Securitization Of Longevity Risk Research Articles

Pricing longevity bond with affine-jump-diffusion multi-cohort mortality model

Facing increasingly severe longevity problems, traditional longevity risk management methods are no longer the final answer. Longevity risk securitization provides a good hedging method, which transfers the longevity risks to a wider capital market and realizes the cross-market transfer of risks. The pricing process of longevity derivatives depends on the underlying risk factors (stochastic processes of mortality and interest rate). We adopt an affine-jump-diffusion process to model the dynamics of mortality and estimate the model parameters with the actual mortality data in China. The measure implied by the annuity market price is chosen as the risk-neutral pricing measure. We use the Chinese annuity market price to calculate the concrete form of the measure transformation and use the risk-neutral pricing measure thereby to price the longevity bond designed by Denuit et al. (2007).

A Discussion on the Impact and Management of Longevity Risk on Households, Enterprises and Governments in the Context of Aging in China

The aging of China's population has become a significant social problem. The resulting longevity risk is a new and growing challenge for households, businesses and governments. This paper discusses the influence of longevity risk on different subjects and management methods by combining theoretical analysis and data analysis. From the perspective of households, based on the life cycle hypothesis, this paper demonstrates that the increase in life expectancy will reduce the total utility by reducing the average consumption level of individuals (families). For the general enterprises and the insurance industry, longevity risk means the rapid accumulation of future operating costs and may even bring liquidity risk. As for the government, they are the manager of the social pension fund, which is faced with the problem of balancing the income and payments under the background of the significant increase in the average life expectancy of the population. As a link, the financial market can transfer and disperse longevity risk among different subjects. However, there is a shortage of investors and issuers in the Chinese financial market. The rate of Chinese households participating financial market is low, and the progress of Longevity risk securitization in financial sectors is slow. Therefore, in managing longevity risk, China should focus on increasing the utilization of capital markets.

Financial Innovation for an Aging World

Over the last half-century, around the world, many nations have seen plummeting fertility rates and mounting life expectancies. These two factors are the engine behind unprecedented global aging. In this paper, we explore how the demographic transition may influence financial markets and, in turn, how financial market innovation might help resolve concerns flowing from global aging trends. We first provide context by reviewing the economics, finance, and insurance-related literature on how global aging patterns may influence capital markets. We then turn to insurance markets, and discuss a range of products and policies, including both retail and wholesale financial offerings for various forms of life annuities, long-term care benefits, reverse mortgages, securitization of longevity risk, inflation-protected assets, reinsurance, guarantees, derivative contracts on residential property price indices, mortality swaps and longevity derivative contracts. We also indicate how new public-private partnerships might be beneficial in enhancing the future environment for old-age risk management.

The Securitization of Longevity Risk and Its Implications for Retirement Security

The economic significance of longevity risk for governments, corporations, and individuals has begun to be recognized and quantified. The traditional insurance route for managing this risk has serious limitations due to capacity constraints that are becoming more and more binding. If the 2010 U.S. population lived three years longer than expected then the government would have to set aside 50% of the U.S. 2010 GDP or approximately $7.37 trillion to fully fund that increased social security liability. This is just one way of gauging the size of the risk. Due to the much larger capacity of capital markets more attention is being devoted to transforming longevity risk from its pure risk form to a speculative risk form so that it can be traded in the capital markets. This transformation has implications for governments, corporations and individuals that will be explored here. The analysis will view the management of longevity risk by considering how defined contribution plans can be managed to increase the sustainable length of retirement and by considering how defined benefit plans can be managed to reduce pension risk using longevity risk hedging schemes.

Securitization of longevity risk – survivor swap perspective

Purpose The purpose of this paper is to present a clear path to securitize the longevity risk with two distinct swaps in order to inspire a new Chinese life market. Design/methodology/approach Studies on longevity risk securitization consist of three aspects, respectively, instrument design, pricing methodology and mortality projection. The swaps designed are referenced, respectively, to vanilla and complex survivor swaps (Dowd et al., 2006; Lin and Cox, 2005). Methods applied are RHH model and Gompertz law for mortality projection, as well as two-factor Wang transformation for pricing. Findings This paper figures out the market price of risk in Chinese annuity market, checks for the sensitivity of the price to parameters and tests the hedging effects by Monte Carlo simulation. Originality/value Based on the theoretical and numerical results, this paper suggests an effective way to possibly witness the birth of New Life Market in China.

Semicoherent Multipopulation Mortality Modeling: The Impact on Longevity Risk Securitization

AbstractMultipopulation mortality models play an important role in longevity risk transfers involving more than one population. Most of the existing multi‐population mortality models are built on the hypothesis of coherence, which assumes that there always exists a force that brings the mortality differential between any two populations back to a constant long‐term equilibrium level. This hypothesis prevents diverging long‐term forecasts, which do not seem to be biologically reasonable. However, the coherence assumption may be perceived by market participants as too strong and is in fact not always supported by empirical observations. In this article, we introduce a new concept called “semicoherence,” which is less stringent in the sense that it permits the mortality trajectories of two related populations to diverge, as long as the divergence does not exceed a specific tolerance corridor, beyond which mean reversion will come into effect. We further propose to produce semicoherent mortality forecasts by using a vector threshold autoregression. The proposed modeling approach is illustrated with mortality data from U.S. and English and Welsh male populations, and is applied to several pricing and hedging scenarios.

