Pricing Annuity Guarantees Under a Regime-Switching Model

Abstract

We consider the pricing problem of equity-linked annuities and variable annuities under a regimeswitching model when the dynamic of the market value of a reference asset is driven by a generalized geometric Brownian motion model with regime switching. In particular, we assume that regime switching over time according to a continuous-time Markov chain with a finite number state space representing economy states. We use the Esscher transform to determine an equivalent martingale measure for fair valuation in the incomplete market setting. The paper is complemented with some numerical examples to highlight the implications of our model on pricing these guarantees.     

变额年金业务的风险度量与分析

变额年金产品具有给付投保人最低保证收益率的特点,使资本市场下滑风险从投保人转移到保险公司,但是风险的大小尚不明确。本文建立资产随机模型并使用破产概率和尾部期望损失两个指标度量保险公司销售最低生存利益保证保险(GMLB)和最低身故利益保证保险(GMDB)承担的风险。结果表明最低保证收益率对GMLB的风险有显著影响,而对GMDB没有,在最低保证收益率既定的条件下保险公司投资于股票的份额对风险有显著影响。     

The Impact of Risk-Based Premiums on FDIC-Insured Institutions

This paper examines the effect of a series of announcements leading to the approval of risk-based deposit insurance premiums on returns to stockholders of commercial banks. Utilizing risk-weighted capital ratios and measures of overall risk, we group banks according to one of the nine-tier insurance categories subsequently defined by the FDIC. During the period in which the new insurance system was considered and approved, we found that stockholders of well-capitalized, healthy banks experienced wealth changes significantly different from those experienced by less than well-capitalized, less than healthy banks. Although many argued the premium range in the initial insurance schedule was insufficient, the results show that this initial risk-basing marked an important change in the relative burdens imposed by FDIC insurance.     

变额年金动态对冲策略的研究与实施

自2010年中国保监会允许国内试点变额年金市场之后,国内还没有相关文章对内部组合对冲模式下变额年金产品在精算领域面临的问题做出系统的阐述,本文在这方面给出了一套方法并结合实际进行了验证。通过经济情景发生器产生合理的经济情景,并基于假设的保单数据分析变额年金保证利益的合理定价区间;然后深入地讨论了动态对冲过程中各环节的设计并对结果进行分析,结果表明动态对冲可以显著降低各期损益以及累积损益的波动性;最后对变额年金的准备金和资本计算进行了国际比较,并给出了反映对冲与不反映对冲情况下的结果比较。     

The Dynamic Impact of Macro Shocks on Insurance Premiums

We develop a model that investigates the relation between insurance premiums and macroeconomic variables, including oil price, interest rate, aggregate supply, and aggregate demand. We then use a multivariate structural vector error correction model to distinguish the effects arising from permanent and transitory components of insurance premiums. Changes in the transitory component indicate that our model captures key historical events. Although real shocks originating from oil price and aggregate supply explain the behavior of insurance premiums well, we show that financial market shocks are the main driving force behind the recent increasing volatility in insurance premiums in the U.S. market.

Regression Modeling for the Valuation of Large Variable Annuity Portfolios

Variable annuities are insurance products that contain complex guarantees. To manage the financial risks associated with these guarantees, insurance companies rely heavily on Monte Carlo simulation. However, using Monte Carlo simulation to calculate the fair market values of these guarantees for a large portfolio of variable annuities is extremely time consuming. In this article, we propose the class of GB2 distributions to model the fair market values of guarantees to capture the positive skewness typically observed empirically. Numerical results are used to demonstrate and evaluate the performance of the proposed model in terms of accuracy and speed.     

