PRICING AND SOLVENCY OF VALUE-MAXIMIZING LIFE ANNUITY PROVIDERS

2013 ◽  
Vol 44 (1) ◽  
pp. 39-61 ◽  
Author(s):  
Maathumai Nirmalendran ◽  
Michael Sherris ◽  
Katja Hanewald
Keyword(s):  
Solvency Ii ◽  
Default Probability ◽  
Product Demand ◽  
Stochastic Mortality ◽  
Life Insurers ◽  
Life Annuity ◽  
Product Pricing ◽  
One Year ◽  
Life Annuities ◽  
The Impact

AbstractThis paper provides a detailed quantitative assessment of the impact of capital and default probability on product pricing and shareholder value for a life insurer providing life annuities. A multi-period cash flow model, allowing for stochastic mortality and asset returns, imperfectly elastic product demand, as well as frictional costs, is used to derive value-maximizing capital and pricing strategies for a range of one-year default probability levels reflecting differences in regulatory regimes including Solvency II. The model is calibrated using realistic assumptions. The sensitivity of results is assessed. The results show that value-maximizing life insurers should target higher solvency levels than the Solvency II regulatory one-year 99.5% probability under assumptions of reasonable levels of policyholder's aversion to insolvency risk. Even in the case of less restrictive solvency probabilities, policyholder price elasticity and solvency preferences are shown to be important factors for a life insurer's value-maximizing strategy.

scholarly journals Mortality data reliability in an internal model

2020 ◽  
Vol 14 (2) ◽  
pp. 420-444
Author(s):  
Fabrice Balland ◽  
Alexandre Boumezoued ◽  
Laurent Devineau ◽  
Marine Habart ◽  
Tom Popa
Keyword(s):  
Data Quality ◽  
Internal Model ◽  
Mortality Rates ◽  
Solvency Ii ◽  
West Germany ◽  
Mortality Data ◽  
Longevity Risk ◽  
Capital Requirement ◽  
Stochastic Mortality ◽  
The Impact

AbstractIn this paper, we discuss the impact of some mortality data anomalies on an internal model capturing longevity risk in the Solvency 2 framework. In particular, we are concerned with abnormal cohort effects such as those for generations 1919 and 1920, for which the period tables provided by the Human Mortality Database show particularly low and high mortality rates, respectively. To provide corrected tables for the three countries of interest here (France, Italy and West Germany), we use the approach developed by Boumezoued for countries for which the method applies (France and Italy) and provide an extension of the method for West Germany as monthly fertility histories are not sufficient to cover the generations of interest. These mortality tables are crucial inputs to stochastic mortality models forecasting future scenarios, from which the extreme 0.5% longevity improvement can be extracted, allowing for the calculation of the solvency capital requirement. More precisely, to assess the impact of such anomalies in the Solvency II framework, we use a simplified internal model based on three usual stochastic models to project mortality rates in the future combined with a closure table methodology for older ages. Correcting this bias obviously improves the data quality of the mortality inputs, which is of paramount importance today, and slightly decreases the capital requirement. Overall, the longevity risk assessment remains stable, as well as the selection of the stochastic mortality model. As a collateral gain of this data quality improvement, the more regular estimated parameters allow for new insights and a refined assessment regarding longevity risk.

Comparing Solvency II and Life and General Insurance Capital approaches to capital determination of a life portfolio in the presence of stress scenarios

2018 ◽  
Vol 13 (1) ◽  
pp. 36-66
Author(s):  
Kangjing Tan ◽  
Aaron Bruhn
Keyword(s):  
Risk Management ◽  
Solvency Ii ◽  
Capital Requirements ◽  
Life Insurers ◽  
General Insurance ◽  
Pillar Structure ◽  
Matching Adjustment ◽  
The Impact ◽  
Capital Intensive

AbstractThe European-centric Solvency II and Australian-centric Life and General Insurance Capital regimes are two examples of risk-based approaches to capital determination and risk management for life insurers. Both consist of a three-pillar structure covering capital, risk management and disclosure requirements. We apply the capital requirements of each regime to three synthetic sets of insurance policies, including a risk, annuity and combined portfolios, and consider the impact on capital arising from three separate and relatively severe stress events. Results highlight the relatively capital intensive nature of annuities, the differences between different capital regimes, the significance of solvency II’s matching adjustment and the robustness of each regime to both pandemic and economic stresses. Results also highlight the nature of diversification benefits from within each capital regime, on overall capital requirements.

scholarly journals Premium Risk Net of Reinsurance: From Short-Term to Medium-Term Assessment

Risks ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 72
Author(s):  
Antonio Pallaria ◽  
Nino Savelli
Keyword(s):  
Risk Model ◽  
Risk Mitigation ◽  
Solvency Ii ◽  
Medium Term ◽  
Short Term ◽  
Life Insurers ◽  
Actuarial Risk ◽  
The Impact ◽  
Solvency Ratio ◽  
Premium Risk

