On a gap between rational annuitization price for producer and price for customer

The paper studies pricing of insurance products focusing on the pricing of annuities under uncertainty. This pricing problem is crucial for financial decision making and was studied intensively, however, many open questions still remain. In particular, there is a so-called "annuity puzzle" related to certain inconsistency of existing financial theory with the empirical observations for the annuities market. The paper suggests a pricing method based on the risk minimization such that both producer and customer seek to minimize the mean square hedging error accepted as a measure of risk. This leads to two different versions of the pricing problem: the selection of the annuity price given the rate of regular payments, and the selection of the rate of payments given the annuity price. It appears that solutions of these two problems are different. This can contribute to explanation for the "annuity puzzle"

Longevity risk and capital markets: The 2009-2010 update

This Special Issue of the North American Actuarial Journal contains ten contributions to the academic literature all dealing with longevity risk and capital markets. Draft versions of the papers were presented at Longevity Five: the Fifth International Longevity Risk and Capital Markets Solutions Conference that was held in New York on 25-26 September 2009. It was hosted by J. P. Morgan and St John’s University and organized by the Pensions Institute at Cass Business School, London, and the Edmondson-Miller Chair at Illinois State University.Longevity Risk; Capital Market

Maximum Market Price of Longevity Risk under Solvency Regimes: The Case of Solvency II.

Longevity risk constitutes an important risk factor for life insurance companies, and it can be managed through longevity-linked securities. The market of longevity-linked securities is at present far from being complete and does not allow finding a unique pricing measure. We propose a method to estimate the maximum market price of longevity risk depending on the risk margin implicit within the calculation of the technical provisions as defined by Solvency II. The maximum price of longevity risk is determined for a survivor forward (S-forward), an agreement between two counterparties to exchange at maturity a fixed survival-dependent payment for a payment depending on the realized survival of a given cohort of individuals. The maximum prices determined for the S-forwards can be used to price other longevity-linked securities, such as q-forwards. The Cairns–Blake–Dowd model is used to represent the evolution of mortality over time that combined with the information on the risk margin, enables us to calculate upper limits for the risk-adjusted survival probabilities, the market price of longevity risk and the S-forward prices. Numerical results can be extended for the pricing of other longevity-linked securities

Maximum Market Price of Longevity Risk under Solvency Regimes: The Case of Solvency II.

Longevity risk constitutes an important risk factor for life insurance companies, and it can be managed through longevity-linked securities. The market of longevity-linked securities is at present far from being complete and does not allow finding a unique pricing measure. We propose a method to estimate the maximum market price of longevity risk depending on the risk margin implicit within the calculation of the technical provisions as defined by Solvency II. The maximum price of longevity risk is determined for a survivor forward (S-forward), an agreement between two counterparties to exchange at maturity a fixed survival-dependent payment for a payment depending on the realized survival of a given cohort of individuals. The maximum prices determined for the S-forwards can be used to price other longevity-linked securities, such as q-forwards. The Cairns–Blake–Dowd model is used to represent the evolution of mortality over time that combined with the information on the risk margin, enables us to calculate upper limits for the risk-adjusted survival probabilities, the market price of longevity risk and the S-forward prices. Numerical results can be extended for the pricing of other longevity-linked securities

Pricing Longevity Bonds Using Affine-Jump Diffusion Models

Historically, actuaries have been calculating premiums and mathematical reserves using a deterministic approach, by considering a deterministic mortality intensity, which is a function of the age only, extracted from available (static) life tables and by setting a flat ("best estimate") interest rate to discount cash flows over time. Since neither the mortality intensity nor interest rates are actually deterministic, life insurance companies and pension funds are exposed to both financial and mortality (systematic and unsystematic) risks when pricing and reserving for any kind of long-term living benefits, particularly on annuities and pensions. In this paper, we assume that an appropriate description of the demographic risks requires the use of stochastic models. In particular, we assume that the random evolution of the stochastic force of mortality of an individual can be modelled by using doubly stochastic processes. The model is then embedded into the well known affine-jump framework, widely used in the term structure literature, in order to derive closed-form solutions for the survival probability. We show that stochastic mortality models provide an adequate framework for the development of longevity risk hedging tools, namely mortality-linked contracts such as longevity bonds or mortality derivatives.Stochastic mortality intensity; Longevity risk; Affine models; Projected lifetables.