Modeling longevity risk transfers as Nash bargaining problems: Methodology and insights

The problem of longevity risk has recently received considerable attention. In this paper, we apply economic modeling methods to longevity risk securitization, which is now regarded by pension and insurance industries as a solution to the problem. Specifically, we model the trade of a longevity security as a two-player bargaining game, and use Nash's bargaining solution to determine the outcome of it. Our work not only offers an alternative method for pricing longevity securities, but also reveals several properties about the market for longevity securities. First, a trade would occur if the longevity security is an effective hedging instrument, and the trade would benefit all agents involved. Second, a trade of longevity risk can reduce pension plans' bankruptcy risk, safeguarding the financial security of pension plan members. Finally, compared to the competitive equilibrium, Nash's bargaining solution yields higher trading prices. Therefore, as the market becomes more competitive, pension plans may hedge longevity risk at a lower cost.

A step-by-step guide to building two-population stochastic mortality models

Two-population stochastic mortality models play a crucial role in the securitization of longevity risk. In particular, they allow us to quantify the population basis risk when longevity hedges are built from broad-based mortality indexes. In this paper, we propose and illustrate a systematic process for constructing a two-population mortality model for a pair of populations. The process encompasses four steps, namely (1) determining the conditions for biological reasonableness, (2) identifying an appropriate base model specification, (3) choosing a suitable time-series process and correlation structure for projecting period and/or cohort effects into the future, and (4) model evaluation.For each of the seven single-population models from Cairns et al. (2009), we propose two-population generalizations. We derive criteria required to avoid long-term divergence problems and the likelihood functions for estimating the models. We also explain how the parameter estimates are found, and how the models are systematically simplified to optimize the fit based on the Bayes Information Criterion. Throughout the paper, the results and methodology are illustrated using real data from two pairs of populations.

Informed Intermediation of Longevity Exposures

ABSTRACTWe examine pension buyout transactions and longevity risk securitization in a common framework, emphasizing the role played by asymmetries in capital requirements and mortality forecasting technology. The results are used to develop a coherent model of intermediation of longevity exposures, between defined benefit pension plans and capital market investors, through insurers operating in the pension buyout market. We derive several predictions consistent with the recent empirical evidence on pension buyouts and offer insights on the role of buyout firms and regulation in the emerging market for longevity‐linked securities. A multiperiod version of the model is used to explore the effects of longevity risk securitization on the capacity of the pension buyout market.

Optimal hedging of demographic risk in life insurance

A Markov chain model is taken to describe the development of a multi-state life insurance policy or portfolio in a stochastic economic–demographic environment. It is assumed that there exists an arbitrage-free market with tradeable securities derived from demographic indices. Adopting a mean-variance criterion, two problems are formulated and solved. First, how can an insurer optimally hedge environmental risk by trading in a given set of derivatives? Second, assuming that insurers perform optimal hedging strategies in a given derivatives market, how can the very derivatives be designed in order to minimize the average hedging error across a given population of insurers? The paper comes with the caveat emptor that the theory will find its prime applications, not in securitization of longevity risk, but rather in securitization of catastrophic mortality risk.

Informed Intermediation of Longevity Exposures

We examine pension buyout transactions and longevity risk securitization in a common framework, emphasizing the role played by asymmetries in capital requirements and mortality forecasting technology. The results are used to develop a coherent model of intermediation of longevity exposures, between defined benefit pension schemes and capital market investors, through insurers operating in the pension buyout market. We derive several predictions consistent with the recent empirical evidence on pension buyouts, and offer insights on the role of buyout firms and regulation in the emerging market for longevity-linked securities. A multi-period version of the model is used to explore the effects of longevity risk securitization on the capacity of the pension buyout market.

Longevity-Indexed Life Annuities

This paper addresses the problem of the sharing of longevity risk between an annuity provider and a group of annuitants. An appropriate longevity index is designed in order to adapt the amount of the periodic payments in life annuity contracts. This accounts for unexpected longevity improvements experienced by a given reference population. The approach described in the present paper is in contrast with group self-annuitization, where annuitants bear their own risk. Here the annuitants bear only the nondiversifiable risk that the future mortality trend departs from that of the reference forecast. In that respect, the life annuities discussed in this paper are substitutes for reinsurance and securitization of longevity risk.

Securitization of Longevity Risk Using Percentile Tranching

AbstractSecuritizations that transfer risk to the financial markets are a potential solution to longevity risk in the annuity business. The classical Lee–Carter model is applied to generate the future stochastic survival distribution. A method to design inverse survivor bonds using percentile tranches and to calculate the security prices is presented. The percentile tranche method is a simple and practical way for the issuer to design and price the security. This method can serve to identify the risk–yield relationship, which can provide investors with clear insight regarding the appropriate choice of tranches.

