Research

735 KiB

Open AccessArticle

A Unified Pricing of Variable Annuity Guarantees under the Optimal Stochastic Control Framework

by Pavel V. Shevchenko and Xiaolin Luo

Risks 2016, 4(3), 22; https://doi.org/10.3390/risks4030022 - 05 Jul 2016

Cited by 18 | Viewed by 5269

In this paper, we review pricing of the 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 [...] Read more.

In this paper, we review pricing of the 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. We also discuss pricing under the complete/incomplete financial market models, stochastic mortality and optimal/sub-optimal policyholder behavior, and in the presence of taxes. For numerical valuation of these contracts in the case of simple risky asset process, we develop a direct integration method based on the Gauss-Hermite quadratures 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 easier to implement and faster 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 present accurate numerical results for pricing of a Guaranteed Minimum Accumulation Benefit (GMAB) guarantee available on the market that can serve as a numerical benchmark for practitioners and researchers developing pricing of variable annuity guarantees to assess the accuracy of their numerical implementation. Full article

(This article belongs to the Special Issue Life Insurance and Pensions)

► Show Figures

Graphical abstract

396 KiB

Open AccessArticle

Spouses’ Dependence across Generations and Pricing Impact on Reversionary Annuities

by Elisa Luciano, Jaap Spreeuw and Elena Vigna

Risks 2016, 4(2), 16; https://doi.org/10.3390/risks4020016 - 25 May 2016

Cited by 14 | Viewed by 3948

Abstract

This paper studies the dependence between coupled lives, i.e., the spouses’ dependence, across different generations, and its effects on prices of reversionary annuities in the presence of longevity risk. Longevity risk is represented via a stochastic mortality intensity. We find that a [...] Read more.

This paper studies the dependence between coupled lives, i.e., the spouses’ dependence, across different generations, and its effects on prices of reversionary annuities in the presence of longevity risk. Longevity risk is represented via a stochastic mortality intensity. We find that a generation-based model is important, since spouses’ dependence decreases when passing from older generations to younger generations. The independence assumption produces quantifiable mispricing of reversionary annuities, with different effects on different generations. The research is conducted using a well-known dataset of double life contracts. Full article

(This article belongs to the Special Issue Life Insurance and Pensions)

► Show Figures

Figure 1

2650 KiB

Open AccessFeature PaperArticle

Participating Life Insurance Products with Alternative Guarantees: Reconciling Policyholders’ and Insurers’ Interests

by Andreas Reuß, Jochen Ruß and Jochen Wieland

Risks 2016, 4(2), 11; https://doi.org/10.3390/risks4020011 - 05 May 2016

Cited by 11 | Viewed by 7212

Abstract

Traditional participating life insurance contracts with year-to-year (cliquet-style) guarantees have come under pressure in the current situation of low interest rates and volatile capital markets, in particular when priced in a market-consistent valuation framework. In addition, such guarantees lead to rather high capital [...] Read more.

Traditional participating life insurance contracts with year-to-year (cliquet-style) guarantees have come under pressure in the current situation of low interest rates and volatile capital markets, in particular when priced in a market-consistent valuation framework. In addition, such guarantees lead to rather high capital requirements under risk-based solvency frameworks such as Solvency II or the Swiss Solvency Test (SST). Therefore, insurers in several countries have developed new forms of participating products with alternative (typically weaker and/or lower) guarantees that are less risky for the insurer. In a previous paper, it has been shown that such alternative product designs can lead to higher capital efficiency, i.e., higher and more stable profits and reduced capital requirements. As a result, the financial risk for the insurer is significantly reduced while the main guarantee features perceived and requested by the policyholder are preserved. Based on these findings, this paper now combines the insurer’s and the policyholder’s perspective by analyzing product versions that compensate policyholders for the less valuable guarantees. We particularly identify combinations of asset allocation and profit participation rate for the different product designs that lead to an identical expected profit for the insurer (and identical risk-neutral value for the policyholder), but differ with respect to the insurer’s risk and solvency capital requirements as well as with respect to the real-world return distribution for the policyholder. We show that alternative products can be designed in a way that the insurer’s expected profitability remains unchanged, the insurer’s risk and hence capital requirement is substantially reduced and the policyholder’s expected return is increased. This illustrates that such products might be able to reconcile insurers’ and policyholders’ interests and serve as an alternative to the rather risky cliquet-style products. Full article

