Long-term Guarantees Research Articles

MODERN LIFE-CARE TONTINES

AbstractThe tendency of insurance providers to refrain from offering long-term guarantees on investment or mortality risk has shifted attention to mutual risk pooling schemes like (modern) tontines, pooled annuities or group self annuitization schemes. While the literature has focused on mortality risk pooling schemes, this paper builds on the advantage of pooling mortality and morbidity risks, and their inherent natural hedge. We introduce a modern “life-care tontine”, which in addition to retirement income targets the needs of long-term care (LTC) coverage for an ageing population. In contrast to a classical life-care annuity, both mortality and LTC risks are shared within the policyholder pool by mortality and morbidity credits, respectively. Technically, we rely on a backward iteration to deduce the smoothed cashflows pattern and the separation of cash-flows in a fixed withdrawal and a surplus from the two types of risks. We illustrate our results using real life data, demonstrating the adequacy of the proposed tontine scheme.

Special Issue “Quantitative Risk Assessment in Life, Health and Pension Insurance”

The high volatility in financial markets, together with the ultra-low interest rates environment and the increased expectation of life, constitute serious threats for providers of long-term investment guarantees and lifelong benefits [...]

A MEAN-FIELD EXTENSION OF THE LIBOR MARKET MODEL

In this paper, we introduce a mean-field extension of the LIBOR market model (LMM) which preserves the basic features of the original model. Among others, these features are the martingale property, a directly implementable calibration and an economically reasonable parametrization of the classical LMM. At the same time, the mean-field LIBOR market model (MF-LMM) is designed to reduce the probability of exploding scenarios, arising in particular in the market-consistent valuation of long-term guarantees. To this end, we prove existence and uniqueness of the corresponding MF-LMM and investigate its practical aspects, including Black’s formula. Moreover, we present an extensive numerical analysis of the MF-LMM. The corresponding Monte Carlo method is based on a suitable interacting particle system which approximates the underlying mean-field equation.

Terms of Reference of The Iraqi Commercial Court

In light of the Iraqi Supreme Judicial Council No. (74) for the year 2000 and its influence on the economic and commercial side, this study attempts to illustrate the viability of founding the Iraqi Commercial Court. It is the whole seed. The goal is to make commercial conflicts more swiftly and efficiently resolved through establishing an expert commercial judiciary. Specialized judges with high expertise and knowledge help ensure that court judgments are successful in both processes and causes. In light of the statement published by the Supreme Judicial Council No. (74) for the year 2020, the research focuses on the efficacy of the Iraqi commercial Court in addressing commercial disputes. This article reveals that the Iraqi legislative attempts to attract international investment and the Iraqi executive branch's continued efforts to resolve investor concerns by modifying the Investment Law. The Iraqi court has successfully developed a stable legal environment for multinational firms. Commercial courts, acknowledged as fair by international businesses, were established to accomplish this. As a result of Iraq's communist past, foreign investment was viewed as a source of skepticism and mistrust for many years. These courts will undoubtedly play a significant role in advancing Iraq's progress. However, courts alone will not provide the long-term guarantees needed to transform Iraq's legal framework for domestic and foreign businesses to operate inside. Civil law countries like Iraq necessitate significant reforms to the country's intellectual property, investment, and arbitration regimes.

Variable annuities: Market incompleteness and policyholder behavior

Variable annuities (VAs) are popular personal savings and investment vehicles with long-term guarantees. They include various exercise-dependent features, and the pricing, valuation and hedging of the guarantees depend critically on the investors’ decision making. I study whether the optimal exercise behavior of a VA investor is affected by market incompleteness, which arises since the VA generates payout profiles that intersect financial risk and idiosyncratic mortality risk and can thus not be (fully) replicated with traditional financial and insurance products.Implementing a generic VA policy with a withdrawal guarantee (GMWB) that reflects typical US product characteristics, I find that the optimal withdrawal behavior derived from a lifecycle utility model is closely approximated by the corresponding (after-tax) value maximization strategy. That is, from the perspective of the investor, the market around VA policies is sufficiently complete to justify the common approach of assessing optimal VA policyholder behavior with a risk-neutral valuation method.

Variable Annuities: Market Incompleteness and Policyholder Behavior

Variable annuities (VAs) are popular personal savings and investment vehicles with long-term guarantees. They include various exercise-dependent features, and the pricing, valuation and hedging of the guarantees depend critically on the investors' decision making. I study whether the optimal exercise behavior of a VA investor is affected by market incompleteness, which arises since the VA generates payout profiles that intersect financial risk and idiosyncratic mortality risk and can thus not be (fully) replicated with traditional financial and insurance products. Implementing a generic VA policy with a withdrawal guarantee (GMWB) that reflects typical US product characteristics, I find that the optimal withdrawal behavior derived from a lifecycle utility model is closely approximated by the corresponding (after-tax) value maximization strategy. That is, from the perspective of the investor, the market around VA policies is sufficiently complete to justify the common approach of assessing optimal VA policyholder behavior with a risk-neutral valuation method.