Pricing longevity risk with the parametric bootstrap: A maximum entropy approach

In recent years, there has been significant development in the securitization of longevity risk. Various methods for pricing longevity risk have been proposed. In this paper we present an alternative pricing method, which is based on the maximization of the Shannon entropy in physics. Specifically, we propose implementing this pricing method with the parametric bootstrap ( Brouhns et al., 2005), which is highly flexible and can be performed under different model assumptions. Through this pricing method we also quantify the impact of cohort effects and parameter uncertainty on prices of mortality-linked securities. Numerical illustrations based on longevity bonds with different maturities are provided.

Securitization, structuring and pricing of longevity risk

Pricing and risk management for longevity risk have increasingly become major challenges for life insurers and pension funds around the world. Risk transfer to financial markets, with their major capacity for efficient risk pooling, is an area of significant development for a successful longevity product market. The structuring and pricing of longevity risk using modern securitization methods, common in financial markets, have yet to be successfully implemented for longevity risk management. There are many issues that remain unresolved for ensuring the successful development of a longevity risk market. This paper considers the securitization of longevity risk focusing on the structuring and pricing of a longevity bond using techniques developed for the financial markets, particularly for mortgages and credit risk. A model based on Australian mortality data and calibrated to insurance risk linked market data is used to assess the structure and market consistent pricing of a longevity bond. Age dependence in the securitized risks is shown to be a critical factor in structuring and pricing longevity linked securitizations.

Longevity bond premiums: The extreme value approach and risk cubic pricing

The purpose of this study is to analyze the securitization of longevity risk with an emphasis on longevity risk modeling and longevity bond premium pricing. Various longevity derivatives have been proposed, and the capital market has experienced one unsuccessful attempt by the European Investment Bank (EIB) in 2004. After carefully analyzing the pros and cons of previous securitizations, we present our proposed longevity bonds, whose payoffs are structured as a series of put option spreads. We utilize a random walk model with drift to fit small variations of mortality improvements and employ extreme value theory to model rare longevity events. Our method is a new approach in longevity risk securitization, which has the advantage of both capturing mortality improvements within sample and extrapolating rare, out-of- sample longevity events. We demonstrate that the risk cubic model developed for pricing catastrophe bonds can be applied to mortality and longevity bond pricing and use the model to calculate risk premiums for longevity bonds.

Securitization of Longevity Risk in Reverse Mortgages

The reverse mortgage market has been expanding rapidly in developed economies in recent years. The onset of demographic transition places a rapidly rising number of households in an age window in which reverse mortgages have potential appeal. Increasing prices for residential real estate over the last decade have further stimulated interest. Reverse mortgages involve various risks from the provider-s perspective that may hinder the further development of these financial products. This paper addresses one method of transferring and financing the risks associated with these products through the form of securitization. Securitization is becoming a popular and attractive alternative form of risk transfer of insurance liabilities. Here we demonstrate how to construct a securitization structure for reverse mortgages similar to the one applied in traditional insurance products. Specifically, we investigate the merits of developing survivor bonds and survivor swaps for reverse mortgage products. In the case of survivor bonds, for example, we are able to compute premiums, both analytically and numerically through simulations, and to examine how the longevity risk may be transferred to the financial investors. Our numerical calculations provide an indication of the economic benefits derived from developing survivor bonds to securitize the “longevity risk component” of reverse mortgage products. Moreover, some sensitivity analysis of these economic benefits indicates that these survivor bonds provide for a promising tool for investment diversification.

Securitization of Longevity Risk in Reverse Mortgages

The reverse mortgage market has been expanding rapidly in developed economies in recent years. The onset of demographic transition places a rapidly rising number of households in an age window where reverse mortgages have potential appeal, and increasing prices for residential real estate over the last decade has further stimulated interest. Reverse mortgages involve various risks from the provider's perspective which may hinder the further development of these financial products. This paper addresses one method of transferring and financing the risks associated with these products through the form of securitization. Securitization is becoming a popular and attractive alternative form of risk transfer of insurance liabilities. Here we demonstrate how to construct a securitization structure for reverse mortgages similar to the one applied in traditional insurance products. Specifically, we investigate the merits of developing survivor bonds and survivor swaps for reverse mortgage products. In the case of survivor bonds, for example, we are able to compute premiums, both analytically and numerically through simulations, and to examine how the risk may be transferred to the financial investors. Our numerical calculations provide an indication of the economic benefits derived from developing survivor bonds to securitize the longevity risk compoent of reverse mortgage products. Moreover, some sensitivity analysis of these economic benefits indicates that these survivor bonds provide for a promising tool for investment diversification.

Securitization of Longevity Risk: Pricing Survivor Bonds With Wang Transform in the Lee‐Carter Framework

AbstractLongevity risk is a major issue for insurers and pension funds, especially in the selling of annuity products. In that respect, securitization of this risk could offer great opportunities for hedging. This article proposes to design survivor bonds which could be issued directly by insurers. In order to guaranty some transparency in the product, the survivor bond is based on a public mortality index. The classical Lee‐Carter model for mortality forecasting is used to price a risky coupon survivor bond based on this index.