Band 3, Heft 2

We present a Bayesian approach to compare models for forecasting mortality rates under the framework of the Lee-Carter methodology. We consider the original normal log-bilinear formulation of the methodology as well as the recently proposed Poisson log-bilinear formulation. For each formulation, we compare three models: the deterministic trend model, the stochastic trend model and the stationary (no trend) model, each of which represents a different future scenario for changing mortalities. Markov-chain Monte Carlo methods are used to sample the predictive distributions from each model and to calculate the marginal likelihoods for the model selection. The approach is applied to Japanese male mortality rates from 1970 to 2003. The results show that the stochastic trend model is most appropriate for forecasting mortality rates both for the normal and the Poisson formulation. We then use the selected model to evaluate longevity risk in Japan by calculating the posterior predictive distributions of the life annuities for the population at age 65.

A dilemma frequently faced by empirical researchers is whether they should keep observations without complete information in the analysis. Assuming missingness is not biased in any perceivable direction, most studies use a complete case analysis approach, whereby only observations with complete information are kept for empirical estimation. However, the literature on statistics (e.g., Little and Rubin 2002) suggests that potential biases may arise from such practice, especially if missing data are not missing completely at random (MCAR). When there are missing data, Little’s MCAR test (1988) can be performed to reveal whether imputation methods are necessary to minimize the problems arising from incomplete data. We take two recently studied insurance data sets as examples to show that missing data issues can be better handled.

This paper proposes a continuous random modeling of catastrophic loss indexes underlying insurance-linked securities (ILS), by convolution of each catastrophic event’s amount of reported claims. This variable is calculated, in turn, as the difference between the catastrophe’s total severity, on one hand, and its amount of incurred-but-not-yet-reported claims, which is considered to be driven by a geometric Brownian motion, on the other hand. Parameters estimation and verification of the goodness-of-fit to a sample of data series on floods in Spain have subsequently been conducted in order to test the model’s validity.

We present surrender rate models with explanatory variables such as the difference between reference rates and crediting rates, policy age since issue, unemployment rates, and economy growth rates, using a logit model. We calculate the values of the surrender options in Korean interest-indexed annuities. It is interesting to note that the values of the surrender options subject to a surrender charge show negative values despite the fact that the surrender options are the right given to policyholders. We then attempt to find the fair surrender charges for the insurance company and its policyholders.

In this paper we estimate the equity beta and cost of capital of Japanese property liability insurance companies. For this, we obtain the overall equity beta and cost of capital for each company and then estimate the equity beta and cost of capital by the business lines. To obtain a company’s overall equity beta, we use the one-factor capital asset pricing model (CAPM) and the three-factor Fama-French (FF) model. To estimate each business line’s equity beta, we use the full-information industry beta (FIB) methodology. Econometric analysis reveals that the CAPM and FF models are well suited to estimating Japanese property-liability insurance companies’ the equity beta and cost of capital. Furthermore, by using the FIB methodology, we find that each the equity beta of each business line is different.

In this paper, we present alternative pricing models of deposit insurance under capital forbearance. The investment behavior of deposit insurance companies and moral hazard of banks are considered and numerical analysis is carried out. We find that If the premium rate reflects forecasting instead of merely assessing the liability in determining premium rate, and considering the effect of the relationship between deposit’s interest rate and insolvency risk of banks, this can help decrease this moral hazard created after the issuance of the insurance contract.

Actuaries have long employed logistic type regression models in their analysis of renewal rates for property and casualty insurance products. This paper introduces an application of such methodology to the prediction of corporate bankruptcy. This is an example of a widerfield area of endeavor where actuaries have the potential to add real value. The results presented in the paper have implications for levels of risk-based capital to be held by insurers and other financial organizations. This paper examines how effectively the default likelihood indicator (DLI) estimated from the Merton model can predict corporate bankruptcy in Australia during 1990-2003. In addition, the performance of the Merton model and the three most popular bankruptcy models, i.e., Altman (1968), Zmijewski (1984), and Shumway (2001) are also compared. Our findings suggest that the Merton model is the most informative model in explaining corporate bankruptcy, followed by the Shumway model. Among accounting and market-based variables in bankruptcy models, only two variables, namely the ratio of total liabilities to total assets (TL/TA) and the idiosyncratic standard deviation of stock returns are most significant in predicting corporate bankruptcy. Finally, the results from our comparative study of bankruptcy prediction models suggest developing a multivariable logistic regression model which includes both financial ratios and Merton’s default likelihood indicator as predictors. We assess the predictive ability of this model by comparing 95% confidence intervals for the predicted probability of default for firms that default and firms that are not observed to default.