A Direct Approach in the Pricing Analysis and Risk Role Matching of a Guaranteed Annuity Option Under Correlated Risks

ABSTRACTIn 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.The Report of the Annuity Guarantees Working Party (Bolton et al., 1997), presented the results of a very interesting survey, as at the end of 1996, of life assurance companies offering guaranteed annuity options. There was no consensus at that time among the companies on how to reserve for such options. The Report discussed several approaches to reserving, but concluded that it was unable to recommend a single approach. This paper is an attempt to fill that gap.We investigate two approaches to reserving and pricing. In the first sections of the paper we consider quantile, and conditional tail expectation, reserves. The methodology we adopt here is very close to that proposed by the Maturity Guarantees Working Party in its Report to the profession (Ford et al., 1980). We show how these policies could have been reserved for in 1985, and what would have been the outcome of using the proposed method.In a later section we consider the feasibility of using option pricing methodology to dynamically hedge a guaranteed annuity option. It is shown that this is possible within the context of the model we propose, but we submit that, in practical terms, dynamic hedging is not a complete solution to the problem since suitable tradeable assets do not in practice exist.Finally, we describe several enhancements to our models and methodology, which would make them even more realistic, though generally they would have the effect of increasing the required contingency reserves

A two-decrement model for the valuation and risk measurement of a guaranteed annuity option

Mortality modelling with regime-switching for the valuation of a guaranteed annuity option

In this paper we derive a market value for Guaranteed Annuity Option using martingale modeling techniques. Furthermore, we show how to construct a static replicating portfolio of vanilla interest rate swaptions that replicates the Guaranteed Annuity Option. Finally, we illustrate with historical UK interest rate data from the period 1980 until 2000 that the static replicating portfolio is extremely effective as a hedge against the interest rate risk involved in the GAO, that the static replicating portfolio is considerably cheaper than up-front reserving and also that the replicating portfolio provides a much better level of protection than an up-front reserve.

Modeling longevity risks using a principal component approach: A comparison with existing stochastic mortality models

A comonotonicity-based valuation method for guaranteed annuity options

An efficient algorithm for the valuation of a guaranteed annuity option with correlated financial and mortality risks

Annuity-contingent derivatives involve both mortality and interest risks, which could have a correlation. In this article, we propose a generalized pricing framework in which the dependence between the two risks can be explicitly modelled. We also utilize the change of measure technique to simplify the valuation expressions. We illustrate our methodology in the valuation of a guaranteed annuity option (GAO). Using both forward measure associated with the bond price as numéraire and the newly introduced concept of endowment-risk-adjusted measure, we derive a simplified formula for the GAO price under the generalized framework. Numerical results show that the methodology proposed in this article is highly efficient and accurate.

It is useful to divide retirement-related risks into three broad categories: investment risk, funding risk, and longevity risk. Investment risk is the risk that retirement resources will earn an inadequate rate of return. Funding risk is the danger that the funds necessary to finance adequate retirement benefits will not be contributed to the plan. For both these categories, defined benefit arrangements place responsibility upon the employer for financing the benefits promised by the plan. Defined contribution arrangements shift the investment and funding risks to the employee. Longevity risk is the danger that a retiree will outlive his retirement resources. The traditional, annuity-paying defined benefit plan provides partial protection against this since such a pension disburses retirement payments periodically and continues such annuity-type payments until the participant's death, often with payments continuing to the participant's surviving spouse. While the defined contribution participant can eliminate his longevity risk by annuitizing his account balance, such individually-purchased annuities typically suffer from the cost-related problem of adverse selection.