Fair and near-optimal coflow scheduling without prior knowledge of coflow size

Achieving the minimum average coflow completion time(CCT) and the isolation guarantees for multi-tenant, is considered a challenge in a cloud environment. This is because the minimum average CCT and isolation guarantees are two conflicting targets, and they cannot be achieved simultaneously. Prior solutions have implemented a single target either minimizing the average CCT or isolation guarantees. The prior solutions are also limited to clairvoyant scheduling. They also assume the availability of the complete knowledge of coflow sizes before the communication starts. In this paper, we propose an efficient scheduling algorithm smallest-height-first DRF(SHFDRF) for near-optimal scheduling and isolation guarantees without prior knowledge of coflow size. SHFDRF achieves the long-term isolation guarantees and the minimum average CCT by the smallest height first and the monopolistic dominant resource fairness bandwidth allocation strategy. The smallest height first and the monopolistic dominant resource fairness bandwidth allocation strategy can also improve link utilization and system throughput. The trace-driven simulation shows that SHFDRF enables communication stages to 1.28 $$\times $$ , 2.27 $$\times $$ , and 6.28 $$\times $$ faster on the 95th percentile compared to DRF, NCDRF, and Per-Flow Fairness. Even compared with minimum CCT, the completion time of coflow only slowed down by 13.9% on the 95th percentile. Overall, the performance of SHFDRF is acceptable, and it can be applied to the actual datacenter without the limitation of complete prior knowledge.

Inter-Cohort Risk Sharing with Long-Term Guarantees: Evidence from German Participating Contracts

Long-term minimum return guarantees sold by European life insurers increasingly become binding as interest rates decline. While participating contracts embedding these guarantees are designed to share market risk across investor cohorts when guarantees are not binding, we study how binding guarantees distort inter-cohort risk sharing. Using regulatory data on participating contracts in Germany, we find that binding guarantees reduced inter-cohort transfer by 10 basis points per year in the period 2000{2018. This is modest compared to the average transfer, which is in the range of 40{150 basis points. However, the effect is concentrated in the recent period of ultra-low interest rates and may grow larger if interest rates remain persistently low.

Life-Care Tontines

The tendency of insurance providers to refrain from offering long-term guarantees on investment or mortality risk has shifted attention to mutual risk pooling schemes like (modern) tontines, pooled annuities or group self annuitization schemes. While the literature has focused on mortality risk pooling schemes, this paper builds on the advantage of pooling mortality and morbidity risks, and their inherent natural hedge. We introduce a modern tontine, which in addition to retirement income targets the needs of long-term care coverage for an ageing population. In contrast to a classical life-care annuity, both mortality and long-term care risks are shared within the pool by mortality and morbidity credits, respectively. Technically, we rely on a backward iteration to deduce the smoothed cashflows pattern and the separation of cash-flows in a fixed withdrawal and a surplus from the two types of risks. We illustrate our results using real life data, demonstrating the adequacy of the proposed tontine scheme.

A Mixed Bond and Equity Fund Model for the Valuation of Segregated Fund Policies

Variable annuity policies are typically issued on mutual funds invested in both fixed income and equity asset classes. However, due to the lack of specialized models to represent the dynamics of fixed income fund returns, the literature has primarily focused on studying long-term investment guarantees on single-asset equity funds. This article develops a mixed bond and equity fund model in which the fund return is linked to movements of the yield curve. Theoretical motivation for our proposed specification is provided through an analogy with a portfolio of rolling horizon bonds. Moreover, basis risk between the portfolio return and its risk drivers is naturally incorporated into our framework. Numerical results show that the fit of our model to Canadian variable annuity data is adequate. Finally, the valuation of variable annuities is illustrated and it is found that the prevailing interest rate environment can have a substantial impact on guarantee costs.