Longevity risks and capital markets: The 2010-2011 update

This Special Issue of Geneva Papers on Risk and Insurance - Issues and Practice contains 10 contributions to the academic literature all dealing with longevity risk and capital markets. Draft versions of the papers were presented at Longevity Six: The Sixth International Longevity Risk and Capital Markets Solutions Conference that was held in Sydney on 9-10 September 2010. It was hosted by the Australian Institute for Population Ageing Research, the Australian School of Business and the University of New South Wales. It was sponsored by PricewaterhouseCoopers, Australian Prudential Regulation Authority (APRA), Coventry Capital, Swiss Re, and Institute of Actuaries of Australia.Longevity Risk; Capital Market

Still living with mortality: The longevity risk transfer market after one decade

This paper updates Living with Mortality published in 2006. It describes how the longevity risk transfer market has developed over the intervening period, and, in particular, how insurance-based solutions – buy-outs, buy-ins and longevity insurance – have triumphed over capital markets solutions that were expected to dominate at the time. Some capital markets solutions – longevity-spread bonds, longevity swaps, q-forwards, and tail-risk protection – have come to market, but the volume of business has been disappointingly low. The reason for this is that when market participants compare the index-based solutions of the capital markets with the customized solutions of insurance companies in terms of basis risk, credit risk, regulatory capital, collateral, and liquidity, the former perform on balance less favourably despite a lower potential cost.We discuss the importance of stochastic mortality models for forecasting future longevity and examine some applications of these models, e.g., determining the longevity risk premiumand estimating regulatory capital relief. The longevity risk transfer market is now beginning to recognize that there is insufficient capacity in the insurance and reinsurance industries to deal fully with demand and new solutions for attracting capital markets investors are now being examined – such as longevity-linked securities and reinsurance sidecars

A conceptual framework for retirement products : Risk sharing arrangements between providers and retirees

Voluntary annuity markets are, in most countries, smaller than what the theoretical and part of the empirical literature would suggest. There are both demand and supply constraints that hamper the development of annuity markets. In particular, traditional products available in most countries can require excessive minimum capital requirements for given investment opportunities available to providers. Investment and longevity risk should be shared between providers and annuitants so that supply constraints can be relaxed. Alternative annuity products, which imply risk sharing, could be backed by substantially lower capital investments or, equivalently, provided at substantially lower prices to consumers.Insurance&Risk Mitigation,Environmental Economics&Policies,Pensions&Retirement Systems,Economic Theory&Research,Non Bank Financial Institutions,Insurance&Risk Mitigation,Pensions&Retirement Systems,Economic Theory&Research,Environmental Economics&Policies,Non Bank Financial Institutions

Assessing Investment and Longevity Risks within Immediate Annuities

Life annuities provide a guaranteed income for the remainder of the recipient’s lifetime, and therefore, annuitization presents an important option when choosing an adequate investment strategy for the retirement ages. While there are numerous research articles studying annuities from a pensioner’s point of view, thus far there have been few contributions considering annuities from the provider’s perspective. In particular, to date there are no surveys of the general risks within annuity books. The present paper aims at filling this gap: Using a simulation framework, it provides a long-term analysis of the risks within annuity books. In particular, the joint impact of mortality risks and investment risks as well as their respective influences on the insurer’s financial situation are studied. The key finding is that, under the model specifications and using annuity data from the United Kingdom, the risk premium charged for aggregate mortality risk seems to be very large relative to its characteristics. Possible reasons as well as economic implications are provided, and potential caveats are discussed