1,721,058 research outputs found
The insurance pricing with mortality dependence forecasts
No full textThe main issue of the paper is to include the dependency structure in the longevity forecasts, in order to search for a “diversification effect” which could influence insurance pricing
The valuation of guaranteed lifelong withdrawal benefit options in variable annuity contracts and the impact of mortality risk
No full textn light of the growing importance of the variable annuities market, in this paper we introduce a theoretical model for the pricing and valuation of guaranteed lifelong withdrawal benefit (GLWB) options embedded in variable annuity products. As the name suggests, this option offers a lifelong withdrawal guarantee; therefore, there is no limit on the total amount that is withdrawn over the term of the policy because if the account value becomes zero while the insured is still alive, he or she continues to receive the guaranteed amount annually until death. Any remaining account value at the time of death is paid to the beneficiary as a death benefit. We offer a specific framework to value the GLWB option in a market-consistent manner under the hypothesis of a static withdrawal strategy, according to which the withdrawal amount is always equal to the guaranteed amount. The valuation approach is based on the decomposition of the product into living and death benefits. The model makes use of the standard no-arbitrage models of mathematical finance, which extend the Black-Scholes framework to insurance contracts, assuming the fund follows a geometric Brownian motion and the insurance fee is paid, on an ongoing basis, as a proportion of the assets. We develop a sensitivity analysis, which shows how the value of the product varies with the key parameters, including the age of the policyholder at the inception of the contract, the guaranteed rate, the risk-free rate, and the fund volatility. We calculate the fair fee, using Monte Carlo simulations under different scenarios. We give special attention to the impact of mortality risk on the value of the option, using a flexible model of mortality dynamics, which allows for the possible perturbations by mortality shock of the standard mortality tables used by practitioners. Moreover, we evaluate the introduction of roll-up and step-up options and the effect of the decision to delay withdrawing. Empirical analyses are performed, and numerical results are provided
Dependency Premium with multiple population forecasts
No full textThe main issue of the paper is to include the dependency structure in the longevity forecasts, in order to search for a “diversification effect” which could reduce the insurance product cost. We propose how to estimate the dependency premium, by introducing a model which improves the so-called coherent mortality forecasts for groups of populations, which guarantees the necessary and sufficient condition of long term convergence. Actuarial interpretations are given in the empirical applications, which are presented to illustrate our results
Risk Classification/Life
No full textThis article gives an overview of the main models used to represent heterogeneity in life insurance. We focus in particular on two classes of models: individual models, which are suitable to represent heterogeneity aspects that are observable at the issue of an insurance; and collective models, which are suitable to assess heterogeneity due to unobservable risk factors.
The adoption of (at least some) individual models is common practice in life insurance, in particular for pricing or, more generally, for risk management. On the other hand, collective models are used for certain mortality investigations, in particular for suggesting an appropriate description of the age-specific mortality shape in some insured portfolios
Solvency Analysis of Deferred Annuities
Get PDFWhile the solvency analysis of immediate life annuity portfolios has been extensively studied, the case of deferred annuities has received comparatively much less attention. We assess the importance and effect of stochastic mortality models and interest rates on the solvency analysis of a portfolio of deferred annuity contracts. Our analysis considers three steps: first, the benchmark case where mortality rates and interest rates are both deterministic; then, the case in which only mortality rates are stochastic is explored; finally, the full model where both mortality rates and interest rates are stochastic. The results demonstrate the model risk stemming from the uncertainty in the mortality models and its impact on the evaluation of solvency margins for life annuities. The role of the deferment period is thoroughly discussed and compared to the case of immediate annuities
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