Долгосрочные мотивации на государственной гражданской службе

The research is aimed at solving the problems of applying long-term motivation to work in the civil service and municipal service. In the civil service, the problem of reducing motivation, which affects the stability of the staff and its professional level, remains. Scientists are given a mixed assessment of the long-term motivations of the delayed nature of incentives as effective methods of stabilization of the personnel. Therefore, the purpose of the work is to answer the question: what is the value of long-term motivation to work when motivating officials to enter the civil service and serve. The methodological basis of the study includes the theory of expectation of V. Vroom, the concept of level motivation of V. Teplov, as well as the works of leading Russian and foreign scientists on the problems of motivation of officials. The study used methods of system analysis, General scientific methods. To achieve this goal, the theory and practice of long-term motivation for work are analyzed, the relationship between long-term motivation and state guarantees of civil servants is established, the attitude of officials to state guarantees is studied, and a study of motivation of civil servants on the basis of two Executive bodies of the Kurgan region in 2018, which was attended by 98 civil servants. The results of the study showed that the majority of officials, among the respondents, long-term motivation in the form of state guarantees of the civil service are perceived as leading motivation for entering the public service and service, and, of particular importance are state guarantees of a social nature. The results confirmed the hypothesis of the importance of long-term motivation to work in the public service, the consolidation of officials in the service and motivation of their activities. The results of the study can be used to improve the Institute of personnel management in the public civil and municipal service. As a prospect for the study of long-term motivations, it seems appropriate to assess the effectiveness of their application in the public civil service of the Russian Federation.

An Optimality Approach to the Application Ratio for the Matching Adjustment in the Solvency II Regime

We refer to the Technical Specifications provided by EIOPA to implement the package of long-term guarantees measures which shall be included into the Solvency II Framework Directive. One of these regulatory measures concerns the Application Ratio, a coefficient defining what portion of the Maximum Matching Adjustment an insurance company can apply to the risk-free rates for discounting her obligations, given the matching properties of the assigned asset portfolio. In this paper we propose an optimization algorithm providing a reliable assessment of the Application Ratio. The Application Ratio provided by the algorithm is optimal in the sense that it has the maximum value given the structure of the asset-liability portfolio. This value corresponds to the minimum attainable level for the losses incurred from forced sales of defaultable bonds with mispriced market value. We show that under natural assumptions this optimality problem has the form of a linear programming problem, which can be easily solved using standard numerical procedures. A matching criterion defined in stronger form can also be applied by imposing appropriate run-off constraints in the linear programming problem. The value of the optimal Application Ratio can be used by a Supervisor as an objective benchmark for checking the appropriateness of the Application Ratio adopted by the undertaking. The optimal liquidation policy provided by the algorithm can also be used by an insurance undertaking which want to apply conservative management actions to her asset-liability portfolio.

A review of Solvency II: Has it met its objectives?

AbstractSolvency II is currently one of the most sophisticated insurance regulatory regimes in the world. It is built around the principles of market consistency and embedding strong risk management and governance within insurance companies. For business with long-term guarantees, the original basis produced outcomes that were unacceptable to the member states. The original design was amended through Omnibus II. The working party has looked back at the outcome of the final regulation and comments on how well Solvency II has fared, principally from a UK perspective, relative to its initial goals of improved consumer protection, harmonisation, effective risk management and financial stability. We review Pillar 1’s market consistent valuation (including the risk margin and transitional measures) as well as the capital requirements (including internal models). We look at the impact this has on asset and liability management, pro-cyclicality and product design. We look at Pillars 2 and 3 in respect of the Own Risk and Solvency Assessment, liquidity and disclosure. Finally, we stand back and look at harmonisation and the implications of Brexit. In summary we conclude that Solvency II represents a huge improvement over Solvency I although it has not fully achieved the goals it aspired to. There are acknowledged shortfalls and imperfections where adjustments to Solvency II are likely. There remain other concerns around pro-cyclicality, and the appropriateness of market consistency is still open to criticism. It is hoped that the paper and the discussion that goes with it provide an insight into where Solvency II has taken European Insurance regulation and the directions in which it could evolve.

Risk measures versus ruin theory for the calculation of solvency capital for long-term life insurances

Abstract The purpose of this paper is twofold. First we consider a ruin theory approach along with risk measures in order to determine the solvency capital of long-term guarantees such as life insurances or pension products. Secondly, for such products,we challenge the definition of the Solvency Capital Requirement (SCR) under the Solvency II (SII) regulatory framework based on a yearly viewpoint. Several methods for the calculation of the solvency capital are presented. We start our study with risk measures as considered in the SII framework and then proceed with the ruin theory approach. Instead of considering the continuous time setting of the ruin theory,we consider the discrete time—the yearly basis—of the accounting viewpoint.We finally give an illustration with a fixed guaranteed rate product along with the equity, interest rate and longevity risks. The latter risk brings us to consider zero-coupon longevity bonds in which we invest the capital. We show that long-term guarantees might be overloaded under the SII regulation.

