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

Pricing and Hedging Guaranteed Returns on Mix Funds

Abstract\ud In this paper we propose a valuation and hedging strategy for a guaranteed minimal rate of return on a mix fund, which participates in both bonds and stocks. For the case where a fixed amount of money is invested, we show that a European put option on the mix fund replicates the cash flows of this guarantee at all times and using the arbitrage-free pricing methodology, the market value of the guarantee can be obtained explicitly. Using historical data, we show that modeling the correlation between equity and bond returns is of fundamental importance when the stochastic nature of the term structure of interest rates is taken into account. For this model we define a hedging strategy which shows how the dependency of the option on the changing yield of the bond fund can be hedged away using mix fund contracts. We also show how Monte Carlo methods can be used to analyze the case where the guarantee is given on periodically invested fixed amounts of money instead of one single payment

A unified pricing of variable annuity guarantees under the optimal stochastic control framework

In this paper, we review pricing of variable annuity living and death guarantees offered to retail investors in many countries. Investors purchase these products to take advantage of market growth and protect savings. We present pricing of these products via an optimal stochastic control framework, and review the existing numerical methods. For numerical valuation of these contracts, we develop a direct integration method based on Gauss-Hermite quadrature with a one-dimensional cubic spline for calculation of the expected contract value, and a bi-cubic spline interpolation for applying the jump conditions across the contract cashflow event times. This method is very efficient when compared to the partial differential equation methods if the transition density (or its moments) of the risky asset underlying the contract is known in closed form between the event times. We also present accurate numerical results for pricing of a Guaranteed Minimum Accumulation Benefit (GMAB) guarantee available on the market that can serve as a benchmark for practitioners and researchers developing pricing of variable annuity guarantees.Comment: Keywords: variable annuity, guaranteed living and death benefits, guaranteed minimum accumulation benefit, optimal stochastic control, direct integration metho

Efficient Hedging and Pricing of Equity-Linked Life Insurance Contracts on Several Risky Assets

The authors use the efficient hedging methodology for optimal pricing and hedging of equitylinked life insurance contracts whose payoff depends on the performance of several risky assets. In particular, they consider a policy that pays the maximum of the values of n risky assets at some maturity date T , provided that the policyholder survives to T . Such contracts incorporate financial risk, which stems from the uncertainty about future prices of the underlying financial assets, and insurance risk, which arises from the policyholder's mortality. The authors show how efficient hedging can be used to minimize expected losses from imperfect hedging under a particular risk preference of the hedger. They also prove a probabilistic result, which allows one to calculate analytic pricing formulas for equity-linked payoffs with n risky assets. To illustrate its use, explicit formulas are derived for optimal prices and expected hedging losses for payoffs with two risky assets. Numerical examples highlighting the implications of efficient hedging for the management of financial and insurance risks of equity-linked life insurance policies are also provided.Financial markets;

The History of the Quantitative Methods in Finance Conference Series. 1992-2007

This report charts the history of the Quantitative Methods in Finance (QMF) conference from its beginning in 1993 to the 15th conference in 2007. It lists alphabetically the 1037 speakers who presented at all 15 conferences and the titles of their papers.

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

A market-consistent framework for the fair evaluation of insurance contracts under Solvency II

The entry into force of the Solvency II regulatory regime is pushing insurance companies in engaging into market consistence evaluation of their balance sheet, mainly with reference to financial options and guarantees embedded in life with-profit funds. The robustness of these valuations is crucial for insurance companies in order to produce sound estimates and good risk management strategies, in particular, for liability-driven products such as with-profit saving and pension funds. This paper introduces a Monte Carlo simulation approach for evaluation of insurance assets and liabilities, which is more suitable for risk management of liability-driven products than common approaches generally adopted by insurance companies, in particular, with respect to the assessment of valuation risk

Valuation and hedging of the ruin-contingent life annuity (RCLA)

This paper analyzes a novel type of mortality contingent-claim called a ruin-contingent life annuity (RCLA). This product fuses together a path-dependent equity put option with a "personal longevity" call option. The annuitant's (i.e. long position) payoff from a generic RCLA is \$1 of income per year for life, akin to a defined benefit pension, but deferred until a pre-specified financial diffusion process hits zero. We derive the PDE and relevant boundary conditions satisfied by the RCLA value (i.e. the hedging cost) assuming a complete market where No Arbitrage is possible. We then describe some efficient numerical techniques and provide estimates of a typical RCLA under a variety of realistic parameters. The motivation for studying the RCLA on a stand-alone basis is two-fold. First, it is implicitly embedded in approximately \$1 trillion worth of U.S. variable annuity (VA) policies; which have recently attracted scrutiny from financial analysts and regulators. Second, the U.S. administration - both Treasury and Department of Labor - have been encouraging Defined Contribution (401k) plans to offer stand-alone longevity insurance to participants, and we believe the RCLA would be an ideal and cost effective candidate for that job