for multi-country mortality dependence modeling. To the best of our knowledge, this is the first paper to apply the LSHAC model to mortality studies. Through an extensive empirical analysis on modelling mortality experiences of 13 countries, we demonstrate that the LSHAC model, which has the advantage of capturing the geographical structure of mortality data, yields better fit, more accurate and robust out-of-sample forecasting, when compared to other benchmark copula models. The LSHAC model also confirms that there is an association between geographical locations and dependence of the overall mortality improvement. These results yield new insights into future longevity risk management. Finally, the model is used to price a hypothetical survival index swap written on a weighted mortality index. The results highlight the importance of dependence modeling in managing longevity risk and reducing population basis risk.

The valuation of special purpose vehicles by issuing structured credit-linked notes

With the intersection of market and credit risk, the first contribution is to derive the analytic formulas of the Credit Linked Notes (CLNs) and the leveraged total return CLNs issued by an Special Purpose Vehicle (SPV) or the protection buyer. The second contribution is to prove that the values of structured CLNs issued by an SPV are higher than the ones issued by the protection buyer. When the credit quality of the reference obligation and protection buyer becomes worse or the leverage effect is higher, it is a superior solution for the structured CLNs issued through an SPV. Third, the empirical results of credit spreads do not incorporate the correlation coefficient of spot rate and market index into their regression models and show that they are positively correlated with the volatilities of spot rate and return on market index; however, we find that the relationship among them depends on the sign of correlation coefficient of spot rate and equity index market. Finally, using the differences in the maturities of the note and the reference obligation as the proxy for basis risk measure, we demonstrate that the purpose of the SPV is not used to eliminate the basis risk but the credit risk of protection buyer.

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.

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.

Spatial Dependence & Aggregation in Weather Risk Hedging

Adverse weather related risk is a main source of crop production loss, and in addition to farmers, this exposure is a major concern and uncertainty for insurers and reinsurers who act as weather risk underwriters. To date, weather hedging has had limited success, largely due to challenges regarding basis risk. Therefore, this paper develops and compares different weather risk hedging strategies for agricultural insurers and reinsurers, through investigating the spatial dependence and aggregation level of systemic weather risks across a country. This paper proposes a flexible time series model that assumes a general hyperbolic (GH) family for the margins to capture the heavy-tail property of the data, together with the Levy subordinated hierarchical Archimedean copula (LSHAC) model to overcome the challenge of high-dimensionality in modeling the dependence of weather risk. Wavelet analysis is employed to study the detailed characteristics within the data from both time and frequency scales. The analysis shows that the LSHAC model proposed in this paper reduces extreme weather downside risk by