Solvency II requirements introduced new issues for actuarial risk management in non-life insurance, challenging the market to have a consciousness of its own risk profile, and also investigating the sensitivity of the solvency ratio depending on the insurance risks and technical results on either a short-term and medium-term perspective. For this aim, in the present paper, a partial internal model for premium risk is developed for three multi-line non-life insurers, and the impact of some different business mixes is analyzed. Furthermore, the risk-mitigation and profitability impact of reinsurance in the premium risk model are introduced, and a global framework for a feasible application of this model consistent with a medium-term analysis is provided. Numerical results are also figured out with evidence of various effects for several portfolios and reinsurance arrangements, pointing out the main reasons for these differences.

scholarly journals A review of the risk margin – Solvency II and beyond

2020 ◽  
Vol 25 ◽  
Author(s):  
A. J. Pelkiewicz ◽  
S. W. Ahmed ◽  
P. Fulcher ◽  
K. L. Johnson ◽  
S. M. Reynolds ◽  
...  
Keyword(s):  
Cost Of Capital ◽  
Working Party ◽  
Solvency Ii ◽  
Risk Margin ◽  
Life Insurers ◽  
Wide Range ◽  
The Difference ◽  
Set Up ◽  
The Uk ◽  
The Impact

Abstract For life insurers in the United Kingdom (UK), the risk margin is one of the most controversial aspects of the Solvency II regime which came into force in 2016. The risk margin is the difference between the technical provisions and the best estimate liabilities. The technical provisions are intended to be market-consistent, and so are defined as the amount required to be paid to transfer the business to another undertaking. In practice, the technical provisions cannot be directly calculated, and so the risk margin must be determined using a proxy method; the method chosen for Solvency II is known as the cost-of-capital method. Following the implementation of Solvency II, the risk margin came under considerable criticism for being too large and too sensitive to interest rate movements. These criticisms are particularly valid for annuity business in the UK – such business is of great significance to the system for retirement provision. A further criticism is that mitigation of the impact of the risk margin has led to an increase in reinsurance of longevity risks, particularly to overseas reinsurers. This criticism has led to political interest, and the risk margin was a major element of the Treasury Committee inquiry into EU Insurance Regulation. The working party was set up in response to this criticism. Our brief is to consider both the overall purpose of the risk margin for life insurers and solutions to the current problems, having regard to the possibility of post-Brexit flexibility. We have concluded that a risk margin in some form is necessary, although its size depends on the level of security desired, and so is primarily a political question. We have reviewed possible alternatives to the current risk margin, both within the existing cost-of-capital methodology and considering a wide range of alternatives. We believe that requirements for the risk margin will depend on future circumstances, in particular relating to Brexit, and we have identified a number of possible changes to methodology which should be considered, depending on circumstances.

scholarly journals Managing Systematic Mortality Risk in Life Annuities: An Application of Longevity Derivatives

Risks ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 2 ◽  
Author(s):  
Man Chung Fung ◽  
Katja Ignatieva ◽  
Michael Sherris
Keyword(s):  
Risk Premium ◽  
Mortality Data ◽  
Longevity Risk ◽  
Stochastic Mortality ◽  
Life Annuity ◽  
Analytical Formulae ◽  
Life Annuities ◽  
Longevity Swap ◽  
Stochastic Mortality Model ◽  
Benefits And Costs

This paper assesses the hedge effectiveness of an index-based longevity swap and a longevity cap for a life annuity portfolio. Although longevity swaps are a natural instrument for hedging longevity risk, derivatives with non-linear pay-offs, such as longevity caps, provide more effective downside protection. A tractable stochastic mortality model with age dependent drift and volatility is developed and analytical formulae for prices of longevity derivatives are derived. The model is calibrated using Australian mortality data. The hedging of the life annuity portfolio is comprehensively assessed for a range of assumptions for the longevity risk premium, the term to maturity of the hedging instruments, as well as the size of the underlying annuity portfolio. The results compare the risk management benefits and costs of longevity derivatives with linear and nonlinear payoff structures.

scholarly journals A CORRELATION SENSITIVITY ANALYSIS OF NON-LIFE UNDERWRITING RISK IN SOLVENCY CAPITAL REQUIREMENT ESTIMATION

2013 ◽  
Vol 43 (1) ◽  
pp. 21-37 ◽  
Author(s):  
Lluís Bermúdez ◽  
Antoni Ferri ◽  
Montserrat Guillén
Keyword(s):  
Sensitivity Analysis ◽  
Solvency Ii ◽  
Capital Requirement ◽  
Solvency Capital Requirement ◽  
The Standard Model ◽  
Solvency Capital ◽  
One Year ◽  
The Impact ◽  
Model Approach

AbstractThis paper analyses the impact of using different correlation assumptions between lines of business when estimating the risk-based capital reserve, the solvency capital requirement (SCR), under Solvency II regulations. A case study is presented and the SCR is calculated according to the standard model approach. Alternatively, the requirement is then calculated using an internal model based on a Monte Carlo simulation of the net underwriting result at a one-year horizon, with copulas being used to model the dependence between lines of business. To address the impact of these model assumptions on the SCR, we conduct a sensitivity analysis. We examine changes in the correlation matrix between lines of business and address the choice of copulas. Drawing on aggregate historical data from the Spanish non-life insurance market between 2000 and 2009, we conclude that modifications of the correlation and dependence assumptions have a significant impact on SCR estimation.

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