变额年金在我国的应用及风险管理探讨

采用对比法和归纳法,从变额年金的风险因素入手,通过对比国外比较成熟的风险管理评估模式和风险管理需要的外部条件等因素的探讨,为变额年金在风险管理模式、最低保证利益设计等方面提出一定的建议。     

马尔科夫体制转换模型下变额年金的风险管理

本文在马尔科夫体制转换模型下探究了变额年金的风险管理问题.保险产品的长期性使其易受到经济周期的影响,马尔科夫体制转换模型因在描述经济周期变化的卓越表现而受到学界和业界的广泛关注.分析显示,在我国马尔科夫体制转换模型相对于Black-Scholes模型在捕获资产变化特征上具有优势.本文利用体制转换模型建模投资账户价值,推...     

Robustly Hedging Variable Annuities With Guarantees Under Jump and Volatility Risks

Recent variable annuities offer participation in the equity market and attractive protection against downside movements. Accurately quantifying this additional equity market risk and robustly hedging options embedded in the guarantees of variable annuities are new challenges for insurance companies. Due to sensitivities of the benefits to tails of the account value distribution, a simple Black–Scholes model is inadequate in preventing excessive liabilities. A model which realistically describes the real world price dynamics over a long time horizon is essential for the risk management of the variable annuities. In this article, both jump risk and volatility risk are considered for risk management of lookback options embedded in guarantees with a ratchet feature. We evaluate relative performances of delta hedging and dynamic discrete risk minimization hedging strategies. Using the underlying as the hedging instrument, we show that, under a Black–Scholes model, local risk minimization hedging can be significantly better than delta hedging. In addition, we compare risk minimization hedging using the underlying with that of using standard options. We demonstrate that, under a Merton's jump diffusion model, hedging using standard options is superior to hedging using the underlying in terms of the risk reduction. Finally, we consider a market model for volatility risks in which the at‐the‐money implied volatility is a state variable. We compute risk minimization hedging by modeling at‐the‐money Black–Scholes implied volatility explicitly; the hedging effectiveness is evaluated, however, under a joint model for the underlying price and implied volatility. Our computational results suggest that, when implied volatility risk is suitably modeled, risk minimization hedging using standard options, compared to hedging using the underlying, can potentially be more effective in risk reduction under both jump and volatility risks.     

Efficient Greek Calculation of Variable Annuity Portfolios for Dynamic Hedging: A Two-Level Metamodeling Approach

The financial risk associated with the guarantees embedded in variable annuities cannot be addressed adequately by traditional actuarial techniques. Dynamical hedging is used in practice to mitigate the financial risk arising from variable annuities. However, a major challenge of dynamical hedging is to calculate the dollar Deltas of a portfolio of variable annuities within a short time interval so that rebalancing can be done on a timely basis. In this article, we propose a two-level metamodeling approach to efficiently estimating the partial dollar Deltas of a portfolio of variable annuities under a multiasset framework. The first-level metamodel is used to estimate the partial dollar Deltas at some well-chosen market levels, and the second-level metamodel is used to estimate the partial dollar Deltas at the current market level based on the precalculated partial dollar Deltas. Our numerical results show that the proposed approach performs well in terms of accuracy and speed.     

税务机关征收养老保险费对征缴率的影响研究

基于养老保险2002—2018年省级面板数据,运用系统GMM估计方法研究社保费征收模式对征缴率的影响。研究发现：社保全征的征缴率高于税务全征,但低于税务代征,后者无统计意义。进一步的机制和异质性检验结果表明：税务全征可能增加企业研发投入或减少雇佣人数,对实际征缴收入产生负面影响;对于系统老龄化程度低于30%,或征缴率高于60%,或参保率高于69.107%的样本,税务全征使征缴率下降10.8～16.2个百分点。可见,税务代征模式更有助于社保体系的可持续发展。     

把握企业年金监管的关键点

中国的企业年金监管工作仍应立足于建立企业年金制度的基本目标和中国的现实国情。     

The Independent Impact of Credit Rating Changes – The Case of Moody's Rating Refinement on Yield Premiums

On April 26, 1982, Moody's Investors Service refined its rating system for the first time in its seventy-three year rating history. We examine the information content of the rating refinement in the study. We find a statistically significant change in the yields on bonds whose ratings were downgraded. The detection of the impact of refinement on bond prices implies that rating agencies perform an important function in financial markets, that is they provide information to investors.     