The impact of longevity risk has not been well studied in most developing countries because of the lack of suitable mortality data. As a result, most pension companies in these countries (especially those on the African continent) do not account for longevity risk in their annual valuation. This can even lead to their collapse if steps are not taken to address it. In this work, we develop a method of assessing longevity risk where there is a severe lack of mortality data. The method is based on the assumption that there is a nearly linear relationship between annuitant’s hazard function and their mortality at higher ages (postretirement age), which permits approximating with the Gompertz model. We tried the method on mortality data from Ghana, and the results are consistent with those in the standard literature. That is, longevity risk is a treat to pension companies in Ghana even though, in the case of Ghana, this treat has partially been mitigated by the high-interest rate in the country. With this method, pension and life companies that are not able to account for longevity risk as a result of lack of data or newly formed pension companies with even 2-year mortality data will be able to assess the longevity risk they face without relying on data or models from other countries. <b>TOPICS:</b>Long-term/retirement investing, pension funds, risk management, frontier markets <b>Key Findings</b> ▪ Longevity risk is present in Ghana, and its impact on life companies in the country is potentially high. ▪ Unlike most developed countries, longevity risk in Ghana has partially been mitigated by the high interest rate in the country. ▪ Ghana’s postretirement mortality could be approximated with the Gompertz model.

Given the rising cost of maintaining defined benefit (DB) pensions, there has been a surge of activities in recent years by DB plan sponsors to transfer their pension risk through strategies such as buy-ins and buy-outs. As buy-in and buy-out transaction pipelines grow, insurers actively participating in the buy-in and buy-out markets are exposed to significant longevity risk embedded in pension schemes. In this paper, we investigate how to maximize a bulk annuity insurer’s value with reinsurance and/or longevity securities, subject to constraints that control longevity and investment risks as well as an overall risk. We apply duality and the martingale approach to derive an optimal longevity risk transfer strategy. Our results show that longevity risk transfer interacts with an insurer’s investment decision for value maximization. Our analysis also highlights the interdependence of different longevity risk management tools to achieve an overall risk target.

Given the rising cost of maintaining defined benefit pensions, there has been a surge of activities in recent years by defined benefit plan sponsors to transfer their pension risk through strategies such as buy-ins and buy-outs. As buy-in and buy-out transaction pipelines grow, insurers actively participating in the buy-in and buy-out markets are exposed to significant longevity risk embedded in pension schemes. In this article, we investigate how to maximize a bulk annuity insurer’s value with reinsurance and/or longevity securities, subject to constraints that control longevity and investment risks as well as an overall risk. We apply duality and the martingale approach to derive an optimal longevity risk transfer strategy. Our results show that longevity risk transfer interacts with an insurer’s investment decision for value maximization. Our analysis also highlights the interdependence of different longevity risk management tools to achieve an overall risk target.

Retirees face longevity risk, or the risk of living longer (or less long) than expected; market risk, or the risk of poor investment returns over the retirement horizon, and finally; failure risk, or the risk of running out of money before death. The authors examine the sensitivity of these three risks to asset allocation and Safe Withdrawal Rates, and offer a model to optimize these factors in order to minimize the three primary risks in the context of personal preferences. Finally, a forecast model is proposed to link Safe Withdrawal Rates to contemporaneous stock market valuations and interest rates, with strong statistical significance.

Under a guaranteed annuity option, an insurer guarantees to convert a policyholder's accumulated funds to a life annuity at a fixed rate when the policy matures. If the annuity rates provided under the guarantee are more beneficial to the policyholder than the prevailing rates in the market the insurer has to make up the difference. Such guarantees are common in many US tax sheltered insurance products. These guarantees were popular in UK retirement savings contracts issued in the 1970's and 1980's when long-term interest rates were high. At that time, the options were very far out of the money and insurance companies apparently assumed that interest rates would remain high and thus that the guarantees would never become active. In the 1990's, as long-term interest rates began to fall, the value of these guarantees rose. Because of the way the guarantee was written, two other factors influenced the cost of these guarantees. First, strong stock market performance meant that the amounts to which the guarantee applied increased significantly. Second, the mortality assumption implicit in the guarantee did not anticipate the improvement in mortality which actually occurred.The emerging liabilities under these guarantees threatened the solvency of some companies and led to the closure of Equitable Life (UK) to new business. In this paper we explore the pricing and risk management of these guarantees.

Guaranteed Annuity Option in the Government Employees Pension Plan