(This article belongs to the Special Issue Life Insurance and Pensions)

► Show Figures

Graphical abstract

344 KiB

Open AccessArticle

Premiums for Long-Term Care Insurance Packages: Sensitivity with Respect to Biometric Assumptions

by Ermanno Pitacco

Risks 2016, 4(1), 3; https://doi.org/10.3390/risks4010003 - 22 Feb 2016

Cited by 11 | Viewed by 6715

Abstract

Long-term care insurance (LTCI) covers are rather recent products, in the framework of health insurance. It follows that specific biometric data are scanty; pricing and reserving problems then arise because of difficulties in the choice of appropriate technical bases. Different benefit structures imply [...] Read more.

Long-term care insurance (LTCI) covers are rather recent products, in the framework of health insurance. It follows that specific biometric data are scanty; pricing and reserving problems then arise because of difficulties in the choice of appropriate technical bases. Different benefit structures imply different sensitivity degrees with respect to changes in biometric assumptions. Hence, an accurate sensitivity analysis can help in designing LTCI products and, in particular, in comparing stand-alone products to combined products, i.e., packages including LTCI benefits and other lifetime-related benefits. Numerical examples show, in particular, that the stand-alone cover is much riskier than all of the LTCI combined products that we have considered. As a consequence, the LTCI stand-alone cover is a highly “absorbing” product as regards capital requirements for solvency purposes. Full article

(This article belongs to the Special Issue Life Insurance and Pensions)

► Show Figures

Figure 1

620 KiB

Open AccessArticle

The Impact of Guarantees on the Performance of Pension Saving Schemes: Insights from the Literature

by Alexander Bohnert

Risks 2015, 3(4), 515-542; https://doi.org/10.3390/risks3040515 - 20 Nov 2015

Cited by 1 | Viewed by 4732

Abstract

Guarantees are often seen as the key characteristics of pension saving products, but securing them can become costly and is of central relevance especially in the course of the current low interest rate environment. In this article, we deal with the question of [...] Read more.

Guarantees are often seen as the key characteristics of pension saving products, but securing them can become costly and is of central relevance especially in the course of the current low interest rate environment. In this article, we deal with the question of how costly the typical types of guarantees are, in the sense that they reduce a pension saving scheme’s financial performance over time. In this context, we aim to provide a presentation of insights from selected literature studying the impact of point-to-point guarantees and cliquet-style interest rate guarantees on the performance of pension contracts. The comparative analysis emphasizes that, in most cases, guarantee costs are not negligible with regard to a contract’s financial performance, especially compared to benchmarks, and that customers knowingly opt for such guarantees (or not) is, thus, indispensable. To further investigate the willingness-to-pay for guarantees in life insurance is an area for future research, in particular for innovative contract design. Full article

(This article belongs to the Special Issue Life Insurance and Pensions)

310 KiB

Open AccessArticle

Life Insurance Cash Flows with Policyholder Behavior

by Kristian Buchardt and Thomas Møller

Risks 2015, 3(3), 290-317; https://doi.org/10.3390/risks3030290 - 24 Jul 2015

Cited by 18 | Viewed by 7175

Abstract

The problem of the valuation of life insurance payments with policyholder behavior is studied. First, a simple survival model is considered, and it is shown how cash flows without policyholder behavior can be modified to include surrender and free policy behavior by calculation [...] Read more.

The problem of the valuation of life insurance payments with policyholder behavior is studied. First, a simple survival model is considered, and it is shown how cash flows without policyholder behavior can be modified to include surrender and free policy behavior by calculation of simple integrals. In the second part, a more general disability model with recovery is studied. Here, cash flows are determined by solving a modified Kolmogorov forward differential equation. We conclude the paper with numerical examples illustrating the methods proposed and the impact of policyholder behavior. Full article

(This article belongs to the Special Issue Life Insurance and Pensions)

► Show Figures

Graphical abstract

613 KiB

Open AccessArticle

A Two-Account Life Insurance Model for Scenario-Based Valuation Including Event Risk

by Ninna Reitzel Jensen and Kristian Juul Schomacker

Risks 2015, 3(2), 183-218; https://doi.org/10.3390/risks3020183 - 04 Jun 2015

Cited by 6 | Viewed by 5930

Abstract

Using a two-account model with event risk, we model life insurance contracts taking into account both guaranteed and non-guaranteed payments in participating life insurance as well as in unit-linked insurance. Here, event risk is used as a generic term for life insurance events, [...] Read more.