Impact of a Flexible Evaluation System on Effort and Timing of Study

This paper examines results of a flexible grading system that allows each student to influence the weight allocated to each performance measure. We construct a stylized model to determine students' optimal responses. Our analytical model predicts different optimal strategies for students with varying academic abilities: a frontloading strategy for those with high academic ability and a gambling strategy for others. We test the model using data gathered from several sections of an Intermediate Accounting course offered by a Canadian university. We find that most students did make decisions that were consistent with our analytical model. Our results suggest that the flexible evaluation system does not uniformly motivate students of differing abilities and does not encourage most students to maintain effort uniformly throughout the semester.     

迟滞企业年金发展的三方主体分析

企业年金的发展需要政府、企业、个人三方主体的努力。本文在已有集中在政府层面研究的基础上,结合国际,更多的从企业、个人两个相关层面来研究。通过实证分析发现,相对于企业年金发达的欧美国家,中国企业建立企业年金将消耗较大比例的企业利润,企业缺乏发展动力是企业年迟滞金发展的表层障碍,当前我国劳动力密集型的产业结构以及缺少一个庞大的中产阶层的社会结构则是企业年金发展迟滞的根本原因。     

Fair Value Measurements of Control Premiums

As the overview of the current state of research within this paper shows, the debate around fair value measurements is far from over. This paper analyzes fair value measurement requirements in a controversial scenario, namely when a control premium exists. The analyses of the paper show that, while measurement rules around control premiums could have a material impact on fair value measurements and the financial statements as a whole, significant fair value measurement issues remain unresolved. The conclusion is that fair value measurements should include or exclude control premiums consistently. It is argued that including control premiums for all fair value measurements is the most faithful representation of the underlying economic phenomenon. This paper contributes to the fair value measurement debate by comparing the merits of alternative fair value measurements for control premiums and highlights an area where researchers, investors, and other users should exercise caution when evaluating financial statements.     

The Impact of Surplus Distribution on the Risk Exposure of With Profit Life Insurance Policies Including Interest Rate Guarantees

This article analyzes the numerical impact of different surplus distribution mechanisms on the risk exposure of a life insurance company selling with profit life insurance policies with a cliquet‐style interest rate guarantee. Three representative companies are considered, each using a different type of surplus distribution: a mechanism, where the guaranteed interest rate also applies to surplus that has been credited in the past, a slightly less restrictive type in which a guaranteed rate of interest of 0 percent applies to past surplus, and a third mechanism that allows for the company to use former surplus in order to compensate for underperformance in “bad” years. Although at the outset all contracts offer the same guaranteed benefit at maturity, a distribution mechanism of the third type yields preferable results with respect to the considered risk measure. In particular, throughout the analysis, our representative company 3 faces ceteris paribus a significantly lower shortfall risk than the other two companies. Offering “strong” guarantees puts companies at a significant competitive disadvantage relative to insurers providing only the third type of surplus distribution mechanism.     

贷款保证担保有效性问题研究

针对我国银行业经营实践中普遍存在贷款不规范(保证)担保现象,以及由此导致的担保对银行债权保障功能缺失问题,本文认为.其中既有深刻复杂的体制性原因,也与人们对保证担保的认识和运用为当有关.本文在回顾既有研究的基础上.对保证担保的本质功能和作用机制进行了系统梳理和分析,运用信息经济学的分析方法,从理论层面解析了导致保证担保功作用机制扭曲、有效性不足的三个方面的重要原因:借款人公司治理不完善、政府救助以及银行的不作为.最后,结合银行大客户贷款数据信息进行了实证统计分析,验证理论分析结论,据以提出政策建议.