Valuation and risk assessment of participating life insurance in the presence of credit risk

In participating life insurance, management decisions regarding the asset composition can substantially impact the value of a policy from the policyholders’ perspective as well as the insurer’s risk situation. Due to the long-term guarantees often embedded in these contracts, life insurers typically invest a considerable portion of their capital in long-term assets such as corporate and government bonds. Besides interest rate risk, the value of these bond investments is thus particularly influenced by credit risk. Thus, the aim of this paper is to examine the impact of market risk associated with the asset composition on fair valuation and risk assessment with focus on credit risk and its interaction with equity risk and interest rate risk. Our analysis emphasizes that the consideration of credit risk associated with bonds has a strong impact on the fair valuation and risk measurement in the context of participating life insurance contracts, even in case of higher grade bond exposures.

Facing the interest rate challenge: A key risk management issue for insurers

Interest rate risk is a key risk management challenge for life insurers. Life savings business is most exposed to interest rate changes, especially when the policies contain fixed, long-term guarantees. Managing interest rate risk via duration matching of assets and liabilities is complicated by various factors, including the lack of securities with very long duration and policy holder behaviour, which is hard to predict. Product features are a key determinant of interest rate sensitivity. As such, product design is the first step in interest rate risk management. Rather than hoping for interest rates to reverse their downtrend, which will not provide any immediate relief, insurers should aim to reduce the interest rate risk arising from the savings policies offered by adjusting the embedded guarantees and options.

Practical valuation of long-term guarantees in inactive financial markets

In this paper we address certain issues in the valuation of long-term (insurance) guarantees from a practical point of view. These issues arise, because markets are incomplete or inactive. We provide a general, arbitrage-free valuation approach in this context and discuss the following topics in more detail: extrapolation of interest rates, treatment of interest rate spreads and counter-cyclical measures in distorted markets. By deriving solutions from a practitioner’s point of view this paper aims to contribute to an effective regulation under Solvency II. Moreover, we hope to provide a starting point for an in-depth academic analysis of these problems.

Valuation and Risk Assessment of Participating Life Insurance in the Presence of Credit Risk

In participating life insurance, management decisions regarding the asset composition can substantially impact the value of a policy from the policyholders’ perspective as well as the insurer’s risk situation. Due to the long-term guarantees often embedded in these contracts, life insurers typically invest a considerable portion of their capital in long-term assets such as corporate and government bonds. Besides interest rate risk, the value of these bond investments is thus particularly influenced by credit (spread) risk. Thus, the aim of this paper is to examine the impact of market risk associated with the asset composition on fair valuation and risk assessment with focus on credit risk and its interaction with equity risk and interest rate risk. Our analysis emphasizes the strong tradeoff between higher coupon payments of lower grade bond portfolios and the increased credit risk as well as the interaction between credit risk, interest rate risk, and equity risk arising from the stock investments.

Omnibus II Effective Measures in Adjusting the Current Solvency II Framework

The article describes some difficulties arising in connection with implementation of Solvency II at the Member State level. The main objective of this paper is to present the problem solving of Solvency II Directive of insurance and reinsurance on long-term guarantee package with the help of the new Omnibus II Directive. For this purpose in the article were investigated the results of last impact assessment with long-term guarantees package to the current Solvency II framework to cope with artificial volatility and low interest rate environment, and to ensure both transparency and level-playing field. After the impact assessment EIOPA analyzed each measure against the objectives and recommended the inclusion of the following measures: extrapolation, classical matching adjustment, transitional measures, and extension of the recovery period, not to include the so-called extended matching adjustment on the basis that it would not provide sufficient policyholder protection.

Collective pension schemes and individual choice

AbstractCollective pension schemes are the dominant form of saving for retirement in the Netherlands. We investigate the introduction of individual choices into a collective pension system without affecting the generally accepted advantages of a collective agreement. Increasing individual choices can be beneficial, as it prevents pension plans from making decisions for the average plan participant that may not be optimal for individual participants. We argue for a system in which individuals choose from a set of low-cost balanced index funds, together with a level of intergenerational guarantees that are exchange-traded. This system maintains the two primary advantages of collective agreements: risk sharing and low implementation costs, while facilitating different risk taking behavior at the individual level. To facilitate individual choices within collective pension schemes, it is important to enhance the transparency associated with intergenerational guarantees to all participants in the scheme, both in terms of their price and quantity. We argue that the current system, in which long-term guarantees are given by the young to the old within a specific fund but not across pension funds, is not transparent and we argue that it can be suboptimal. We propose a system ofPension Guarantee Exchanges(PGEs) that increase transparency and allow pension funds with different age distributions to trade with each other. Knowing the price of such guarantees facilitates the introduction of individual portfolio choices within collective pension schemes.