Using a two-account model with event risk, we model life insurance contracts taking into account both guaranteed and non-guaranteed payments in participating life insurance as well as in unit-linked insurance. Here, event risk is used as a generic term for life insurance events, such as death, disability, etc. In our treatment of participating life insurance, we have special focus on the bonus schemes “consolidation” and “additional benefits”, and one goal is to formalize how these work and interact. Another goal is to describe similarities and differences between participating life insurance and unit-linked insurance. By use of a two-account model, we are able to illustrate general concepts without making the model too abstract. To allow for complicated financial markets without dramatically increasing the mathematical complexity, we focus on economic scenarios. We illustrate the use of our model by conducting scenario analysis based on Monte Carlo simulation, but the model applies to scenarios in general and to worst-case and best-estimate scenarios in particular. In addition to easy computations, our model offers a common framework for the valuation of life insurance payments across product types. This enables comparison of participating life insurance products and unit-linked insurance products, thus building a bridge between the two different ways of formalizing life insurance products. Finally, our model distinguishes itself from the existing literature by taking into account the Markov model for the state of the policyholder and, hereby, facilitating event risk. Full article

(This article belongs to the Special Issue Life Insurance and Pensions)

► Show Figures

Figure 1

330 KiB

Open AccessArticle

Portability, Salary and Asset Price Risk: A Continuous-Time Expected Utility Comparison of DB and DC Pension Plans

by An Chen and Filip Uzelac

Risks 2015, 3(1), 77-102; https://doi.org/10.3390/risks3010077 - 13 Mar 2015

Cited by 3 | Viewed by 5201

Abstract

This paper compares two different types of private retirement plans from the perspective of a representative beneficiary: a defined benefit (DB) and a defined contribution (DC) plan. While salary risk is the main common risk factor in DB and DC pension plans, one [...] Read more.

This paper compares two different types of private retirement plans from the perspective of a representative beneficiary: a defined benefit (DB) and a defined contribution (DC) plan. While salary risk is the main common risk factor in DB and DC pension plans, one of the key differences is that DB plans carry portability risks, whereas DC plans bear asset price risk. We model these tradeoffs explicitly in this paper and compare these two plans in a utility-based framework. Our numerical analysis focuses on answering the question of when the beneficiary is indifferent between the DB and DC plan. Most of our results confirm the findings in the existing literature, among which, e.g., portability losses considerably reduce the relative attractiveness of the DB plan. However, we also find that the attractiveness of the DB plan can decrease in the level of risk aversion, which is inconsistent with the existing literature. Full article

(This article belongs to the Special Issue Life Insurance and Pensions)

► Show Figures

Figure 1

1325 KiB

Open AccessArticle

Safety Margins for Systematic Biometric and Financial Risk in a Semi-Markov Life Insurance Framework

by Andreas Niemeyer

Risks 2015, 3(1), 35-60; https://doi.org/10.3390/risks3010035 - 19 Jan 2015

Cited by 2 | Viewed by 4860

Abstract

Insurance companies use conservative first order valuation bases to calculate insurance premiums and reserves. These valuation bases have a significant impact on the insurer’s solvency and on the premiums of the insurance products. Safety margins for systematic biometric and financial risk are in [...] Read more.

Insurance companies use conservative first order valuation bases to calculate insurance premiums and reserves. These valuation bases have a significant impact on the insurer’s solvency and on the premiums of the insurance products. Safety margins for systematic biometric and financial risk are in practice typically chosen as time-constant percentages on top of the best estimate transition intensities. We develop a risk-oriented method for the allocation of a total safety margin to the single safety margins at each point in time and each state. In a case study, we demonstrate the suitability of the proposed method in different frameworks. The results show that the traditional method yields an unwanted variability of the safety level with respect to time, whereas the variability can be significantly reduced by the new method. Furthermore, the case study supports the German 60 percent rule for the technical interest rate. Full article

(This article belongs to the Special Issue Life Insurance and Pensions)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Life Insurance and Pensions

Share This Special Issue

Special Issue Editor

Special Issue Information

Keywords

Published Papers (9 papers)

Research

Further Information

Guidelines

MDPI Initiatives

Follow MDPI