Yijia Lin

Natural Hedging of Life and Annuity Mortality Risks

Abstract The values of life insurance and annuity liabilities move in opposite directions in response to a change in the underlying mortality. Natural hedging utilizes this to stabilize aggregate liability cash flows. We find empirical evidence that suggests that annuity writing insurers who have more balanced business in life and annuity risks also tend to charge lower premiums than otherwise similar insurers. This indicates that insurers who have a natural hedge have a competitive advantage. In addition, we show how a mortality swap might be used to provide the benefits of natural hedging.

Mortality Regimes and Pricing

Abstract Mortality dynamics are characterized by changes in mortality regimes. This paper describes a Markov regime-switching model that incorporates mortality state switches into mortality dynamics. Using the 1901-2005 U.S. population mortality data, we illustrate that regime-switching models can perform better than well-known models in the literature. Furthermore, we extend the 1992 Lee-Carter model in such a way that the time-series common risk factor to all cohorts has distinct mortality regimes with different means and volatilities. Finally, we show how to price mortality securities with this model.

Enterprise Risk Management: Strategic Antecedents, Risk Integration and Performance

The current literature on the adoption of enterprise risk management (ERM) abstracts from the issue of its strategic context. Accounting for the interplay between ERM and various individual risk management (IRM) practices, this paper presents a theoretical basis to study the strategic determinants, risk integration, and value creation of ERM. We tested hypotheses with data from the US property and casualty (PC) insurance industry. Our results show that insurers with more reinsurance purchase and greater geographic diversification are more likely to adopt ERM. After ERM initiation, the magnitude of certain IRM adjustments is substantial. Interestingly, the market responds negatively to ERM adoption. ERM displays a strong negative correlation with firm value with a discount of 5% (4%) in terms of Tobins Q (ROA).

Mortality Portfolio Risk Management

We provide a new method, the “MV+CVaR approach,” for managing unexpected mortality changes underlying annuities and life insurance. The MV+CVaR approach optimizes the mean–variance trade‐off of an insurers mortality portfolio, subject to constraints on downside risk. We apply the method of moments and the maximum entropy method to analyze the efficiency of MV+CVaR mortality portfolios relative to traditional Markowitz mean–variance portfolios. Our numerical examples illustrate the superiority of the MV+CVaR approach in mortality risk management and shed new light on natural hedging effects of annuities and life insurance.

Managing Capital Market and Longevity Risks in a Defined Benefit Pension Plan

This paper proposes a model for a defined benefit pension plan to minimize total funding variation while controlling expected total pension cost and funding downside risk throughout the life of a pension cohort. With this setup, we first investigate the plan’s optimal contribution and asset allocation strategies, given the projection of stochastic asset returns and random mortality evolutions. To manage longevity risk, the plan can use either the ground-up hedging strategy or the excess-risk hedging strategy. Our numerical examples demonstrate that the plan transfers more unexpected longevity risk with the excess-risk strategy due to its lower total hedge cost and more attractive structure.

Downside Risk Management of a Defined Benefit Plan Considering Longevity Basis Risk

To control downside risk of a defined benefit pension plan arising from unexpected mortality improvements and severe market turbulence, this article proposes an optimization model by imposing two conditional value at risk constraints to control tail risks of pension funding status and total pension costs. With this setup, we further examine two longevity risk hedging strategies subject to basis risk. While the existing literature suggests that the excess-risk hedging strategy is more attractive than the ground-up hedging strategy as the latter is more capital intensive and expensive, our numerical examples show that the excess-risk hedging strategy is much more vulnerable to longevity basis risk, which limits its applications for pension longevity risk management. Hence, our findings provide important insight on the effect of basis risk on longevity hedging strategies.

Portfolio Risk Management with CVaR-Like Constraints

Abstract A current research stream in the portfolio allocation literature develops models that take into account the asymmetric nature of asset return distributions. Our paper contributes to this research stream by extending the Krokhmal, Palmquist, and Uryasev approach. We add CVaR-like constraints in the traditional portfolio optimization problem to reshape the tails of the portfolio return distribution while not significantly affecting its mean and variance. We illustrate how to apply this approach, called the “MV + CVaR approach,” to manage tail risk of an insurer’s asset-liability portfolio. Finally, we compare the MV + CVaR approach with the traditional Markowitz method and a method recently introduced by Boyle and Ding. Our numerical analysis provides empirical support for the effectiveness of the MV + CVaR approach in controlling downside risk. Moreover, we find that the MV + CVaR approach may improve skewness of mean-variance portfolios, especially for high-variance portfolios.

WTO and the Chinese Insurance Industry

This paper provides new information on the impact of the entry of foreign firms on a financial services industry by examining the Chinese insurance industry surrounding Chinas accession to the World Trade Organization (WTO). Our analysis reveals that insurers experienced significant growth in total factor productivity over the sample period. We also observe a structural improvement in efficiency after WTO accession, but geographic and product market restrictions placed on foreign firms reduce these positive effects. Overall, the results are consistent with there being a significant increase in social welfare during our sample period, but they also lend support for further deregulation.

Pension Risk Management in the Enterprise Risk Management Framework

This paper presents an enterprise risk management (ERM) model for a firm that is composed of a portfolio of capital investment projects and a defined benefit (DB) plan for its workforce. The firm faces the project, operational and hazard risks from its investment projects as well as the financial and longevity risks from its DB plan. The firm maximizes its capital market value net of pension contributions subject to constraints that control project, operational, hazard, financial and longevity risks as well as an overall risk. The analysis illustrates the importance of integrating pension risk into the firm’s ERM program by comparing firm value with and without integrating pension risk with other risks in an ERM program. We also show how pension hedging strategies can impact the firm’s net value under the ERM framework. While the existing literature suggests that a longevity swap is less expensive than a pension buy-out because the latter is more capital intensive, this analysis shows that the buy-out is more effective in increasing firm value.

Pricing Buy-Ins and Buy-Outs

Pension buy-ins and buy-outs have become an important aspect of managing pension risk in recent years. As a step toward understanding these pension de-risking instruments, we develop models for pricing investment risk and longevity risk embedded in pension buy-ins and buy-outs. We also bring a contingent-claims framework to price credit risk of buy-in bulk annuities. Overall, our model can be used to assess the pricing of investment, longevity, and credit risks being transferred in pension buy-in and buy-out transactions.